infinity infinity jurnal ilmiah program studi matematika stkip siliwangi bandung, vol 5, no. 1, februari 2016 50 pemanfaatan web khan academy dalam pembelajaran matematika oleh: joko soebagyo stt wastukancana, purwakarta jokosoebagyo@student.upi.edu abstrak artikel ini bertujuan untuk mengobservasi pemanfaatan web khan academy siswa smk swasta di jakarta utara. observasi dilakukan untuk mengamati aktivitas siswa dalam menggunakan web khan academy selama proses pembelajaran matematika. pemanfaatan teknologi dalam proses pembelajaran matematika sudah sepatutnya dilakukan oleh pihak-pihak yang ikut bertanggungjawab atas keberhasilan belajar matematika perserta didik. teknologi merupakan hal yang tidak bisa dipisahkan dalam kehidupan sehari-hari dan salah satu bentuk teknologi yang sering dimanfaatkan saat ini adalah website dimana akitifitas pekerjaan, pendidikan, hiburan dan hubungan sosial, semuanya dapat dialami melalui website. dibutuhkan sebuah website yang bias mengakomodir siswa dalam proses pembelajaran matematika baik di dalam kelas maupun di luar kelas. kriteria web yang baik haruslah memberikan kemudahan dalam pemanfaatannya, salah satu web tersebut adalah web khan academy. kata kunci : pembelajaran matematika, web khan academy abstract this paper aims to observe the use of web khan academy private vocational students in north jakarta. observations carried out to observe the activities of the students in using web khan academy during the learning process of mathematics. the use of technology in the learning process of mathematics has been duly carried out by parties who share responsibility for the success of students studying mathematics participants. technology is something that can not be separated in everyday life and one form of technology that is often used today is a website where the activity, employment, education, entertainment and social relationships, all of which can be experienced through the website. it takes a biased website to accommodate students in mathematics learning process both in the classroom and outside the classroom. criteria for good web should provide ease of use, one of the web is a web khan academy. keywords: learning mathematics, web khan academy i. pendahuluan pembelajaran matematika sampai saat ini masih menjadi momok bagi mayoritas siswa di seluruh dunia tidak terkecuali indonesia. rendahnya kemampuan matematika menjadi indikator bagi para guru dan para penggiat pembelajaran matematika yang dapat dilihat dari hasil the programme for international student assessment (pisa) tahun 2009 dan 2013. kita tengah menghadapi siswa yang hidup dalam era digital (y generation), sesuai pendapat (hirsch, martin, hopfensperger, & zbiek, 2013) bahwa teknologi merupakan hal yang tidak bisa dipisahkan dalam kehidupan sehari-hari.menurut (brckalorenz, haeger, nailos, & rabourn, 2013) salah satu bentuk teknologi yang sering dimanfaatkan saat ini adalah website infinity jurnal ilmiah program studi matematika stkip siliwangi bandung, vol 5, no. 1, februari 2016 51 dimana akitifitas pekerjaan, pendidikan, hiburan dan hubungan sosial, semuanya dapat dialami melalui website. a. pentingnya teknlogi menurut (goos & bennison, 2008), banyak peneliti dari berbagai negara yang menyatakan bahwa teknologi memainkan peranan penting dalam pembelajaran matematika di dalam kelas yang meliputi: (a) keterampilan dan pengalaman menggunakan teknologi; (b) waktu dan kesempatan untuk belajar; (c) pengetahuan tentang bagaimana teknologi terintegrasi ke dalam pembelajaran matematika; (d) belief tentang teknologi dalam pembelajaran; (e) belief tentang matematika dan bagaimana mempelajarinya. perkembangan internet menyediakan kekayaan informasi bagi guru matematika dan siswa di semua tingkat dan sangat berlimpah dengan sebuah keberlebihan sumber daya yang sebelumnya tidak tersedia. melalui media ini, menurut (cherkas & welder, 2011) berbagai bahan berbasis web yang bertujuan untuk meningkatkan pengajaran dan pembelajaran matematika terus-menerus dan sedang dikembangkan. dengan demikian dalam proses pembelajaran matematika, sudah saatnya guru matematika memanfaatkan web guna meningkatkan kemampuan matematis siswa. b. kriteri web yang baik ketika kita searching di google dengan keyword “web pembelajaran matematika” akan muncul 239.000 hasil pencarian. semua hasil tersebut dapat saja digunakan sebagai sumber pembelajaran matematika. tetapi menurut (sunil & saini, 2013) sebuah web layak dijadikan sebagai sumber pembelajaran jika memenuhi beberapa kriteria yaitu: (1) choosing an appropriate learning approach depending on the style of the learner; (2) choosing content depending on the learning style and approach choosing the appropriate content; (3) choosing learning modules that can create a learning activity path; (4) the knowledge that the learner has acquired and needs to acquire are then mapped appropriately to the learning activity mechanism that controls the generation of learning content in the recommender based learning management system. salah satu website yang memenuhi kriteria tersebut adalah www.khanacademy.org. ii. pembahasan a. khan academy khan academy adalah organisasi nirlaba dengan misi memberikan pendidikan bagi siapa sajasecara gratis, berkelas dunia,dapat digunakan kapan saja dan di mana saja. berdasarkan observasi yang dilakukan oleh penulis terhadap web khan academy, banyak didapati soalsoal matematika seperti pada soal matematika di pisa dan un sehingga siswa diharapkan mendapat wawasan matematika lebih banyak dari sumber belajar tersebut. http://www.khanacademy.org/ infinity jurnal ilmiah program studi matematika stkip siliwangi bandung, vol 5, no. 1, februari 2016 52 gambar 1. logo khan academy keuntungan bagi siswa ketika siswa belajar matematika di khan academy khususnya mengerjakan soal-soal matematika dan menjawab dengan benar maka ia akan mendapati jawaban tercentang (lihat gambar 2). gambar 2. menjawab soal dengan benar namun ketika mengalami kesulitan menjawabnya, ia dapat melihat petunjuk baik dengan menonton video ataupun jawaban yang tersedia tetapi ia akan mendapati jawaban dengan tanda silang (lihat gambar 3). infinity jurnal ilmiah program studi matematika stkip siliwangi bandung, vol 5, no. 1, februari 2016 53 gambar 3. menjawab soal dengan salah dan masih banyak keuntungan lain yang diperoleh siswa ketika belajar matematika di khan academy. penulis hanya memberikan beberapa contoh di atas. keuntungan bagi guru dan orang tua bagi guru dan orangtua pasti ingin mengetahui apakah anak/siswanya belajar matematika pada hari ini? materi apakah yang dipelajari? sejauh mana kemajuannya? dan sebagainya. belajar matematika di khan academy memungkinkan semua hal tersebut terwujud, dimana jika dengan pembelajaran matematika konvensional tidak dapat dilakukan secara detail. sebagai contoh, abdul fatah seorang siswa di sebuah smk swasta sudah mempelajari 132 skills matematika seperti terlihat pada gambar 4. gambar 4. skill matematika yang dipelajari seorang siswa infinity jurnal ilmiah program studi matematika stkip siliwangi bandung, vol 5, no. 1, februari 2016 54 penjelasan pada gambar 4 adalah salah satu keuntungan bagi guru atau orangtua tentang kondisi anak/siswa-nya. masih banyak penjelasan lain yang lebih rinci dan detail dalam pembelajaran matematika dengan memanfaatkan khan academy. kekurangan khan academy setiap alat/media pembelajaran pasti memiliki kelemahan dan kekurangan, demikian juga dengan khan academy. pembelajaran matematika di khan academy memerlukan penguasaan bahasa inggris yang baik, komputer/laptop/gadget untuk mengakses dan koneksi internet yang baik walaupun ada versi offline-nya. tanpa hal-hal tersebut, sulit rasanya untuk melakukan pembelajaran matematika di khan academy. pada saat penulis melakukan penelitian dengan memanfaatkan web khan academy, masalah bahasa dapat ditanggulangi dengan menggunakan fasilitas google translate. nah, yang paling dirasa sulit adalah menyediakan komputer, laptop atau gadget seperti android atau smartphone yang lain dan koneksi internet pada saat belajar di dalam kelas. di beberapa sekolah di jakarta, pembelajaran matematika dengan memanfaatkan khan academy mungkin dapat dilakukan. tetapi, kenyataan di lapangan mengatakan mayoritas sekolah tidak dapat melakukan pembelajaran matematika dengan memanfaatkan khan academy. b. beberapa penelitian yang relevan menurut (gönül & solano, 2013) menyatakan “khan experience does not significantly raise the exam score but does increase time in exam. a diligent or a conscientious student may achieve proficiency in more skill-sets and also spend more time completing the exam, perhaps double-checking before clicking the “submit” button”. dengan kata lain, khan academy tidak meningkatkan skor secara signifikan tetapi meningkat dalam waktu pengerjaan. dan untuk siswa yang rajin dapat meningkatkan keterampilan matematis lebih banyak lagi. iii. kesimpulan hasil observasi yang dilakukan penullis, memberikan kesimpulan antara lain bahwa aktivitas siswa yang memperoleh pembelajaran matematika dengan pemanfaatan web khan academy secara keseluruhan semakin baik setelah beberapa kali pertemuan. hal ini terlihat selama proses pembelajaran matematika, siswa terlihat lebih semangat dalam belajar matematika, lebih menyenangkan, dana adanya interaksi antar teman, eksplorasi, mengamati, serta menikmati dalam mengerjakan soal-soal di web khan academy. daftar pustaka brckalorenz, a., haeger, h., nailos, j., & rabourn, k. (2013). student perspectives on the importance and use of technology in learning. california: indiana university. cherkas, b., & welder, r. m. (2011). interactive web-based tools for learning mathematics: best practices. in a. a. al.], teaching mathematics online: emergent technologies and methodologies (p. 275). united states of america: information science reference. infinity jurnal ilmiah program studi matematika stkip siliwangi bandung, vol 5, no. 1, februari 2016 55 gönül, f. f., & solano, r. a. (2013). innovative teaching: an empirical study of computeraided instruction in quantitative business courses. journal of statistics education, 123. goos, m., & bennison, a. (2008). surveying the technology landscape: teachers’ use of technology in secondary mathematics classrooms. mathematics education research journal, 103. hirsch, c. r., martin, w. g., hopfensperger, p. w., & zbiek, r. m. (2013). core math tools and its affordances for mathematics teacher educators and for prospective teachers. amte conference (p. 4). orlando, florida: nctm. sunil, l., & saini, d. k. (2013). design of a recommender system for web based learning. world congress on engineering (p. 1). london: world congress on engineering. infinity journal of mathematics education p–issn 2089-6867 volume 6, no. 2, september 2017 e–issn 2460-9285 doi 10.22460/infinity.v6i2.p177-182 177 the relation between self-efficacy toward math with the math communication competence sylvia rahmi 1 , rifka nadia 2 , bibih hasibah 3 , wahyu hidayat 4 1 smp negeri 25 pekanbaru, jl. kartama, maharatu, marpoyan damai, pekanbaru, riau, indonesia 2 smp negeri 10 banda aceh, jl. poteumereuhom, kuta alam, banda aceh, indonesia 3 smp negeri 1 soreang, jl. ciloa no. 3, pamekaran, soreang, bandung, indonesia 4 stkip siliwangi, jl. terusan jenderal sudirman, cimahi, indonesia 1 sylviarahmi.sr@gmail.com, 2 rifkanadia28@yahoo.com, 3 bibih_hasibah@yahoo.com, 4 wahyu@stkipsiliwangi.ac.id received: june 08, 2017 ; accepted: september 11, 2017 abstract the aim of this research is to analyze the relationship between self-efficacy toward mathematics with mathematical communication competence. the design of this research is survey and correlation technique. the research instruments used in this research are math communication competence test and attitude scale. the instruments used are 5 questions about math communication competenca teat and 28 statements about self-efficacy. the research population is all student of smp negeri 1 soreang. with samples of this research were 70 students of 7th grade student chosen by cluster random sampling. the data analyzed quantitatively done through math communication data and self-efficacy attitude scale. spss 20 used in this research. the result shows that student self-efficacy influences students math communication competence. keywords: communication skills mathematics, self-efficacy. abstrak penelitian ini bertujuan untuk menganalisis hubungan antara self-efficacy terhadap matematika dengan kemampuan komunikasi matematik. desain penelitian ini adalah survey dengan teknik korelasi. instrumen penelitian yang digunakan dalam penelitian ini berupa tes kemampuan komunikasi matematik dan skala sikap self-efficacy siswa. intrumen yang digunakan yaitu 5 soal kemampan komunikasi matematik dan 28 pernyataan mengenai self-efficacy. populasi dalam penelitian ini adalah seluruh siswa smp negeri 1 soreang dengan sampel penelitian ini adalah 70 siswa kelas vii sebanyak dua kelas yang dipilih secara cluster random sampling. analisis data dilakukan secara kuantitatif yang dilakukan terhadap data kemampuan komunikasi matematik dan skala sikap self-efficacy. dalam perhitungan statistik menggunakan spss 20, hasil penelitian menunjukkan bahwa self-efficacy siswa mempengaruhi kemampuan komunikasi matematik siswa. kata kunci: kemampuan komunikasi matematik, self-efficacy. how to cite: rahmi, s., nadia, r., hasibah, b., & hidayat, w. (2017). the relation between self-efficacy toward math with the math communication competence. infinity, 6 (2), 177182. doi:10.22460/infinity.v6i2.p177-182 mailto:bibih_hasibah@yahoo.com rahmi, nadia, hasibah, & hidayat, the relation between self-efficacy toward math … 178 introduction education is one important aspects that will determine the quality of life of a person and a nation. in formal education, one of the subjects in school that can be used to build the students' way of thinking is mathematics. therefore, math lessons at schools not only emphasize the giving formulas but also teach students to be able to communicate ideas related to everyday life. one of the mathematical skills that must be possessed by the students is the ability of mathematical communications. mathematical communication can be interpreted as a student's ability to convey something he knows through dialogue events or interrelationships that occurr in the classroom environment, where there is a transfer of the message. displaced messages contain mathematical materials that learn, such a concepts, formulas, or a problemsolving strategies. parties involved in communication events in the classroom are teacher and student. the way the message can be transmitted can be smoken or written. in order for student’s mathematical communication skills to develop well, then in the process of learning mathematics, teachers need to provide opportunities for students to be able to improve their ability to communicating mathematical ideas. pimm (lindawati, 2013) states that children are given the opportunity to work in a groups in collecting and presenting data, show good progress as they listen to one anothers’s ideas, discuss it together and then draw up the conclusions that the group views. apparently they learn most from communicating and constructing their own knowledge. according anggraeni (2013) summarizes the opinions of some experts and nctm and identifies some mathematical communication skills such as: a) stating a situation, into drawings, diagrams, language, symbols, expressions or mathematical models; b) state image, diagrams, language, symbols, expressions or mathematical models in their own language; c) listening, discussing, writing mathematics; d) read a mathematical presentation with understanding; e) revisit a mathematical description in its own language; and f) compile questions about mathematics.through mathematical communication students exchange and explain their ideas or understanding to their friend. the communication process helps students construct the meaning of a series of mathematical processes and make generalizations. in an effort to explore and develop students’ mathematical communication skills, teachers should expose students to a variety of contextual issues and invite them to communicate their respective ideas (hidayat, 2017). in the 2013 curriculum also said that in mathematics learning hard skills and soft skills including mathematics education values in the culture and character that should be developed simultaneously and balanced through learning scientific approach. one of the soft skills that mathematics is self-efficacy. self-efficacy leads to a person's beliefs about its ability to organize and carry out a series of actions to achieve results (bandura, 1997). it can be concluded self-efficacy is the belief that students need to have in order to succeed in the learning process. pintrich and de groot (khaerunisak, kartono, hidayah, and fahmi, 2017) found that students who believed they could perform academic tasks using cognitive and metacognitive strategies were more and still doing better than unbelieving students. self-efficacy makes a difference in the way people act, as a follow-up of feelings and thoughts. people who believe they can do something that has the potential to transform environmental events are more likely to act and more likely to succeed than those with low self-efficacy. behavior is influenced by the extent to which a person believer can perform the actions required by the particular situation. volume 6, no. 2, september 2017 pp 177-182 179 method this research design is a survey by using correlation technique, where writer take two class as sample of research. this research conducted in smp negeri 1 soreang. the development of self-efficacy variables students about math starting with the 28-point declaration preparation is complete with 4 choices. the scale used is a likert scale. with a choice of answers ss (strongly agree), s (agree), ts (disagree), and sts (strongly disagree). for determination calculations using score ss = 4, c = 3, ts = 2, and sts = 1 for statements favorable (positive), whereas a score ss = 1, s = 2, ts = 3, and sts = 4 for statements unfavorable (negative). the instrument was then consulted with the supervisor in order to have the validity of the content. meanwhile, in order to have the empirical validity of the instrument is then tested to determine the validity, reliability, distinguishing power and distress index. math test used was a test of mathematical communication skills. the test of mathematical communication ability is arranged in the form of description. the reason for preparation of the test in the form of description because it is tailored to the purpose of this study which prioritizesthe process of the results. tests in the form of description is not much to give a chance to speculate, it can even encourage students to dare to express their opinions in their own and language. the steps taken in the preparation of this instrument is (1) make a grid of test based indicators matematic communication skills, (2) make the scoring guidelines, (3) preparing test problems; (4) assess conformity between material, indicators and test questions. results and discussion results to see how strong the relationship between self-efficacy and mathematical communication skills, then the correlation test pearson with and the hypothesis is h0: ρ = 0 h1: ρ ≠ 0 with the criteria: if sig> 0.05 then h0 accepted table1. correlation guildfrord’s criteria range criteria 0.01 to 0.20 very weak 0.20 to 0.40 weak 0.40 to 0.70 strong enough 0.70 to 0.90 strong 0.90 to 1.00 very strong rahmi, nadia, hasibah, & hidayat, the relation between self-efficacy toward math … 180 table 2. results of self-efficacy correlation and mathematical communication skills self efficacy posttest pearson correlation self-efficacy 1,000 0,424 postes 0,424 1,000 sig. (one-tailed) self-efficacy 1,000 0,000 postes 0,000 1,000 n self efficacy 70 70 postes 70 70 based on table 2, the result of correlation between self-efficacy dam mathematical communication ability of students is 0.424 and the significance value (sig) of 0.000. correlation values (r) obtained was 0.424, which means is quite powerful. due to the significant value of 0,000 is smaller than = 0.05, h0 is rejected, meaning that there is a relationship between self-efficacy toward mathematics with mathematical communication skills. to determine the influence ofanatar self-efficacy with mathematical communication skills then tested using a regression coefficient of linear regression analysis. this analysis was conducted to see the direct influence of self-efficacy of students' mathematical communication abilities of students. the hypothesis tested were: h0 : self-efficacy students about math does not affect students' mathematical communication skills h1 : self-efficacy affects students about math mathematical communication skills of students with criteria: if sig> 0.05 then h0 accepted results of the analysis are shown in table 3 table 3. regression analysis self-efficacy with communication capabilities of mathematical model unstandardized coefficients standardized coefficients t sig. b std. error beta 1 (constant) 72,888 2,935 24,832 0,000 postes 0,190 0,049 0,424 3,865 0,000 based on table 3, it can be seen the regression equation y = 72.888 + 0,190x which means, the greater the value of self-efficacy,the greater the students' mathematical communication skills of students, and vice versa. because the significance value of 0.000 is smaller than = 0.05, it can be concluded under h0 is rejected it means significantly self-efficacy affects students toward math mathematical communication skills of students. discussion based on the analysis of data to test the hypothesis, the conclusions from the findings made by that self-efficacy of students towards mathematics in general affect students' mathematical communication skills. self-efficacy affects the ability of mathematical communications volume 6, no. 2, september 2017 pp 177-182 181 because a higher level of confidence in one's self to the higher mathematics mathematical communication skills. this is shown by the significant value of 0.024, which means smaller than = 0.05, which means self-efficacy affect the ability of mathematical communications. the correlation coefficient of 0.380 and a positive value indicating that a positive relationship and have the power relationships within the category of being between two variables. this supports the hypothesis that there is evidence of the relationship between self-efficacy toward mathematics with mathematical communication skills. self-efficacy is one of the factors that influence the adjustment to the ability of the student (sumarmo, hidayat, zulkarnaen, hamidah, & sariningsih, 2012; irfan & suprapti, 2014; haji & abdullah, 2016; hendriana, 2017). in addition, the results are also in line with those proposed by hendriana, rohaeti & hidayat (2016) that mathematical communication ability is also influenced by various factors, including self-efficacy factor. conclusion based on the analysis the conclusion is: (1) there is a relationship between self-efficacy toward mathematics with mathematical communication skills. (2) self-efficacy influences students toward math mathematical communication skills. references anggraeni, d. (2013). meningkatkan kemampuan pemahaman dan komunikasi matematik siswa smk melalui pendekatan kontekstual dan strategi formulate-share-listen-create (fslc). infinity journal, 2(1), 1-12. bandura (1997). self-efficacy: the excercise of control. new york: w.h freeman and company. hendriana, h., rohaeti, e. e., & hidayat, w. (2016). metaphorical thinking learning and junior high school teachers’ mathematical questioning ability. journal on mathematics education, 8(1), 55-64. hendriana, h. (2017). senior high school teachers’ mathematical questioning ability and metaphorical thinking learning. infinity journal, 6(1), 51-58. hidayat, w. (2017). adversity quotient dan penalaran kreatif matematis siswa sma dalam pembelajaran argument driven inquiry pada materi turunan fungsi. kalamatika jurnal pendidikan matematika, 2(1), 15-28. irfan, m., & suprapti, v. (2014). hubungan self-efficacy dengan penyesuaian diri terhadap perguruan tinggi pada mahasiswa baru fakultas psikologi universitas airlangga. jurnal psikologi pendidikan dan perkembangan, 3(3), 172-178. khaerunisak, k., kartono, k., hidayah, i., & fahmi, a. y. (2017). the analysis of diagnostic assesment result in pisa mathematical literacy based on students selfefficacy in rme learning. infinity journal, 6(1), 77-94. lindawati, s. (2013). pembelajaran matematika dengan pendekatan inkuiri terbimbing untuk meningkatkan kemampuan pemahaman dan komunikasi matematis siswa sekolah menengah pertama. jurnal pendidikan, 2(2), 16-29. haji, s., & abdullah, m. i. (2016). peningkatan kemampuan komunikasi matematik melalui pembelajaran matematika realistik. infinity journal, 5(1), 42-49. doi:http://dx.doi.org/10.22460/infinity.v5i1.190 http://dx.doi.org/10.22460/infinity.v5i1.190 rahmi, nadia, hasibah, & hidayat, the relation between self-efficacy toward math … 182 sumarmo, u., hidayat, w., zukarnaen, r., hamidah, m., & sariningsih, r. (2012). kemampuan dan disposisi berpikir logis, kritis, dan kreatif matematik (eksperimen terhadap siswa sma menggunakan pembelajaran berbasis masalah dan strategi thinktalk-write). jurnal pengajaran mipa, 17(1), 17-33. sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 8, no. 2, september 2019 e–issn 2460-9285 https://doi.org/10.22460/infinity.v8i2.p239-246 239 teacher’s and student’s needs for mathematical problems in disaster context nuzulidar 1 , rahmah johar *2 , sulastri 3 1,2,3 universitas syiah kuala article info abstract article history: received sept 5, 2019 revised sept 27, 2019 accepted sept 30, 2019 indonesia is an archipelagic country lies on the pacific ring of fire, resulting in the country being vulnerable to disaster. teachers need to accustom students to manage natural disaster situation in a more logical approach. therefore, it is necessary to develop mathematical problems in disaster contexts. this research is an early stage of developmental research. the purpose of this study was to analyze the needs of teachers and students of mathematical problems in disaster contexts. the participants in this study were a mathematics teacher and 53 year 7 and 8 students at one of the public junior high school, located in a tsunami affected area, in banda aceh. data collection involved an open questionnaire, and data analysis was carried out descriptively. the results showed that the teacher often provided mathematical problems in learning but had never read mathematical problems in disaster contexts. also, only three students had ever read such problems. the results also revealed that nearly half of the students (41.5%) liked to solve mathematical problems. besides, both the teacher and 71.7% of the students agreed and were willing to participate in the learning process involving mathematical problems in disaster contexts. the results of the study also showed that the mathematical questions in disaster contexts were limited. thus, it is necessary to develop mathematical problems in disaster contexts. keywords: disaster context, mathematical problems copyright © 2019 ikip siliwangi. all rights reserved. corresponding author: rahmah johar, departement of mathematics education, universitas syiah kuala, jl. tgk. hasan krueng kalee, kopelma darussalam, banda aceh, aceh 24415, indonesia email: rahmah.johar@unsyiah.ac.id how to cite: nuzulidar, n., johar, r., sulastri, s. (2019). teacher’s and student’s needs for mathematical problems in disaster context. infinity, 8(2), 239-246. 1. introduction indonesia, geographically, is a disaster-prone country due to the circum-pacific belt, the earthquake zone surrounding the pacific ocean. this circumstance requires resilience in every element of society toward disaster risk. disasters are events that occur due to natural or non-natural factors that lead to casualties and damage to infrastructure (mcdonald, 2003). disaster events can be triggered by natural events, human actions or a combination of both (amri, 2017). an important part of disaster management is the mitigation, the measures to reduce disaster risk, by improving the physical development, the awareness and the ability to mailto:rahmah.johar@unsyiah.ac.id nuzulidar, johar, sulastri, teacher’s and student’s needs for mathematical problems … 240 confront disaster threats. disaster mitigation efforts are efforts to save one self from natural disasters that occur suddenly and threaten one’s life (setiawan, 2016). communities threatened by disasters are so diverse that the most strategic way to educate people about disaster mitigation is through formal and informal education. one of the efforts that the school can do as a formal educational institution in reducing disaster risk is through the integration of disaster risk education in extracurricular activities and various subjects (amri, 2017). one of which through the regular lesson, such as mathematics (shadiq, 2016) because mathematics is a clear and logical means of thinking to solve contextual problems (apec, 2012). aceh is one of 34 provinces in indonesia, with a total of 2,000 schools in a highrisk disaster area (sinambela & nugrahini, 2016). since ten years after the tsunami in aceh, disaster risk reduction has been integrated into the school curriculum, and schoolbased disaster preparation programs have also been carried out (tdmrc unsyiah, 2014). so, disaster is used as one of the contexts in learning mathematics. the contexts provided in learning can be gained from nature, social life, culture, economy, and religion. therefore, the content of learning materials is inseparable from the student’s learning environment and the daily life (zakiyah & rusdiana, 2014). contexts play an important role in achieving the goals of learning mathematics because they can help students understand the materials meaningfully (johnson, 2002). they also benefit the students in solving mathematical problems, making it easier for students to choose the way to solve problems and to provide students with strategic solutions in solving problems (van den heuvel-panhuizen, 2005). provision of contexts in the learning environment can provide answers to students' problems "why should i study this?" and can bring meaningful learning (johar & hanum, 2016). schools have a critical role in developing knowledge to build the community resilience to disasters (oktari, shiwaku, munadi, & shaw, 2015). previous researchers, such as fatmawati (2016), have developed the mathematical problems in disaster contexts but the availability of such questions remains lacking. besides, research that examines the needs of students and teachers for mathematical problems in the context of disaster is limited. therefore, the purpose of this study was to analyze the needs of teachers and students of mathematical problems in disaster contexts. 2. method this study is an early stage of developmental research, particularly the preliminary stage of the tessmer model (tessmer, 2013). the participants were a mathematics teacher and 53 year 7 and 8 students in one of the public junior high school, located in a tsunami affected area, in banda aceh. the participants could define disaster well, provide some examples of disasters, and explain what needs to do in the event of an emergencies. they mentioned some places to use as an early evacuation site, including the evacuation building, hill or mountain, floating ship of a diesel power plant, tsunami museum, tall buildings, and mosques. they admitted that they obtain information about disaster through electronic media, books, schools, and parents. the data collection involved an open questionnaire and interview with several participants to analyze the unique cases of student answers deeply. both the questionnaire and the interview were used to investigate the teacher’s and student’s needs for mathematical problems in disaster contexts. data analysis was conducted descriptively. the example of mathematical problems in disaster contexts provided in the questionnaire were adapted from khalid & ali (2016) and presented as follows. volume 8, no 2, september 2019, pp. 239-246 241 abu was standing on a beach when he heard the tsunami warning siren. he immediately decided to run to a safe place. he had two choices: going to a small hill or a shelter built for tsunami, which can be reached via two ways. the hill is 500 metres and the shelter is 800 metres away from the beach. however, to reach the top of the hill, abu need to climb 300 steps of staircases. abu can run at an average rate of 5m/s and he can climb the stairs at the rate of 3 steps/s. he may also use the curved road (specially made for the shelter) which is 900 metres long, where he can run at 6m/s. in your opinion, which way should abu choose? please explain! the finding of research conducted by khalid & ali (2016) revealed that students were motivated to solve the problem and he suggested teachers to guide students in solving contextual problem in disaster context. in this study, students were asked to respond to the problem in a disaster context, whether they had read/solved such a problem before, and whether they were interested in and willing to solve such a problem? 3. results and discussion the results of teacher questionnaire showed that the mathematics teacher, who taught year 7 and 8, had often provided mathematical problems in mathematics learning but she had never read/solved mathematical problems in disaster contexts. the teacher agreed that mathematical problems in disaster contexts should be given in mathematics learning because it can improve students’ mathematical literacy. the questionnaire results of year 7 students about the student’s needs for mathematical problems in disaster contexts are presented in figure 1. figure 1. year 7 students’ needs for mathematical problems in disaster contexts figure 1 shows all students’ preferences, meaning that 20 students were happy with mathematical problems, but only 17 students were interested in the problems in disaster contexts. only three students had ever read/solved mathematical problems in disaster contexts. in addition, 26 students agreed if the teacher gives mathematical problems in disaster contexts in learning and they were willing to solve mathematical problems in disaster contexts. the questionnaire results of year 8 students concerning the students’ needs for mathematical problems in disaster contexts displayed in figure 2. 20 3 26 17 26 0 10 20 30 preference participation approval interest willingness nuzulidar, johar, sulastri, teacher’s and student’s needs for mathematical problems … 242 figure 2. year 8 students’ needs for mathematical problems in disaster contexts only two of year 8 students felt happy with mathematical problems. however, 12 students said that they were interested in mathematical problems in disaster contexts. all students had never read/solved mathematical problems in disaster contexts. also, 12 students asserted that they agreed if the teacher gives mathematical problems in disaster contexts in mathematics learning, and they were willing to solve such mathematical problems. seven students admitted that they were not happy with the mathematical problems, but they attracted to mathematical problems in disaster contexts. providing contextual problems can increase student motivation in learning mathematics (khalid & ali, 2016). that’s why the participants who were not pleased with the mathematical problem showed positive attitudes towards mathematical problems in disaster contexts. the questionnaire results of year 7 and 8 students regarding the students’ needs for mathematical problems in disaster contexts are presented in figure 3. figure 3. the student’s needs of mathematical problems in disaster contexts figure 3 illustrated the preferences of all students. twenty-two students (41.5%) were happy with mathematical problems, and nearly half of the students (49.1%) were interested in the problems in disaster contexts. only three out of 53 students (5.6%) had ever read/solved mathematical problems in disaster contexts. in addition, more than 70% of the students agreed if the teacher gives mathematical problems in disaster contexts, and they were willing to solve mathematical problems in disaster contexts. 2 0 12 9 12 0 5 10 15 preference participation approval interest willingness 22 3 38 26 38 0 10 20 30 40 preference participation approval interest willingness volume 8, no 2, september 2019, pp. 239-246 243 table 1 presents the questionnaire results of year 7 students about the students’ needs for mathematical problems in disaster contexts. table 1. the year 7 students’ needs for mathematical problems in disaster contexts subject question number 1. do you like to solve mathematical word problems? 2. have you ever read/solved mathematical problems in disaster problems? 3. do you agree if the teacher gives a mathematical word problems in disaster context as the example? 4. are you interested of mathematical problems in disaster context as the example? 5. are you willing to solve mathematical problems in disaster context (see an example)? a not happy never disagree not interested willing b happy never agree not interested willing c happy never agree interested willing d not happy never agree not interested willing e happy never disagree not interested not willing f happy never agree not interested willing g not happy never agree not interested willing h not happy never agree interested willing i not happy never agree interested willing j not happy never agree interested willing k happy ever agree interested willing l happy ever agree not interested willing m happy ever agree interested willing n not happy never agree interested willing o happy never agree interested willing p happy never agree interested willing q happy never agree interested willing r not happy never agree not interested not willing s happy never agree not interested willing t not happy never agree interested not willing u happy never agree interested willing v happy never agree not interested willing w happy never disagree not interested willing x happy never disagree not interested not willing y happy never agree interested willing z not happy never disagree not interested not willing aa not happy never agree not interested willing ab happy never agree interested willing ac happy never agree interested willing ad happy never agree interested willing ae happy never agree interested willing here are the interview excerpts with one of the participants (k). k was one out of three year 7 students who had ever read/solved a mathematical problems in disaster context: q : do you like mathematics? a : yes miss. q : which one do you prefer, problems on number or word problems? a : word problems miss q : you answered question number 2. what is the problem and where do you read it? a : yes mis, the problem was about how much medicine needs for disaster victim. i read it in the elementary school, "thematics" book. both the questionnaire and the interview results of k showed that she liked mathematics and word problems. she had read/completed mathematical problems in disaster contexts from the book "thematics" when she was in elementary school. nuzulidar, johar, sulastri, teacher’s and student’s needs for mathematical problems … 244 "thematics" book consists of themes to link the contents of several subjects and to develop materials based on the environment to provide a meaningful experience for students. five out if six students interviewed mentioned similar answer concerning their reasons for the low interest in mathematical problems in disaster contexts. here is an interview excerpt with student b. q : do you like mathematics? a : not really miss q : which one do you prefer, problems on number or word problems? a : both of them miss q : why did you said happy for number 1 but your response was not interested for number 4? a : because of the length of the problem miss. both the results of the interview and questionnaire of b represented five other people who mentioned a similar reason. thus, it can be concluded that they liked mathematics. they agreed and would solve the problem if the teacher gave it, but they had a low interest in mathematical word problems in disaster contexts. the negative response was due to the length of the problem, indicating that they tried to abstain from more complex problems. the responses to student questionnaires and the interviews with several participants concluded that there were some students who were happy with mathematical problems but were not interested in mathematical problems in disaster contexts because the sample form presented was too long. however, students should accustom to solving contextual problems because those without this experience will face difficulties in the future, even leading to the refusal to solve them. contextual problems alone cannot directly help students in understanding the concept or motivate them (boaler, 1993; carraher & schliemann, 2002). moreover, the problems do not necessarily guarantee students to learn meaningfully. so, teachers need to engage students to interpret the contexts and to explore ideas in solving mathematical problems (widjaja, 2013). students who are not familiar with solving contextual problems will experience difficulties in learning because they need to connect their knowledge and real-life applications. therefore, mathematics contextual problems should also be developed by using a sentence that easily understood by relatively average student. in regard to the textbooks in indonesia, wijaya, van den heuvel-panhuizen, & doorman (2015) found that only 10% of the tasks in the textbooks are context-based. the use of contextual problems support students to develop mathematical understandings (dolk, widjaja, zonneveld, & fauzan, 2010). therefore further research needs to develop mathematics problem or mathematics textbooks in the context of disasters and analyze their impacts on students' problem solving skills. 4. conclusion this study on the importance of mathematical problems in disaster contexts resulted in several findings. the teacher often provided mathematical problems in learning but had never read mathematical problems in disaster contexts. besides, nearly half of the students (41.5%) liked to solve mathematical problems, but only three students had ever read the problems in disaster contexts. both the teacher and 71.7% of the students agreed and were willing to participate in the learning process involving mathematical problems in volume 8, no 2, september 2019, pp. 239-246 245 disaster contexts. further research developing mathematical problems in disaster contexts is necessary to develop literacy skills and raise students' awareness of disasters. acknowledgements we would like to thank direktorat riset dan pengabdian masyarakat (drpm) from kementerian ristek dikti republik indonesia for funding this research through the graduate thesis grant, the year 2019, no: 099/sp2h/lt/drpm/2019, date: 8 march 2019. references amri, a. (2017). pendidikan tangguh bencana: mewujudkan satuan pendidikan aman bencana di indonesia. jakarta: kementerian pendidikan dan kebudayaan. apec. (2012). the role of education for natural disasters. an extraction from the proceedings of the criced 10th anniversary symposium. japan: university of tsukuba. boaler, j. (1993). the role of contexts in the mathematics classroom: do they make mathematics more" real"?. for the learning of mathematics, 13(2), 12-17. carraher, d.w. & schliemann, a.d. (2002). is everyday mathematics truly relevant to mathematics education. journal for research in mathematics education monograph, 11, 131-153. dolk, m., widjaja, w., zonneveld, e., & fauzan, a. (2010). examining teachers’ role in relation to their beliefs and expectations about students’ thinking in design research. a decade of pmri in indonesia, 175-187. fatmawati, d. (2016). pengembangan soal matematika pisa like pada konten change and relationship untuk siswa sekolah menengah pertama. mathedunesa, 5(2). johar, r., & hanum, l. (2016). strategi belajar mengajar. yogyakarta: deepublish. johnson, e. b. (2002). contextual teaching and learning: what it is and why it's here to stay. corwin press. khalid, m., & ali, d. h. p. h. (2016). inculcating tsunami awareness in a mathematics lesson: improving students’ collabirative problem solving via lesson study. southeast asian mathematics education journal. 6(1), 19-31. mcdonald, r. (2007). introduction to natural and man-made disasters and their effects on buildings. routledge. oktari, r. s., shiwaku, k., munadi, k., & shaw, r. (2015). a conceptual model of a school–community collaborative network in enhancing coastal community resilience in banda aceh, indonesia. international journal of disaster risk reduction, 12, 300-310. setiawan, b. (2016). agenda pendidikan nasional. yogyakarta: ar-ruzz media. shadiq, f. (2016). how can seameo witep in mathematical help indonesian mathematics teachers to help their students to be independent learners in the case of disaster risk reduction (drr)?. southeast asian mathematics education journal, 6(1), 3-17. nuzulidar, johar, sulastri, teacher’s and student’s needs for mathematical problems … 246 sinambela, a., & nugrahini, e. (2016). media komunikasi dan inspirasi: jendela pendidikan dan kebudayaan iv/agustus-2016. media komunikasi dan inspirasi: jendela pendidikan dan kebudayaan, 4, 04-20. tdmrc unsyiah. (2014). recovery assessment after 10th years earthquake and tsunami aceh 2004. final report. banda aceh (in press). tessmer, m. (2013). planning and conducting formative evaluations. routledge. van den heuvel-panhuizen, m. (2005). the role of contexts in assessment problems in mathematics. for the learning of mathematics, 25(2), 2-23. widjaja, w. (2013). the use of contextual problems to support mathematical learning. indonesian mathematical society journal on mathematics education, 4(2), 157-168. wijaya, a., van den heuvel-panhuizen, m., & doorman, m. (2015). opportunity-to-learn context-based tasks provided by mathematics textbooks. educational studies in mathematics, 89(1), 41-65. zakiyah, q. y., & rusdiana. (2014). pendidikan nilai: kajian teori dan praktik di sekolah. bandung: cv pustaka setia. infinity journal of mathematics education p–issn 2089-6867 volume 5, no. 2, september 2016 e–issn 2460-9285 doi 10.22460/infinity.v5i2.214 75 prospective teachers’ ability in mathematical problem-solving through reflective learning yunika lestaria ningsih 1 , rohana 2 1,2 department of mathematics education, pgri palembang university, south sumatera, indonesia 1 yunika@univpgri-palembang.ac.id, 2 rohana_pgri@yahoo.com received: may 30, 2016; accepted: august 22, 2016 abstract the research aims to determine the mathematical problem-solving ability of prospective teachers’ through reflective learning. reflective learning is a learning process that provides students the opportunity to examine and investigate the problems that is triggered by experience, analyzing of individual the experiences, and facilitate the learning of the experiences. these lessons are identified to improve mathematical ability students. by using a descriptive qualitative research. the subject of this study were students of mathematics education program in one of private universities in palembang, consisting of 34 students. this study was conducted in odd semester academic year of 2015/2016. the instruments in this study were mathematical problem-solving ability test, observation sheet, and interview guide. the data were analyzed descriptively. based on analysis of the data are found that the average mathematical problem-solving ability of students’ through reflective learning in good categories. keywords: reflective learning, mathematical problem-solving ability abstrak tujuan penelitian ini adalah untuk mengetahui kemampuan pemecahan masalah matematis mahasiswa calon guru melalui penerapan pembelajaran reflektif. pembelajaran reflektif adalah suatu proses pembelajaran yang memberikan kesempatan kepada pebelajar untuk menguji dan menyelidiki persoalan yang menarik perhatian yang dipicu oleh pengalaman, melakukan analisis atas pengalaman individual yang dialami dan memfasilitasi pembelajaran dari pengalaman tersebut. pembelajaran reflektif ini diidentifikasi dapat meningkatkan kemampuan matematis pebelajar. penelitian ini menggunakan metode penelitian deskriptif kualitatif. subjek penelitian ini adalah mahasiswa program studi pendidikan matematika fkip universitas pgri palembang semester genap tahun akademik 2015/2016 yang berjumlah 34 orang. data penelitian dikumpulkan melalui tes dan wawancara. data dianalisis secara deskriptif. berdasarkan hasil analisis data diketahui bahwa rata-rata kemampuan pemecahan masalah matematis mahasiswa setelah diterapkan pembelajaran reflektif termasuk dalam kategori baik. kata kunci: pembelajaran reflektif, kemampuan pemecahan masalah matematis how to cite: ningsih, y.l. & rohana (2016). prospective teachers’ ability in mathematical problem-solving through reflective learning. infinity, 5 (2), 75-82. ningsih & rohana, prospective teachers’ ability in mathematical problem-solving … 76 introduction according to the regulation of the minister of national education in indonesia number 20/2006, the purposes of mathematics learning are students able to: (1) have knowledge of mathematics (the concept, the relationship between concepts and algorithms), (2) use of reasoning, (3) solve the problems, (4) communicate ideas through symbols, tables, diagrams, or other media to clarify the situation or problem, and (5) have an attitude that appreciate the usefulness of mathematics. moreover, the purpose of learning mathematics is also formulated by the national council of teachers of mathematics (2000), namely that the students have the competence: (1) to solve the problem; (2) reasoning; (3) communication; (4) relate the idea; and (5) positive attitudes towards mathematics. based on explanation above is known that the problem-solving ability is very important in learning mathematics. arthur (2008) stated that problem-solving is a part of think. as part of the thinking, problem-solving exercises can improve high-level thinking ability that requires the modulation and control more over routine or basic skills. this opinion suggests that in problem-solving, the students not only require routine or basic skills, but also have a variety of other skills to manage all the thinking process in order to solve their problems. it means the students have control and sort ability all their knowledge, finally they can find the best way to solve it. the speed and accuracy in selecting and sorting relevant knowledge is crucial in problem-solving. as effendi's statement (2012) that through problem-solving ability, students can solve their various problems, both in the mathematical problems as well as problems in daily life. the mathematical problem-solving ability is not only important for students but also for prospective mathematics teachers. according to widjajanti (2010), a prospective mathematics teacher must know, understand, and can apply the process of mathematical problem-solving. because in the future they should guide the students to have ability of mathematical problem solving. but the facts, the learning process in college is too much emphasis on the doing aspect but less on the thinking aspect (fahinu, 2007). what is taught in the classroom more concerned to manipulative skilled. several results of research in indonesia that showed the low ability of mathematical problem-solving at the level of prospective teachers' of mathematics as proposed by widjajanti (2010), karlimah (2010), and prabawanto (2012).. therefore, as an effort to achieve the goal of learning mathematics, especially on improving mathematical problem-solving ability of students, researchers applied a reflective learning. according to insuasty and castillo (2010), the reflection should be a fundamental part for the development of teachers. it caused, teachers have an obligation to be able to evaluate and restructure capability of teaching in order to optimize the teaching-learning process. a reflective teacher too, must be able to be critical of his own teaching abilities so that students could get a dynamic learning experience, valuable and meaningful to their lives. furthermore zeichner and liston in radulescu (2013) stated that the concept of reflective learning as a means to develop the professional capabilities of teachers. it is caused by the concept of reflective learning consists of several processes, which generally aims to foster an attitude of exploration and investigation so as to raise the awareness of prospective teachers as well as being factors that affect the learning process of students. the application of this volume 5, no. 2, september 2016 pp 75-82 77 learning model can improve the ability of students’ mathematical thinking (lasmawati 2011; nainggolan, 2011; rohana, 2015). in the world of education, reflective learning has been developed by many education experts. so a lot of variety of reflective learning comes to us. one of reflective learning model is formulated by the international center for jesuit education (icaje) is ignatian pedagogical paradigm (sirajuddin, 2009). reflective learning that is based on the ignatian pedagogical paradigm has been applied to the jesuit schools worldwide (icaje, 1993). according drost (sirajuddin, 2009) concept of reflective thinking through reflective learning is the core of reflective learning. there are three major elements, namely experience, reflection (reflection), and action. figure 1. ignatian paradigm (icaje, 1993) to carry out these three elements, the supporting elements are required, pre-learning element (context) and post-learning element (evaluation). thus, the reflective learning includes five steps such as: 1) context; 2) experience; 3) (reflection); 4) action; and 5) evaluation. based on the explanation above, the purposes of this study is determine the mathematical problem-solving ability of prospective teacher through the reflective learning. the indicator of the students’ mathematical problem-solving abilitiy that were examined in this study include: (1) identify the adequacy of the data to solve the problem, (2) create a mathematical model and how to solve it, (3) select and implement strategies to solve mathematical problems and or outside mathematics , (4) explain and check the correctness of the answer. method the subjects of this study were students of mathematics education program of private universities in palembang, consisting of 34 students. this study was conducted in 4 th semester academic year of 2015/2016. the instruments in this study were mathematical problemsolving ability test, observation sheet, and interviewing guide. the test consisted of six questions the description has been prepared based on indicators of mathematical problemsolving ability and has been declared valid and reliable. the data of students’ mathematical problem-solving ability after their participation in reflective learning was collected. the data were analyzed descriptively. the students’ mathematical problem-solving ability is obtained by examining the test answer sheets according to the scoring rubric. then the data were analyzed descriptively to see the achievement of mathematical problem-solving ability of students in the lecture. on average the final value obtained is used to view the categories of mathematical problem-solving ability ningsih & rohana, prospective teachers’ ability in mathematical problem-solving … 78 of students. interviews were conducted orally to students with different levels of mathematical skills. interview data were analyzed descriptively and used as supporting data test mathematical problem-solving ability of students. results and discussion results the learning activities are carried out in class 4a by the number of students as many as 34 people, divided into 7 groups with heterogeneous mathematical skills. the research was conducted as many as five sessions, with one test at the last meeting. mathematical statistics 1 material studied in this research is limited on combinatorial analysis, probability and conditional probability. researchers applied reflective learning at every meeting. the reflective learning includes five steps are as follows: (1) context. lecturers presented the topic of learning as new knowledge that will be discussed, and then do the debriefing to check the prerequisite knowledge and skills possessed by students. lecturers are also directs students through the questions that triggered the students to relate their prior knowledge of the topic to be discussed. (2) experience. lecturer raises new issues related to the topic will be discussed and presented in the student worksheet (mfi). it is intended to stimulate the students understand their own thinking process. in this step, students examine the problems that arised, seeks to sharpen the problem and identify strategies for problem-solving, using these strategies to solve problems, and to determine the factors that allegedly led to the emergence of problems. (3) reflection. lecturer direct students to find a variety of information (collect data to support), formulated the layout and boundary issues, as well as the settlement of possible problems. lecturers take a part as the facilitator and mediator to provide scaffolding for groups in need through reflection questions. (4) action. lecturers provide opportunities for students to present their answers and sharing in class discussions. answers submitted student is not the result of an agreement because a student group may disagree with the group. furthermore, lecturers steer students to be able to implement the settlement proceeds obtained (newly acquired knowledge of students) in other situations. in this case, the lecturer can give new problems as the continued problems related to issues that have been resolved by the students, that students should always modify the understanding that has been incorporated (prior knowledge) in order to solve new problems. (5) evaluation. to determine individual student achievement to the topic that has been studied, lecturer evaluate by asking students to answer some questions. in addition, the lecturers also ask students to write a reflective journal as a training tool for students to be able to assess and monitor the success of the learning process. volume 5, no. 2, september 2016 pp 75-82 79 to obtain a picture of the quality of mathematical problem-solving ability of students, test data were analyzed descriptively. summary of test results of mathematical problem-solving ability of students is presented in table 1. table 1. the students’ mathematical problem-solving ability test result postest score frequency category 81 – 100 61 – 80 41 – 60 7 20 7 excellent good fairly from table 1, the result of mathematical problem-solving ability test students show the excellent categories equal to 20.59% (7 people), good categories equal to 50.82% (20 people), and fairly categories equal to 20.59% (7 people). while the test average score is 69.5 in good categories. the test results for each indicator mathematical problem-solving ability of students can be seen in table 2. table 2. the score of mathematical problem-solving ability for each indicator no. the indicator of students’ mathematical problem-solving ability average score category 1. identify the adequacy of the data to solve the problem 74,26 good 2. create a mathematical model and how to solve it. 66,91 good 3. select and implement strategies to solve mathematical problems and or outside mathematics 60,29 fairly 4. explain and check the correctness of the answer 70,59 good average 69,49 good discussion results of this study have shown that the average mathematical problem-solving ability of students through the application of reflective learning falls into good categories. these findings reinforce and complement the results of previous research on reflective learning, among other research conducted by nainggolan (2011), lasmanawati (2011), and rohana (2015) found that learning can improve the mathematical thinking ability. in each steps of reflective learning, students are given the opportunity to play an active role in the learning process and are involved in considering the success of their learning. for example, in step experience, students are faced with a problem based questions that they are working in groups. students are trained and familiarized reflective thinking mathematically through questions based on those problems. social interaction through group discussions such as asking each other, respond or criticize answers friend, giving students the opportunity to have a very big role in the effort to understand the concepts, develop procedures, found the principles and apply the concepts, procedures, and principles in solving a given problem , ningsih & rohana, prospective teachers’ ability in mathematical problem-solving … 80 in addition, according hmelo & ferrari (song, koszalka, and grabowski, 2005) lecturer's role as a facilitator in the reflective learning by giving instructions or scaffolding through questions reflections give to students to practice solving mathematical problems. the same thing also expressed wahyudin (2008) that teachers have an important role in helping to empower the development of habits of reflective thinking by asking questions like: "before we go, whether we believe already understand this?", "why we think this is true ? ". these questions make students tend to learn responsibility to reflect on their own work and make the adjustments necessary when solving problems. based on the test results of mathematical problem-solving ability, it is known that the lowest average scores of students with enough catagory located on the third indicator, the ability to select and implement strategies to solve mathematical problems and or outside mathematics. this is the example of questions and answers of students to measure theirs ability in third indicators. figure 2. the result anwers for the third indicator to solve the problem on this indicator, the student should be able to determine the number of ways or the structure menu that can be eaten by dina. students can use some solving dina is enjoying the original food in palembang city. the menus which are available in ‘wak aba’ store are pempek, model, kemplang, and many kind of drinking. pempek is including pempek telur, pempek kulit, pempek adaan, and pempek krupuk. model is including model ikan and model gandum. kemplang is consisting of fried kempang and baked kemplang. the drinking is consisting of peanut’s ice and cincau ice. determine in two different ways the illustration of dina’s choices to get all kind of the food and drink. volume 5, no. 2, september 2016 pp 75-82 81 strategies such as: a tree diagram, sequential pair, placement rules or the rules of multiplication. figure 2 shows that the students used a tree diagram and placement rules to address these problems. based on these answers, the third indicator has been reached. based on analysis of student work on this indicator, six students answered correctly and completely. students who answered correctly but incomplete on this indicator only write one problem-solving strategies. this mistakes made by students when answering after further explored through an oral interview is a student did not interpret the question correctly. in addition, students who incorrectly answered caused due to poor understanding of the concept of algebra, so the problem of combinatorial analysis could not be solved correctly. conclusion based on the results of this study, concluded that the average score of students’ mathematical problem-solving ability of students is fall into good category. from the analysis of problemsolving abilities per indicator, known to students classified as either on (1), (2) and (4), while quite indicator (3). thus a good problem solvers, students are able to identify the adequacy of the data to solve the problem, is able to create a mathematical model of a problem and explain or check the correctness of the answer, but students are not quite capable of selecting and implementing a strategy to resolve the problem. references arthur, l. b. (2008). problem-solving. u.s.: wikimedia foundation, inc. [online]. available: http://en.wikipedia.org/wiki/problemsolving. [7 th april 2008]. effendi, l. a. (2012). pembelajaran matematika dengan penemuan terbimbing untuk meningkatkan kemampuan representasi dan pemecahan masalah matematis siswa smp. jurnal penelitian pendidikan, 13(2), 1 – 10. fahinu. (2007). meningkatkan kemampuan berpikir kritis dan kemandirian belajar matematika pada mahasiswa melalui pembelajaran generatif. bandung: dissertasion in mathematics education, school of post graduate studies, upi. icaje, the international centre for jesuit education in rome. (1993). ignatian pedagogy: a practical approach. [online]. available: http://www.rockhurst. edu/media/filer_private/ uploads/ignatian_pedagogy_apractical_approach.pdf. [27 th desember 2013]. insuasty, e.a. dan castillo, l.c.z. (2010). exploring reflective teaching through informed journal keeping and blog group discussion in the teaching practicum. profile: issues in teachers` professional development vol.12 no.2, october 2010. issn 1657-0790. bogotá, columbia. pages 87-105. karlimah. (2010). pengembangan kemampuan komunikasi dan pemecahan masalah serta disposisi matematis mahasiswa pgsd melalui pbm. bandung: dissertasion in mathematics education, school of post graduate studies, upi. lasmanawati, a. (2011). pengaruh pembelajaran menggunakan pendekatan proses berpikir reflektif terhadap peningkatan kemampuan koneksi dan berpikir kritis matematis siswa. bandung: thesis in mathematics education, school of post graduate studies, upi. http://en.wikipedia.org/wiki/problemsolving http://www.scielo.org.co/scielo.php?script=sci_serial&pid=1657-0790&lng=en&nrm=iso http://www.scielo.org.co/scielo.php?script=sci_serial&pid=1657-0790&lng=en&nrm=iso ningsih & rohana, prospective teachers’ ability in mathematical problem-solving … 82 nainggolan, l. (2011). model pembelajaran reflektif untuk meningkatkan pemahaman konsep dan kemampuan komunikasi matematis. bandung: thesis in mathematics education, school of post graduate studies, upi. prabawanto, s. (2012). peningkatan kemampuan pemecahan masalah, komunikasi, dan self-efficacy matematis mahasiswa melalui pembelajaran dengan pendekatan metacognitive scaffolding. bandung: disertation in mathematics education, school of post graduate studies, upi. radulescu, c. (2013). reinventing reflective learning methods in teacher education. procedia social and behavioral sciences, 78, 11 – 15. rohana. (2015). peningkatan kemampuan penalaran matematis mahasiswa calon guru melalui pembelajaran reflektif. infinity, 4(1), 105 – 119. sirajuddin. (2009). model pembelajaran reflektif: suatu model belajar berbasis pengalaman. in didaktika jurnal kependidikan, 4(2), 189-200. song, h.d., koszalka, t. a., dan grabowski, b. (2005). exploring instructional design factors prompting reflective thinking in young adolescents. in canadian journal of learning and technology, 31(2), 49-68. wahyudin (2003). peranan problem-solving. makalah seminar technical cooperation project for development of mathematics and science for primary and secondary education in indonesia, 25 th agustus 2003. widjajanti, d., b. (2010). analisis implementasi strategi perkuliahan kolaboratif berbasis masalah dalam mengembangkan kemampuan pemecahan masalah, kemampuan komunikasi matematis, dan keyakinan terhadap pembelajaran matematika. bandung: disertation in mathematics education, school of post graduate studies, upi. infinity journal of mathematics education p–issn 2089-6867 volume 5, no. 2, september 2016 e–issn 2460-9285 doi 10.22460/infinity.v5i2.216 99 analysis of students mathematical representation and connection on analytical geometry subject muchamad subali noto 1 , wahyu hartono 2 , mohammad dadan sundawan 3 1,2,3 department of mathematics education, swadaya gunung djati university, cirebon indonesia 1 balimath61@gmail.com received: may 20, 2016; accepted: august 10, 2016 abstract the importance ability of mathematical representation and connection to owned by the student really help students in understanding the mathematical concepts in the form of pictures, symbols, and the written word. the use of mathematical representation and the correct connection by students will help students make mathematical ideas more concrete and can connect a concept to another concept, so that students can develop a view of mathematics as a whole integration. this research aims to describe and analyze the ability of representation and mathematical connection on the topics of analytical geometry. the research method was descriptive with the subject as much as 22 mathematics students. data collected through tests and interviews. the results show that the average ability of representation is 46.00; the average mathematical connection ability is 36.77. this means both the abilities still belongs to low, particularly for the ability of mathematical connection. keywords: mathematical representation, mathematical connection, and analytical geometry abstrak pentingnya kemampuan representasi dan koneksi matematis untuk dimiliki oleh mahasiswa sangat membantu mahasiswa dalam memahami konsep matematis berupa gambar, simbol, dan kata-kata tertulis. penggunaan representasi dan koneksi matematis yang benar oleh mahasiswa akan membantu mahasiswa menjadikan gagasan-gagasan matematis lebih konkrit dan dapat menghubungkan suatu konsep ke konsep yang lain, sehingga mahasiswa dapat mengembangkan pandangan matematika sebagai integrasi yang utuh. penelitian ini bertujuan untuk mendeskripsikan dan menganalisis kemampuan representasi dan koneksi matematis mahasiswa calon guru matematika pada matei geometri analitik. metode penelitian adalah penelitian deskriptif dengan subjek mahasiswa calon guru matematika sebanyak 22 mahasiswa. teknik pengumpulan data menggunakan tes dan wawancara. hasil menunjukkan bahwa rata-rata kemampuan representasi sebesar 46,00; rata-rata kemampuan koneksi matematis sebesar 36,77. ini berarti kedua kemampuan tersebut masih tergolong rendah, terutama untuk kemampuan koneksi matematis. kata kunci: representasi matematis, koneksi matematis, dan geometri analitik how to cite: noto, m.s., hartono, w. & sundawan, m.d. (2016). analysis of students mathematical representation and connection on analytical geometry subject. infinity, 5 (2), 99-108 noto, hartono & sundawan, analysis of students mathematical representation … 100 introduction a committee on undergraduate mathematics or cupm recommends that each program should include activities that help students in developing analytical thinking, critical reasoning, problem solving, communication skills and acquire the habit of thinking mathematically. those activities should be designed to promote and measure progress of students in learning mathematics, one of them with communicating mathematical ideas clearly and coherence through writing and speaking. student understanding of the mathematical concepts, and the ability of students in using mathematical ideas can be seen from how students choose the right way in representing its mathematical ideas. nctm (2000) states that when students have access to mathematical representation and ideas that they show, then they have a bunch of tools that will significantly expand their capacities in thinking mathematically. as expressed by jones (2000), there is a need for some reason the ability of representation, namely: is the ability to build basic concepts and mathematical thinking, and to have a good understanding of the concepts that can be used in problem solving. wahyudin (2008) also added that representation could help the students to organize his thoughts. learning by emphasizing mathematical representation is a demanding mental activity learning students optimally in understanding a concept. bruner (hasanah, 2004) said that to understand the most important mathematical concepts is not storage of past experience but how to get back the knowledge that has been stored in memory and are relevant to the needs and can be used when needed. the importance of the ability of mathematical representation for the owned by the student really help students in understanding the mathematical concepts in the form of pictures, symbols, and the written word. the use of the right of representation by students will help students make mathematical ideas more concrete. a complex problem would be much simpler if you use a representation that corresponds to a given problem, otherwise false representation of construction make the problem difficult to be solved. with regard to the theory of bruner, according to ruseffendi (2006), in mathematical learning needs to pay attention to the four propositions, namely; drafting (construction), the notation, contrast and diversity (variation), and connectivity. the evidence for the preparation explaining that in studying mathematics, it will be more embedded if student conduct themselves the order of representation. the evidence for notation explained that in the learning needs to consider the use of a notation which corresponds to the mental development of the child. the evidence for contrast and diversity explaining that in order to make the concept becomes more meaningful, it should be a contrasting concept dishes and diverse. while the evidence for connectivity explains that the learning process needs to consider the opportunity of studying the relation between concepts, topics, and between branches of mathematics. the ability to connect between the concepts, topics and between branches of mathematics called mathematical connection abilities. according to fisher, daniels, & anghileri (suhendar, 2007) making connection is a way to create understanding and instead understand something means making a connection. to understand an object in depth one must know: (1) the object itself; (2) his relations with other similar objects; (3) the relationship with other volume 5, no. 2, september 2016 pp 99-108 101 similar objects; (4) the dual relation with other objects of its kind; and (5) relationship with other objects in the theory (suhendar, 2007). the mathematical connection means the activities connect between mathematical concepts; connect mathematical concepts with the concept of other lessons; apply thought and modeling mathematics to solve the problems that appear in other disciplines such as art, music, psychology, science and business; even also is the activities connect the concept of mathematics with the daily life. nctm popularising the mathematical connection in his native language of english called mathematical connection and make it as one of the six curriculum standards. in addition, students who have the ability of a good connection will be easier to learn the multitude of learning materials with how to connect the material to one another. nctm (2000) justify the statement and proposed that without the mathematical connection ability, students must learn and remember many concepts. continued nctm (2000), when the students are able to connect a concept to other concepts, then they have developed views of mathematics as a whole integration. this means that the purpose of the mathematical connection is intended to broaden the students, see mathematics as a unified whole not stand alone and know the relationship and the benefits of mathematics both in school and outside the school. the geometry is a mathematics lesson materials that need a good mathematical ability to understand it. according to nctm (siregar, 2009: 5) abilities that must be owned by the student in learning geometry is: 1) the ability to analyze the characters and the nature of the geometry either two dimensional or three dimensional, and able to build these arguments regarding the relationship mathematics geometry with the other; 2) the ability to determine the position of a point with more specific and image spatial relationship with using the coordinates geometry and connect it with the other system; 3) application abilities transformation and its use in the symmetric to analyze mathematical situation; 4) is able to use visualization, spatial reasoning, and model geometry to solve problems. by mastering the abilities, students are expected to master the material in the geometry with better. sunardi (2007) stated that in comparison with other math materials, the geometry of the position of the most concern. the difficulty of college students in learning geometry occurs starting from elementary school to college (pt). if studied more about the link between geometry objects that abstract with the difficulty students in learning geometry, then it would appear that there are indeed problems in learning geometry in school are associated with the formation of abstract concepts. learn the abstract cannot be done only with the transfer of information, but it takes a process of formation of concepts through a series of activities that is experienced directly by the student. the series of activities of formation of abstract concepts that hereafter the process of abstraction. nurhasanah (2010) states that fit the characteristics of geometry, abstraction processes must be integrated with the process of learning that goes so should pay attention to some aspects like, learning methods, models of learning, learning materials, availability and use of props or teacher skills in managing learning activities. one of the branches of the geometry is analytic geometry. this courses are intended to give an understanding to the students about the basic concept in the analytically geometry so that the students can solve the problems related to the concepts in analytically geometry. the noto, hartono & sundawan, analysis of students mathematical representation … 102 courses of analytic geometry also has an important role in providing a strong foundation for students to learn more advanced courses such as transformation geometry, calculus ii, advance calculus i and ii. this courses presents many visual representation such as a picture or graph, representation symbols as the common denominators of mathematics and demanding the student to explain it verbally/orally. based on these problems, this article will discuss the related to the ability of mathematical representations and connection students of analytical geometry with the formulation of the problem as follows. 1. how the mathematical representation ability of mathematics students? 2. how the mathematical connection ability of mathematics students? method this research is a descriptive research, with the aim to describe and analyze the ability of mathematical representation and connection students based on the data obtained. description of the method is selected for researchers attempting to uncover the factual situation regarding the ability of mathematical representation and representation students. research subject as much as 22 students of mathematics from unswagati that contracted courses analytical geometry. data collection method in the form of a test and an interview. research instruments include test of mathematical representation and connection, and interview sheet. results and discussion based on the mathematical representation of ability, obtained the following results. table 1 shows the results of a mathematical representation ability (mra). table 1. statistics krm n valid 22 missing 0 mean 46,0000 median 46,0000 mode 10,00 based on table 1 of the output above, seen that the results of the average (mean) and median are the same value. average mra reach 46.00. this shows the average mra are not optimal, because it is still under 50. it means to mra remains to be improved again. seen from the mode value of 10.00. these values are still below average, it means the mra unswagati student tend to the left. median value = 46.00, meaning that there is a 50% (100 students) get value under 46.00. this indicates that the mra is still low or less than optimal, it also reinforced with a value of mode which is still below average. volume 5, no. 2, september 2016 pp 99-108 103 table 2. max and min mra value n valid 22 missing 0 std. deviation 24,82510 variance 616,286 minimum 9,00 maximum 95,00 percentiles 15 11,3500 25 27,2500 50 46,0000 75 65,0000 based on the table 2, obtained that the standard deviation 24,82. this means that the spread of the mra data is 24,82 from the average. minimum value = 9 and maximum value 95.00, this means that there is a student with low and the highest mra. there are 25% (22 students) that mra is under 27.25 and 15% is under 33.33. in the percentiles 75, the value of mra is 65, it means that 25 percent students get mra value above the average. based on its achievements of each mathematical representation indicator, presented in table 3 below. table 3. achievements of mra no. measured indicator average score max. scor e achieveme nts (%) r1. presents the mathematical problems in the visual model. 1. drawing straight lines forming a specific angle with another straight line. 5 10 50 5. drawing a circle with the center of the known and alluded to a straight line. 4,82 10 48,2 r2. identify and use the object, process and procedures that are appropriate in various representation. 3. determine the equation of a tangent on circles if known gradient. 2,59 10 25,9 4. identify the center, radius and the equation of a circle through three points. 19,59 40 48,98 noto, hartono & sundawan, analysis of students mathematical representation … 104 no. measured indicator average score max. scor e achieveme nts (%) r3. linking the procedures and processes in various representations in relevant concept. 2. determine the area of the image of the triangle through the long sides. 8,64 20 43,2 table 3 above shows that the indicator r1-r3 measured with questions no 1-5 obtained its achievements by 50%; 43.2%; 25.9%; 48,98%; 48,2%. this shows that overall the indicator the average has not yet reached 75%. the first indicator is measured with questions no. 1 and 5, presented the problems related to the straight line and the circle, students complete the problem with are modeling visually to describe the straight line and the circle. there are 25 percent of the total amount of students are modeling problems visually correctly, the remaining 75% mistaken in applying the concept to resolve the issue so the model that made it wrong. the second indicator is measured with questions no. 3 and 4, identify and use the object, process and procedures that are appropriate in a representation of the circle equation. 10% of students can identify and use the three coordinates of the point that passed by the circle, to apply the procedure of elimination or substitution the linier equation to get the circle equation, 80% mistaken in the concept of the count and one procedure of elimination or substitution. the third indicator is measured with questions no. 2, linking the procedures and processes in various representations relevant concept. 36% of students can linking procedures and the process of searching for broad and provide an explanation in writing related to the two straight lines that are perpendicular to each other on a visual representation in the form of a picture triangle. 36% of students can linking with appropriate procedures and processes, 64% mistaken in the concept and count. based on the mathematical connection ability data obtained the following result. table 4 shows the results of the students mathematical connection ability (mca). table 4. statistics mca n valid 22 missing 0 mean 36,7727 median 30,5000 mode 25,00 based on the table 4 in the above output, seen that the results of the average (mean) and median almost the same value. the average mca reach 36,00. this shows the average mra is not optimal, because the value is below 50. that means the mca also still must be improved again. the mode is 25.00, below the average, that means mra unswagati students tend to the left. the median value = 30.00, that means 50% (100 students) get under 36.00 volume 5, no. 2, september 2016 pp 99-108 105 value. this shows that the mca still low or less than optimal, is also strengthened by mode value that is still below the average. table 5. max and min value of mca n valid 22 missing 0 std. deviation 25,4893 7 variance 649,708 minimum 6,00 maximum 81,00 percentiles 15 7,4500 25 10,5000 50 30,5000 75 62,5000 based on the table 5, obtained that the standard deviation 25,48. this means that the spread of mca data is approximately 25,48 from the average. minimum value = 6 and maximum value 81,00, this means that there is a student with low mca and the highest mr a of 81. there are around 25% (22 students) that mra under 10,50 and 15% under 7.45. there is also 25 percent students get mca value above the average. based on its achievements of each mathematical connection indicator, presented in table 6 below. table 6. achievements of mca no. measured indicator average score max. score achieveme nts (%) k1. looking for relations of various representations of the concept. 6. explain the relationship between the two straight line based on the image. 5,62 10 56,2 k2. apply math in other fields or in everyday life. 7. apply the concept of an elliptical surface in the field of health 1,72 10 17,20 8. apply the concept of an elliptical surface in the the bridge construction 1,90 10 19,00 noto, hartono & sundawan, analysis of students mathematical representation … 106 no. measured indicator average score max. score achieveme nts (%) 9. apply the concept of a circle related to the problem of radar 7,45 15 49,70 table 6 above shows that the indicator k1 and k2 measured with questions no.6-9 obtained its achievements of 56.2%; 17.2%; 19%; 49,70%. this shows that overall the indicator the average has not yet reached 75%. the indicator k1 measured with questions no.6, presented the problems related to the straight line, students explain the relationship between the representation visually, that explain the relationship between the two straight line based on the image of the given triangle. there are 40 percent of the total amount of students can give an explanation about the relationship between the two straight lines is analytically correctly, the remaining 60% mistaken in applying the concept and create a symbol. the indicator k2 measured with questions no. 7-9, apply mathematics in other areas or in everyday life. 22,7% students can apply the concept of an elliptical surface in the field of health or related to the bridge construction, 77.3% mistaken in the concept and count. 36,36% students can apply the concept of a circle related to the problem of radar, 63,64,3% mistaken in the concept and count. conclusion the ability of mathematical representation students on the material of analytical geometry especially related to the system of the coordinates kartesius, straight line, circle and ellipse still low. they are not able to apply the concepts, error in performing operations, cannot visuallize (drawing a straight line or circle) and cannot use the procedures related to the specific representation. mathematical connection ability of the mathematics students also still low. they are not able to understand the problem, cannot apply the concepts in everyday life, error in performing operations and cannot create a symbol properly. after knowing the mathematical abilities, the authors give suggestions for the next researcher: 1) implementing a learning geometry software-assisted model related in mathematical representation and connection ability, the purpose using this software is to assist students in visualizing geometric objects, so that it can build an internal representation of the students. 2) designing teaching materials with the activities of mathematical representations and connection on the analytical geometry. the development of teaching materials must be based to the description of the abilities of the attention to the difficulty/confusion created by the students. volume 5, no. 2, september 2016 pp 99-108 107 references committee on the undergraduate program in mathematics. (2004). undergraduate programs and courses in the mathematical sciences: cupm curriculum guide 2004. http://www.maa.org/cupm/summary.pdf. coxford, a.f. (1995). the case for representation.dalam p.a. house dan a.f coxford (eds). yearbook connecting mathematics across the curriculum. reston, va: the national council of teachers of mathematics. hasanah,a. (2004). mengembangkan kemampuan pemahaman matematika siswa smp melalui pembelajaran berbasis masalah yang menekankan pada representasi matematika.tesis pps upi. bandung: tidak diterbitkan. hudojo, h. (2002). representasi belajar berbasis masalah.journalmatematika atau pembelajarannya. issn:085-7792. tahun viii, edisi khusus. hwang,w. y., chen, n. s., dung, j. j., & yang, y. l. (2007). multiple representation skill and creativity effects on mathematical problem solving using a multimedia whiteboard system.educational technology and society.vol 10 no. 2: 191-212. jones, b.f., & knuth, r.a. (1991).what does research about mathematics?[online]. tersedia: http://www. ncrl.org/sdrs/areas/stw_esys/2math.html. jones, a.d. (2000). the fifth process standard: an argument to include representation in standar 2000. [online]. available: http://www.math.umd.edu/~dac/650/jonespaper.html. kaput, j. j dan goldin, g. a. (2004).a join perspective on the idea of representation in learning and doing mathematics.[online]. tersedia: http://www.simmalac.usmassad.edu. nctm (2000).principles and standards for school mathematics.reston: virginia. nurhasanah, f. (2010).abstraksi siswa smp dalam belajar geometri melalui penerapan model van hiele dan geometer’s sketchpad (junior high school students’ abstraction in learning geometry through van hiele’s model and geometer’s sketchpad). tesis sps upi bandung: tidak diterbitkan. ruseffendi, e.t. (2006). pengantar kepada membantu guru mengembangkan kompetensinya dalam pengajaran matematika untuk meningkatkan cbsa. bandung: tarsito. siregar, n. (2009). studi perbandingan kemampuan penalaran matematik siswa madrasah tsanawiyah kelas yangbelajar geometri berbantuan geometer’s sketchpad dengan siswa yang belajar tanpa geometer’s sketchpad. tesis sps upi bandung: tidak diterbitkan. http://www.maa.org/cupm/summary.pdf http://www/ http://www.math.umd.edu/~dac/650/jonespaper.html. http://www.simmalac.usmassad.edu/ noto, hartono & sundawan, analysis of students mathematical representation … 108 suhendar (2007). meningkatkan kemampuan komunikasi dan koneksi matematika siswa smp yang berkemampuan rendah melalui pendekatan konstektual dengan pemberian tugas tambahan. tesis pada sps upi: tidak diterbitkan. sumarmo, u. (2010). berfikir dan disposisi: apa, mengapa dan bagaimana dikembangkan pada peserta didik. fpmipa upi.: tidak diterbitkan. sunardi.(2007). hubungan tingkat penalaran formal dan tingkat perkembangan konsep geometri siswa. jurnal ilmu pendidikan. jakarta: lptk dan ispi. wahyudin. (2008). pembelajaran dan model-model pembelajaran. bandung: upi. sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 10, no. 1, february 2021 e–issn 2460-9285 https://doi.org/10.22460/infinity.v10i1.p31-40 31 students’ mathematical thinking skill viewed from curiosity through problembased learning model on integral calculus zetriuslita*, rezi ariawan universitas islam riau, indonesia article info abstract article history: received apr 25, 2020 revised sep 22, 2020 accepted sep 23, 2020 this study aims to find out the improvement of students’ mathematical critical thinking viewed from curiosity through teaching materials with problem based learning model. this is quasi-experimental research. the samples are, where the overall population consists of 75 samples divided into two classes. this research employed a simple random sampling technique. the instruments were the mathematical critical thinking skill test and curiosity questionnaire. the technique of data collection was carried out with test and non-test techniques. the data were analyzed through a two-way anova test. based on the analysis and interpretation of the research findings, it was found that: there was an improvement in students’ mathematical critical thinking skill from high curiosity by using teaching materials with problem based learning model; 1) there was an improvement from average curiosity through learning with integral calculus teaching materials; 2) there was an improvement from low curiosity; 3) there was no improvement from the level of curiosity (high, medium, low) through problem-based learning. 4) there was no influence between the level of curiosity and learning in improving students’ mathematical critical thinking skills. do more in-depth studies related to improving mathematical critical thinking skills by reviewing other affective aspects keywords: curiosity, integral calculus, mathematical critical thinking, problem-based learning, teaching material copyright © 2021 ikip siliwangi. all rights reserved. corresponding author: zetriuslita, department of mathematics education, universitas islam riau, jl. kaharuddin nasution no.113, bukit raya, pekanbaru, riau 28284, indonesia. email: zetriuslita@edu.uir.ac.id how to cite: zetriuslita, z., & ariawan, r. (2021). students’ mathematical thinking skill viewed from curiosity through problem-based learning model on integral calculus. infinity, 10(1), 31-40. 1. introduction calculus is a course that nearly exists in every university, especially in mathematics and science majors. it is also one of the compulsory courses and skills for students majoring in science, especially in mathematics. they are expected to excel in this important subject. as a result, some researchers have carried out a research to evaluate and improve students’ ability in learning calculus (hartono & noto, 2017; lumbantoruan, 2017; mutakin, 2013; parma & saparwadi, 2015; ramdani, 2012; romadiastri, 2013; sopiany & rikayanti, 2018; usman et al., 2015). https://doi.org/10.22460/infinity.v10i1.p31-40 zetriuslita & ariawan, students’ mathematical thinking skill viewed from curiosity … 32 furthermore, the researcher has also conceived her own studies related to calculus, namely: an analysis of students’ mathematical critical thinking, connecting on integral calculus problem solving based on the students’ academic level, gender, cognitive style (ariawan & nufus, 2017; zetriuslita et al., 2016a; 2016b). practicality teaching material based on the problem based learning to improve mathematical critical thinking ability (zetriuslita & ariawan, 2016). based on the previous studies, the researcher focused on mathematical critical thinking ability. critical thinking ability is quite necessary in calculus. klurik and rudnick (zetriuslita et al., 2018) argued that critical thinking in mathematics involves testing, questioning, connecting, evaluating all aspects in any situations or problems. it doesn’t only demand knowledge and comprehension but also more than that. the given problem consists of analytical ability. ennis (2011) stated that critical thinking is a summary of logical thinking (logic) and reflective which emphasizes on decision making about what we believe or do. according to johnson (2007), it’s a focused and clear process which is employed in mental activities such as problem solving, decision making, persuasion, assumption analysis, and conducting scientific research. in line with the statement, ennis (2011) mentioned that the aspects of critical thinking are focus, reasons, inference, situation, clarity, and overview. from the statements above, it indicates that critical thinking can make and train someone to do math. students don’t learn mathematical rules or formulas by heart but learn mathematics by action and active discovery. consequently, critical thinking is very important to develop. in general, developing critical thinking or improving mathematics learning outcome can be achieved by using teaching materials or learning media (bien et al., 2019; dewi, 2016; guntur et al., 2017; hikmawati et al., 2013; melisa, 2014; putra et al., 2017; saparwadi & yuwono, 2019). based on the researcher’s teaching experience, there was a problem related to the lack of determination and curiosity. it was seen from the students’ unwillingness to find out the answers to the given problems, especially in calculus integral subject. they didn’t try to ask the teacher about the problem they didn’t understand. this level of curiosity can affect the students’ activity in learning and also lead to their comprehension. carin (1997) defined curiosity as one’s willingness and need to obtain answers from a question or things that spark curiosity. curiosity can foster internal motivation for learning and understanding something, therefore it can be developed in the learning process (ameliah & munawaroh, 2016; mardhiyana, 2017; nurkamilah, 2017; solehuzain & dwidayanti, 2017). in accordance with the findings, the researcher did some studies in regards to students’ mathematical curiosity (zetriuslita et al., 2017). from the review of related literature and identification of the problem above, students’ curiosity is a cognitive aspect that seeks attention and serious consideration. subsequently, the researcher’s interest focuses on improving students’ mathematical critical thinking ability viewed from curiosity. the researcher applied teaching materials based on problem based learning. the researcher suggested the following hypotheses, such as: (1) there is a significant difference in terms of high curiosity between students who use calculus integral teaching materials based on problem-based learning model and those who follow conventional learning; (2) there is a significant difference in terms of medium curiosity between students who use calculus integral teaching materials based on problem-based learning model and those who follow conventional learning; (3) there is a significant difference in terms of low curiosity between students who use calculus integral teaching materials based on problembased learning model and those who follow conventional learning; (4) there is a significant difference in terms of curiosity (high, medium, low) between students who used calculus integral teaching materials based on problembased learning model and those who follow volume 10, no 1, february 2021, pp. 31-40 33 conventional learning; and (5) there is an interaction effect between level of curiosity and learning towards the improvement of mathematical critical thinking ability. 2. method this study is a quantitative research. quantitative research is the process of using data in numerical form as a means to find out knowledge (creswell & creswell, 2017; sugiyono, 2011). the type of research is quasi-experimental research with pre-test and posttest non-equivalent group design described in table 1. table 1. pre-test and post-test non-equivalent group design (cohen et al., 2007) pre-test treatment posttest experiment o1 x o2 control o1 o2 description: o1 : pretest of experiment classes and control classes o2 : postest of experiment classes and control classes x : treatment using integral calculus-based teaching materials problem based learning : treatment with does not use teaching materials problem-based integral calculus the samples of this research were the 2nd semester students of mathematics education fkip uir who took integral calculus subject. there were two classes. saturated sampling was used because the samples were selected from the overall population by using simple random sampling technique. the lottery showed that 2a was chosen as the control class (conventional learning) and 2b as the experiment class (using calculus integral teaching materials with problem-based learning model). this research was conducted in the even semester of academic year 2018/2019. the instruments of this research consisted of mathematical critical thinking ability worksheet and curiosity questionnaire. the data collection was carried out by using both instruments for test and non-test technique respectively. the test about critical thinking ability was given in the first and last meeting, while the questionnaire of curiosity was distributed in the first meeting only. the data obtained from the test and questionnaire was analyzed by using descriptive statistics and inferential statistics with spss version 22 software. in order to determine the level of curiosity, the researcher used the following interval in table 2. table 2. interval group level of curiosity (zetriuslita et al., 2016b) group level of curiosity interval high 𝑥 ≥ �̅� + 𝜎 medium �̅� + 𝜎 < 𝑥 < �̅� + 𝜎 low 𝑥 ≤ �̅� − 𝜎 description: x = students’ curiosity score �̅� = mean score of students’ curiosity σ = standard deviation of students’ curiosity score zetriuslita & ariawan, students’ mathematical thinking skill viewed from curiosity … 34 meanwhile, the improvement of mathematical ability intended is normalized gain obtained from the pre-test and post-test results, with the following formula by meltzer (2002). 𝑁𝐺𝑎𝑖𝑛 = 𝑃𝑜𝑠𝑡𝑒𝑠𝑡 − 𝑃𝑟𝑒𝑡𝑒𝑠𝑡 𝐼𝑑𝑒𝑎𝑙 𝑆𝑐𝑜𝑟𝑒 − 𝑃𝑟𝑒𝑡𝑒𝑠𝑡 in order to the test hypothesis of the research, t-test, one-way anova test and two-way anova test were used. 3. results and discussion 3.1. results the data analysis of improving mathematical critical thinking ability was obtained from n-gain result. it was classified into the level of curiosity, starting from grouping the students based on their curiosity level. from the result of curiosity score, the data were obtained as follows: the data of improving mathematical critical thinking ability viewed from curiosity is presented in table 3. table 3. description of students’ total in terms of curiosity level of curiosity learning pmbakipbl ptmbakipbl high 5 (13.16%) 5 (13.5%) medium 26 (68.42%) 27 (72.97%) low 7 (18.42%) 5 (13.51%) total 38 (100%) 37 (100%) description: pmbakipbl : learning using integral calculus teaching materials based on problembased learning ptmbakipbl : learning does not use integral calculus teaching materials based on problem-based learning table 3 shown that in experimental class is better than control class. students in the experimental class and the control class with curiosity were not significantly different from the level of curiosity. this indicates that the curiosity of the experimental class and control class students is almost the same. basically, if the curiosity is not much different, then the resulting mathematics learning outcomes should not be different either. however, with different treatment with the use of problem-based learning materials, the learning outcomes can be presented in the following table. by using spss version22, the calculation of hypotheses 1, 2, and 3 are presented in the table 4. volume 10, no 1, february 2021, pp. 31-40 35 table 4. the improvement of mathematical critical thinking level of curiosity statistics (t-test) conclusion high sig. (2-tailed) = 0.000 < 0,05 hypothesis is accepted medium sig. (2-tailed) = 0.000 < 0.05 hypothesis is accepted low sig. (2-tailed) = 0.000 ≤ 0.05 hypothesis is accepted table 4 show that on average the improvement of students’ mathematical critical thinking ability from high level of curiosity, medium and low who followed problem based learning is better than studentswho follow conventional learning. then, hypothesis was tested by using one-way anova test (table 5). table 5. one-anova test of improvement critical thinking based on curiosity sum of squares df mean square f sig. between groups 0.003 2 0.002 0.50 0.952 within groups 2.287 72 0.032 total 2.290 74 from table 5, it was obtained the sig = 0,952 ≥ α, with α= 0,05. it means h0 is accepted and h1 is rejected. when h1 is rejected, the hypothesis “there is a significant difference of improving mathematical critical thinking ability between students from curiosity level who follow problem based learning and conventional learning” is rejected. in other words, there is no significant difference of improving the students’ critical thinking ability viewed from level of curiosity. next, hypothesis 5 was tested by using two-way anova test with the spss version 22 software. the result was obtained as follows in table 6. table 6. two-way anova test source type iii sum of square df mean square f sig. corrected model 1.271a 5 0.254 17.204 0.000 intercept 9.226 1 9.226 624.620 0.000 curiosity 0.001 2 0.000 0.021 0.980 kelas 0.949 1 0.949 64.239 0.000 curiosity*kelas 0.067 2 0.033 2.263 0.112 error 1.019 69 0.015 total 18.307 75 corrected total 2.290 74 table 6 show that sig. = 0.112 > 0.05, where hypothesis h1 is rejected, meaning there is no interaction effect between level of curiosity and learning towards the improvement of mathematical critical thinking ability. the curiosity has no significant effect on the improvement, it’s indicated with sig. = 0.980 > 0.05 (table 6), meanwhile the class or in this case learning has a significant effect on the improvement shown by sig = 0.000 < 0.05. zetriuslita & ariawan, students’ mathematical thinking skill viewed from curiosity … 36 3.2. discussion the result of inferential statistics show that the improvement of mathematical critical thinking ability for the students who follow problem based learning in integral calculus is higher than those who follow conventional learning. it means that the use of integral calculus teaching materials with problem based learning is effective in improving students’ mathematical critical learning ability. this is in line with a research finding by guntur et al. (2017) which stated that the effect between intensively, rarely, and never using comics towards students’ selflearning. dewi (2016) said that the average rank of experimental group is higher than that of control group. in other words, students’ learning outcome in learning with screencast-o-matic media is better than students who follow conventional learning. so this research reinforce the assumption that using screencasto-matic is effective to increase students’ learning outcome in integral calculus subject. hikmawati et al. (2013) stated that there was an influence of the use of instructional media and cognitive styles on mathematics learning outcomes of grade viii madrasah tsanawiyah students and there was no interaction between the use of instructional media and cognitive style on mathematics learning outcomes of grade viii madrasah tsanawiyah students. bien et al. (2019) stated that the use of teaching calculus textbooks was effective in increasing the ability to understand student concepts. farhan and retnawati (2014) stated that pbl can make students more active when they are working on worksheets based on pbl made by teachers. gordah and fadillah (2014) stated that increasing students' mathematical representation ability through the use of differential calculus teaching materials based on the open ended approach was classified as moderate, there was no difference in increasing students' mathematical representation ability in terms of gender (male and female); 3) there is a difference in the improvement of students 'mathematical representation ability in terms of the initial level of students' ability (upper, middle, and lower). meanwhile, if viewed based on the level of curiosity, thenthere is no difference in the increase in mathematical critical thinking ability reviewed based on curiosity (high, medium, low) between students who learn by using integral calculus based on problem based learning with those not. furthermore, there is also no interaction effect between learning and curiosity on the improvement of mathematical critical thinking ability. there are several analyzes that researchers can convey why there are no differences in enhancement and interaction, including: (1) the questionnaire researchers do before curiosity study or research is carried out, with the aim only to determine the condition of student curiosity. even though if the questionnaire was given after they learned by using integral calculus based learning materials based on problem based learning, maybe their curiosity would be better; (2) the structure of teaching materials is designed to improve critical thinking ability, so that attention to students' curiosity lacks attention. the results of this study are in line with research conducted by zetriuslita et al. (2017) which states that after being given treatment, mathematical curiosity of students does not/ experience a significant increase. this is due in the learning process, lecturers are not maximized in developing students' mathematical curiosity, and other factors are the lack of maximum learning tools for student worksheets or lkm. furthermore solehuzain and dwidayati (2017) stated that there was a significant influence between curiosity on students' mathematical creative thinking abilities on the problem based learning model of learning with open-ended problems. the variable of curiosity affects the variable of mathematical creative thinking ability by 77.4% and the rest is influenced by other factors. volume 10, no 1, february 2021, pp. 31-40 37 4. conclusion the conclusion of this research are: (1) improvement of mathematical critical thinking ability of students who learn to use integral calculus based problem based learning is better than improvement in mathematical critical thinking ability of students who learn not to use integral based learning calculus based on problem based learning both in terms of high, medium, high curiosity levels low; (2) there is no increase in mathematical critical thinking ability of students who learn to use integral based learning calculus based on problem based learning compared to the students who learn not to use integral based learning calculus based on problem based learning based on curiosity (high, medium, low ); (3) there is no effect of interaction between levels of curiosity and learning on improving students' mathematical critical thinking ability. there are a number of things that researchers can advise on the results of this study, namely: it is recommended that a more in-depth study is conducted related to improving mathematical critical thinking skills by reviewing other affective aspects, a study in the form of further development of calculus root material which is not only based on active learning models, but by using the help of mathematical software such as matlab, geogebra and others. studies are more extended, not only focus on integral calculus, but focus on the study of calculus (differential calculus, and calculus of many variables or advanced calculus). future studies must use a comprehensive research method in the form of a mix method, which combines data obtained qualitatively with data obtained quantitatively. acknowledgments the author would like to thank universitas islam riau for the support in funding and the research team for their commitment in this research. references ameliah, i. h. 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(2018). association among mathematical critical thinking skill, communication, and curiosity attitude as the impact of https://doi.org/10.21580/phen.2013.3.1.179 https://doi.org/10.22460/infinity.v5i1.p56-66 https://doi.org/10.5539/ies.v10n7p65 zetriuslita & ariawan, students’ mathematical thinking skill viewed from curiosity … 40 problem-based learning and cognitive conflict strategy (pblccs) in number theory course. infinity journal, 7(1), 15-24. https://doi.org/10.22460/infinity.v7i1.p15-24 https://doi.org/10.22460/infinity.v7i1.p15-24 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 8, no. 2, september 2019 e–issn 2460-9285 https://doi.org/10.22460/infinity.v8i2.p179-188 179 mathematical anxiety among engineering students rully charitas indra prahmana* 1 , tri sutanti 2 , aji prasetya wibawa 3 , ahmad muhammad diponegoro 4 1,2,4 universitas ahmad dahlan 3 universitas negeri malang article info abstract article history: received sept 2, 2019 revised sept 21, 2019 accepted sept 30, 2019 mathematical anxiety has a negative relationship with mathematics performance and achievement. further explained, mathematics anxiety has an indirect effect on mathematics performance. this research explores sources or factors related to mathematics anxiety among engineering students at a private university in indonesia. a total of 47 engineering students participated in this survey that randomly chosen based on gender, major, and age. two main factors are affecting the mathematics anxiety of engineering students, namely internal and external factors. the results show that mathematics anxiety among engineering students is manifested into three aspects. firstly, the home aspects are talking about the influence of parents and sibling. secondly, society's issues are discussing self-efficacy, social reinforcement to hate mathematics, and social stereotypes. lastly, the classroom aspects are talking about the traditional mathematics learning process and classroom culture, namely the experience of learning mathematics in classrooms and relationships between friends during learning. the details of the statements under the aspects also highlight unique problems and are not covered by previous research in mathematical anxiety. next, differences in mathematics anxiety by gender and faculty were examined. keywords: descriptive quantitative, engineering student, gender, higher education, math anxiety copyright © 2019 ikip siliwangi. all rights reserved. corresponding author: rully charitas indra prahmana, master program on mathematics education, universitas ahmad dahlan, jl. pramuka 42, pandeyan, umbulharjo, yogyakarta, indonesia. email: rully.indra@mpmat.uad.ac.id how to cite: prahmana, r. c. i., sutanti, t., wibawa, a. p., & diponegoro, a. m. (2019). mathematical anxiety among engineering students. infinity, 8(2), 179-188. 1. introduction nowadays, mathematics and its ability is an essential and frequent phenomenon in education (hannula, 2012; sundayana, herman, dahlan, & prahmana, 2017). mathematical anxiety determines more than mathematics that overcomes the manipulation of numbers and the ability to solve mathematical problems both in everyday life and in the academic world (gresham, 2010). mathematical anxiety is the adequacy of intelligence for intelligent people to overcome quantification, faced with mathematical problems. in his research, blazer (2011) challenged mathematics universally as a non-intellectual factor that mailto:rully.indra@mpmat.uad.ac.id prahmana, sutanti, wibawa, & diponegoro, mathematical anxiety among engineering … 180 inhibited mathematical achievement. mathematical anxiety raises negative attitudes towards subjects, and results in poor and reasonable academic performance, increasing student performance in the mathematics learning process (gresham, 2010). therefore, it is necessary to have a discussion that discusses mathematics. mathematics underlies the universal development of technology (stoet & geary, 2018). mathematical knowledge is directly related to the ability to do logic, analytic, systematic, critical, and creative thinking (hoover, mosvold, ball, & lai, 2016; widodo, istiqomah, leonard, nayazik, & prahmana, 2019). engineers have to study math during lectures to support their work on technology innovation. in fact, prospective engineers still have difficulty in learning mathematics (vitasari, herawan, wahab, othman, & sinnadurai, 2010). engineering students have low comprehension and negative attitudes toward mathematics (kargar, tarmizi, & bayat, 2010; vitasari et al., 2010). they tend to avoid mathematics since their beliefs cannot solve math problems (bates, latham, & kim, 2011; charalambous & philippou, 2010). students with mathematical difficulties will look confusing, helpless, shy, nervous, and feel weak in concentration (charalambous & philippou, 2010; cranfield, 2013; hersh & john-steiner, 2010). engineering students still have a problem in learning mathematics because of their beliefs that affect their physical and emotional condition. engineering students have an affiliation with mathematics, where mathematics is essential for engineering as a language for describing physical, chemical, and other formulations in terms of mathematical inquiry (vitasari et al., 2010). furthermore, erden & akgül (2010) stated that high mathematical anxiety correlated with poor mathematical performance proposed at the university. students need a high level of concentration compared to other subjects so that it is possible to create anxiety about mathematics among engineering students (vitasari et al., 2010). mathematics anxiety feelings arise from the consideration of having symptoms such as fear, loss of interest, lack of concentration, impatience, confusion, and tension (gresham, 2010). on the other hands, female students more anxious than male in learning mathematics (goetz, bieg, lüdtke, pekrun, & hall, 2013; taylor & fraser, 2013). therefore, engineering students need a high level of concentration and low mathematics anxiety to learn mathematics, and female students don't have both of them yet. in this paper, we present a survey to explore mathematical anxiety among engineering students. this survey aims to explore sources or factors related to mathematics anxiety among engineering students at a private university in yogyakarta, indonesia. furthermore, the differences in mathematics anxiety base on gender and majors were examined. this survey involves extracting quantitative data from voluntary engineering student questionnaire groups, grouping variables under the theme, gender, and describe several aspects of the engineering students' mathematics anxiety based on their majors. 2. method the respondents were 47 students, consisting of 29 males and 18 females. they were informed to fill in the questionnaires based on what they experienced and learned during the lecture. these undergraduate students are from four engineering department: informatics engineering department (ifd), industrial engineering department (ied), electrical engineering department (eed), and chemical engineering department (ced). the previous research on mathematics anxiety used to develop the mathematics anxiety questionnaire. this survey contains ninety-two items with four scales: strongly disagree (1), disagree (2), agree (3), and strongly agree (4). students have to answer questions based on their experiences, feelings, and thoughts about mathematical anxiety volume 8, no 2, september 2019, pp. 179-188 181 felt while studying on campus. reliability and validity tests have been carried out. the result of the reliability test is 0.940, more than 0.70 as recommended by raykov & marcoulides (2011), accessing construct validity was interpreted by inter-correlation items (drost, 2011). the instrument used to measure the mathematics anxiety of engineering students consisted of 92 items, developed from shields (2005), whyte & anthony (2012), and also zakariya (2018) instruments, as shown in table 1. table 1. the rubric of mathematics anxiety questionnaires aspect indicator item number total items home 1. parents and siblings give a low status to the students’ mathematical ability and judgment that mathematics is complicated 2. parents let the child stop trying when the child has a mathematical fracture 3. parents demand excessive math success in children. 42, 65, 67, 68, 69, 70, 71, 72, 73, 74, and 75. 11 society 1. self-efficacy (men are better than women in mathematics). 2. social reinforcement to hate mathematics. 3. social stereotype (language skills are more critical and socially acceptable than mathematical abilities). 11, 15, 24, 25, 26, 27, 28, 34, 36, 37, 39, 43, 48, 49, 51, 52, 53, 54, 59, 60, 63, 64, 66, 77, 78, 79, 81, and 82. 28 classroom 1. the classroom aspects whose talk about the traditional mathematics learning process and classroom culture 2. the experience of learning mathematics in classrooms 3. relationships between friends during learning 5, 8, 9, 14, 16, 17, 18, 19, 22, 31, 32, 33, 38, 44, 45, 46, 47, 55, 56, 62, 76, 80, 83, 84, 85, 86, 87, 88, 89, 90, 91, and 92. 32 personal 1. physical and behavioral symptoms 2. perception of difficulty 3. low motivation 1, 2, 3, 4, 6, 7, 10, 12, 13, 20, 21, 23, 29, 30, 35, 40, 41, 50, 57, 58, and 61. 21 the survey was conducted during the holiday period after students finished the final examination. the inspector consulted several lecturers in each department to select some students to fill the questionnaire. next, the inspector gives a questionnaire link to be filled by voluntary respondents, who assumed had no awareness in learning mathematics anxiety. the time required for respondents to complete the survey was less than 60 minutes. students must read and answer questions as guided by the inspector. afterward, they have to answer the poll based on their learning experience. 3. results and discussion table 2 presents the demographic data of respondents. the results showed differences found in mathematics anxiety between engineering students on aspects, gender expectations, and variations based on majors. data analysis uses statistics descriptive data analysis. prahmana, sutanti, wibawa, & diponegoro, mathematical anxiety among engineering … 182 table 2. the demographic data of respondents demographic information frequency percentage gender male female 29 18 61.7% 38.3% department eed ied ifd ced 12 17 11 7 25.5% 36.2% 23.4% 14.9% age 18-20 21-23 24 above 2 29 12 4.3% 65.9% 29.8% total 47 100% 3.1. the home aspects: the influence of parents and sibling in engineering students' mathematics anxiety the home aspects were explained such as improving math scores when students increase their study time at home, parents' attention to mathematics learning outcomes, parents and siblings assessment of mathematics learning outcomes, and parents and siblings judgment about mathematics. figure 1 shows that informatics engineering students get the highest while industrial engineering students get the lowest home aspects score in mathematics anxiety. it means that the home aspect has the weakest contribution to the factors affecting mathematics anxiety for informatics engineering students. figure 1. the influence of parents and sibling in engineering students' mathematics anxiety the result was supported by shields (2005) that parents who suffer from math anxiety can accidentally transfer it to their children. parents, especially mother, are a consistent example for their children because their children pay close attention to the attitude of the mother. the position of mathematics attitude that shown to children in the way mothers sees mathematics as a valuable and understandable lesson (makur, prahmana, & gunur, 2019). however, parents can inadvertently increase mathematical anxiety in their children by giving them reasons to stop trying when they are frustrated or upset because of 28 29 30 31 32 33 34 electrical engineering industrial engineering informatics engineering chemical engineering volume 8, no 2, september 2019, pp. 179-188 183 difficulties with math assignments (stolpa, sloan, daane, & giesen, 2004). therefore, parents who suffer from math anxiety can inadvertently transfer this anxiety to their children. 3.2. the society issues: self-efficacy, social reinforcement to hate mathematics, and social stereotypes the society issues consist of several aspects affecting the engineering students’ math anxiety. the first aspect is self-efficacy, which stated that boys are better than girls in mathematics. the next aspect is social reinforcement to hate mathematics. the last aspect is the social stereotype that language skills are more critical and socially acceptable than mathematical abilities. figure 2 showed that electrical engineering students get the highest and informatics engineering students to get the lowest society issues to score in mathematics anxiety questionnaire. it means that social problems contribute the weakest to the factors affecting mathematics anxiety for electrical engineering students. social factors such as mathematical myths can also induce or strengthen mathematics anxiety for some students, i.e., the myth that boys are better than girls in mathematics and that only a few people have a 'mathematical mind' can damage positive self-confidence (whyte & anthony, 2012). a study confirmed that failure in mathematics was socially acceptable participants were less embarrassed about the lack of mathematical skills compared to language skills (latterell, 2005). figure 2. the society issues score 3.3. the classroom aspects: the traditional mathematics learning process and relationships between friends during learning the classroom aspects discuss the traditional mathematics learning process and classroom culture, the experience of learning mathematics in classrooms, and the relationships between friends during learning. here, most engineering students agree that mathematics is boring. however, although they also have difficulty in learning mathematics, they still want to learn mathematics successfully. simple observation found that some the students feel boring because of lack of calculation activities, the students more interest in reading than count (vitasari et al., 2010). mathematics requires higher levels of concentration compared than other subjects (rattan, good, & dweck, 2012). figure 3 describes that electrical engineering students reach the top of the lowest classroom aspects to score in mathematics anxiety, which means that this factor does not give significant influence to them. 68 70 72 74 76 78 80 electrical engineering industrial engineering informatics engineering chemical engineering prahmana, sutanti, wibawa, & diponegoro, mathematical anxiety among engineering … 184 figure 3. the classroom aspects score personal characteristics and academic variables have a rare influence on mathematics anxiety (karimi & venkatesan, 2009). traditional teaching can contribute to mathematics anxiety and also class culture defined as the behaviors and norms that guide class interaction (whyte & anthony, 2012). traditional teaching means teacher center learning with direct instruction without discussion. the experience of learning mathematics in a structured and rigid classroom includes several opportunities to debate or discuss, focus on finding the right answers, offer limited encouragement to reflect on thinking, expect quick responses, and emphasize the test of time (shields, 2005). in such classrooms, the possibility of teacher’s behavior implicitly grows students' mathematical anxiety (mensah, okyere, & kuranchie, 2013). 3.4. the personal aspects: physical and behavioral symptoms, perception of difficulty, and low motivation the personal aspects consist of three issues, namely physical and behavioral symptoms, perception of difficulty, and low motivation. this aspect represented in 21 of 92 questions in the mathematics anxiety questionnaire. the problem started about the student condition during math class, such as my limbs trembled, sweated a lot, had difficulty breathing, my heartbeat fast, felt weak, and cold and hot contribute the significant score for engineering students mathematics anxiety. students who are nervous, bored, afraid, or believe that mathematics is not essential; tend to avoid learning mathematics (furner & berman, 2003), yet want to get a satisfactory grade in mathematics. overcoming this anxiety of the students for mathematics is the real challenge of every lecturer and also made a good mathematics instruction to solve them (mensah et al., 2013; tanujaya, prahmana, & mumu, 2017). figure 4 describes that electrical engineering students get the highest while informatics engineering students get the lowest of personal aspects to score in mathematics anxiety questionnaire. it means that the personal aspects contribute the weakest to the factors affecting mathematics anxiety for electrical engineering students. 80 82 84 86 88 90 92 94 electrical engineering industrial engineering informatics engineering chemical engineering volume 8, no 2, september 2019, pp. 179-188 185 figure 4. the personal aspects score 3.5. the differences effects of gender and engineering major towards mathematic anxiety the differences in gender towards engineering students’ mathematic anxiety were investigated. the results show that female engineering students more anxious than male engineering students as stated by karimi & venkatesan (2009). female students may perform the same level as the male students when they are given the right educational tools and have visible excelling in mathematics (else-quest, hyde, & linn, 2010). figure 5 shows that the male electrical engineering students get the highest and male informatics engineering students to get the lowest mathematics anxiety score in mathematics anxiety. figure 5. the differences effects of gender towards mathematic anxiety the differences effects of engineering major towards mathematics anxiety were examined. electrical engineering students get the highest score in 3 of 4 aspects that affecting engineering students’ mathematics anxiety. it means that these aspects contribute the lowest to the factors affecting mathematics anxiety for electrical engineering students as showed in figure 6. 46 47 48 49 50 51 52 53 54 electrical engineering industrial engineering informatics engineering chemical engineering 0 50 100 150 200 250 300 electrical engineering industrial engineering informatics engineering chemical engineering female male prahmana, sutanti, wibawa, & diponegoro, mathematical anxiety among engineering … 186 figure 6. the differences effects of engineering major towards mathematic anxiety 4. conclusion mathematics may cause learning anxiety among engineering students. mathematical anxiety among engineering students is manifested in four aspects: personal, classroom, community, and home aspects. the difference in scores on mathematics anxiety found that females were more anxious than male students. furthermore, informatics engineering has the highest level of mathematics anxiety compared to other department. therefore, investigations to reduce mathematics anxiety must be sought to improve student academic performance. it can help engineering students overcome their fear and improve of the quality of learning mathematics. for better and more comprehensive research, further discussion of a mathematics anxiety should be focused on other majors, educational levels, and diversity of sources. acknowledgements the authors would like to thank the director general of strengthening research and development, ministry of research technology and higher education of the republic of indonesia that supported and funded this research under the research grant namely penelitian dasar unggulan perguruan tinggi based on decree number 6/e/kpt/2019 and 7/e/kpt/2019. the researcher also thanks to universitas ahmad dahlan for giving the opportunity and facilities to complete this research. lastly, the authors thank all respondents and their lecturer for their participations in this research. references bates, a. b., latham, n., & kim, j. a. 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https://iopscience.iop.org/article/10.1088/1742-6596/1188/1/012087/meta https://iopscience.iop.org/article/10.1088/1742-6596/1188/1/012087/meta http://ijopr.com/index.php/ijopr/article/view/43 http://ijopr.com/index.php/ijopr/article/view/43 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 8, no. 2, september 2019 e–issn 2460-9285 https://doi.org/10.22460/infinity.v8i2.p209-218 209 developing of calculus teaching materials based on audiovisual akbar nasrum* 1 , herlina 2 1,2 universitas sembilanbelas november kolaka article info abstract article history: received august 8, 2019 revised sept 21, 2019 accepted sept 26, 2019 millennials community right now prefer video media as a learning resource rather than reading textbooks. to understand the contents of books, we need to have a reasonably high literacy ability. unlike the case with learning videos, explanations accompanied by images in the video can help someone to understand the material in that media. the first goal of this study was to make audiovisual teaching materials that could serve as a supplementary textbook teaching materials. the second goal was to test the effectiveness of teaching materials that have been created. the method used was the development method using the addie model (analyze, design, development, implementation, and evaluation). the process of developing teaching materials began with creating multimedia learning, recording stages, editing stages, and completion stages. material experts and media experts then validated the teaching materials that had been produced and tried out on students. the results of the try out documents to the students showed that there were significant changes both in terms of motivation, enthusiasm for learning, interaction in the classroom, and from student learning outcomes. these results made the student's response to the use of teaching materials excellent. this audiovisual teaching material was worthy and effectively of being used as a learning media, both as a supplementary or primary source. keywords: audiovisual teaching materials, learning videos copyright © 2019 ikip siliwangi. all rights reserved. corresponding author: akbar nasrum, department of mathematics education, universitas sembilanbelas november kolaka, jl. pemuda, kolaka, southeast sulawesi 93561, indonesia. email: akbar.nasrum@gmail.com how to cite: nasrum, a., & herlina, h. (2019). developing of calculus teaching materials based on audiovisual. infinity, 8(2), 209-218. 1. introduction calculus is a compulsory subject given to students at the beginning of the semester. besides being compulsory, this course is essential because the knowledge gained here is the basis for programming advanced calculus courses, the real analysis i, real analysis ii, and differential equations. even though the material in calculus is primary material, this course is a scourge of problems for students so that it has an impact on less than optimal learning outcomes (shodikin, 2017). in order to obtain maximum learning outcomes, the learning process should be supported by adequate learning facilities and resources, especially in terms of teaching materials. however, the importance of calculus material is not directly proportional to the mailto:akbar.nasrum@gmail.com nasrum & herlina, developing of calculus teaching materials … 210 availability of teaching materials such as calculus books at the campus library. students interest in buying books also lacks because the price of this book is quite high. the difficulty of obtaining calculus teaching materials makes students less than optimal in learning. they only rely on the material obtained during the lecture, even though the density of calculus material and the limited time of lectures make this material sometimes incomplete. focusing on the completeness of learning outcomes will cause the learning material to lag. conversely, pursuing the completion of the material in one semester can lead to incomplete learning outcomes. these two variables are essential to note because they can cause failures in courses that require calculus basics. on this basis, we took the initiative to develop calculus teaching materials from textbooks into audiovisual teaching materials. this teaching material can function as a complement or even replace the role of textbooks as the primary source of teaching materials. the process of making teaching materials involves some software, one of which is geogebra software. the representation of the concepts of functions, limits, derivatives, and integrals in calculus is increasingly easily understood if geometrically explained using geogebra (caligaris, schivo, & romiti, 2015). besides takači, stankov, & milanovic (2015) said that using geogebra, student learning achievement in checking and drawing function graphics is better than without using it. teaching materials in the form of videos can be stored on a mobile device that can be carried anywhere (moving learning) making it easier for students to study anywhere and anytime (bano, zowghi, kearney, schuck, & aubusson, 2018). besides, they can construct knowledge from independent learning activities carried out using videos so that the process of developing thinking skills for students occurs. ownership of mobile devices by students supports the creation of outside-class learning using mobile learning (crompton & burke, 2018). the use of video learning in mobile learning is a promising learning strategy, relevant and can improve the quality of education (forbes et al., 2016). however, it is not an easy thing to make exciting learning videos, so it is still rarely used. it takes its creativity to make teaching videos more exciting and varied (christ, arya, & chiu, 2017). teaching materials in the form of videos can also support youtube channels as learning tools in education by uploading videos there (orús et al., 2016). in the era of digital, students tend to prefer to access youtube to search literature videos or educational videos rather than open textbooks. it is not difficult to find good educational videos. surfers can use visitor ratings as an indicator to look for good educational videos (shoufan, 2019). with this teaching video, students are expected to be able to understand the material more quickly because of the presentation of material in teaching materials in the form of visual and sound (audio). according to purwanti (2015), video media tends to be easier to remember and understand because it uses two senses, namely the sense of sight and hearing. unlike the case with a textbook that requires students to read and try to understand the material itself. apart from that, the explanation of still images in textbooks is explained visually moving on audiovisual teaching materials so that they are easier to understand. the explanation in audiovisual teaching materials is designed to resemble explanations in the classroom. in essence, this teaching material is a combination of textbooks and classroom learning. so, the formulation of the problem in this study, i.e., "are the audiovisual teaching materials that have been made feasible and effective to be used as learning media? volume 8, no 2, september 2019, pp. 209-218 211 2. method this research is development research using the addie model (nadiyah & faaizah, 2015). as the name implies, this model consists of several processes, namely: analyze, design, development, implementation, and evaluation. in the analysis phase, researchers must know the student's ability to learn, student attitudes, the conditions of the facilities and infrastructures used for learning, and others. all factors that cause disparities in learning outcomes must be analyzed in order to design instructional media that are suited to the conditions and abilities of students. in the design phase, information that has been obtained from the analysis phase is used to design learning prototypes. how to choose the right media, design a user interface, design a graphic design or display, so users are not bored, and learning objectives can be achieved. the next stage of development is the stage of teaching material production by integrating all technologies that will be used to achieve learning objectives. in this stage, consultation with material experts and learning design experts is needed. the next stage is implementation. in this stage, prototypes of teaching materials that have been produced and examined by experts are then tested on students and ensuring that students can obtain knowledge and skills from the media used. finally, the evaluation stage aims to find out the improvement of student competencies, students' attitudes towards learning activities, and the benefits of the instructors with this learning media. this process produces teaching materials produced in the form of learning videos. the research design used to test the effectiveness of this teaching material was one group pre-test post-test design. the effectiveness of instructional materials was tested by taking 48 students of the 4th semester of mathematics education at the university of sembilanbelas november kolaka as research subjects. forty-eight of these students are all 2017 mathematics education students. sources of data in this study are learning media experts, material experts, and students. data were collected using several instruments including in the form of material evaluation instruments by material experts, evaluation instruments for instructional media experts, learning outcome test instruments consisting of pre-tests and post-tests and questionnaires for student responses to the use of instructional materials. the development of this teaching materials is in dire need of advice from material experts and media experts. in its development, researchers collaborated with material experts and media experts so that the resulting teaching materials could be better. the content focuses on the primary material before entering calculus material, i.e., the introduction of functions. the evaluation results from media experts and material experts are input to improve the quality of teaching materials. furthermore, to see the effectiveness of these teaching materials, the scores of students' pre and post-test were compared. besides, the magnitude of the increase can be measured using n-gain values (marx & cummings, 2007). the last, the researcher gave a questionnaire to students was to see how well the students responded to the use of teaching materials. 3. results and discussion explanation of the results of the following research is two parts. first, it will explain the results of developing teaching materials and then explain the results of the effectiveness of teaching materials. nasrum & herlina, developing of calculus teaching materials … 212 table 1. list of learning video links material name link download definition of function https://youtu.be/5acqu7z87qc linear function i https://youtu.be/e8ykeetjyak linear function ii https://youtu.be/hbxr_jao5z4 quadratic function https://youtu.be/jilm1uhom88 shipting graph https://youtu.be/_aujkivv64c absolute function https://youtu.be/tew7wge6fbk table 2. suggestions for media repair by media and material experts no. aspect recommendation for improvement 1 2 3 4 design sounds and pictures material quality sounds and pictures add learning achievements to the media the image quality is at least 720 pixels so that the image quality does not break when enlarged the presentation time is too fast there is a mismatch between the speaker's sound and the cursor motion on some videos 3.1. results there are several results obtained after the research is carried out. first, the results obtained from the addie process, i.e., several learning videos that can be download from the link in the table 1. the results were obtained through several evaluation processes, both evaluations from material experts and media experts. there are some suggestions for improvement from media experts and material experts in the first stage of evaluation summarized in table 2. these suggestions provide input for researchers to correct some of the deficiencies that exist in the media. after revision, a validation sheet is again given to the material expert and media expert for the final evaluation. the results can be seen in table 3 and table 4. teaching materials that have been made through a consultation process from two expert fields are then tested on a limited basis. two students were taken from the category of a high, medium, and low learning outcomes as a small sample. after media testing on these students, almost no significant problems were found. only the problem of slow understanding of students with low learning outcomes. however, the problem can be solved in a class by re-explaining material that is not understood. table 3. score of the feasibility of learning videos by media experts no. aspect score media expert i media expert ii 1 2 3 design sounds and pictures software engineering 4.25 4.60 4.00 4.00 4.40 4.00 mean 4.28 4.13 https://youtu.be/5acqu7z87qc https://youtu.be/e8ykeetjyak https://youtu.be/hbxr_jao5z4 https://youtu.be/jilm1uhom88 https://youtu.be/_aujkivv64c https://youtu.be/tew7wge6fbk volume 8, no 2, september 2019, pp. 209-218 213 table 4. the score of learning video eligibility by material experts no. aspect score material expert i material expert ii 1 2 3 4 material relevance with syllabus material quality language aspect (sound) functions and benefits 4.67 4.00 4.00 4.00 4.67 4.40 4.00 4.33 mean 4.17 4.35 after limited trials have been conducted, audiovisual teaching materials are ready to be implemented in large classes. forty-eight registered students were used as research subjects but only forty-four people who actively participated in lectures. the final results of the application of media in large classes can be seen in figure 1. figure 1. the average pre-test, post-test, and n-gain besides, to see student responses to the use of instructional video media, a closed questionnaire was given. the results of questionnaire data processing can be seen in the table 5. table 5. student responses to the use of media no indicator category high medium low 1 feeling happy 68.18% 31.82% 0.00% 2 ease of understanding material 78.79% 17.42% 3.79% 3 motivation to follow lessons 68.18% 31.82% 0.00% 4 active in the learning process 63.64% 18.18% 18.18% 5 influence on results 45.45% 50.00% 4.55% 6 interest 97.73% 2.27% 0.00% 0.00 20.00 40.00 60.00 80.00 pre-test post-test n-gain mean 24.37 66.48 0.57 average nasrum & herlina, developing of calculus teaching materials … 214 3.2. discussion 3.2.1. analyze the primary ability of student calculus that researchers pay attention from year to year is the basis for making audiovisual teaching materials. advanced calculus courses, the real analysis i, real analysis ii, and differential equations cannot be taught without this essential knowledge. repeating that fundamental concept in the classroom certainly takes much time so that an appropriate method is needed so that the lecture process is not interrupted. video learning is one of the best choices in various methods. by using video learning media, teaching and learning process can run more effectively. this is consistent with the results of research from nurdin et al. (2019) which says that learning videos were effective and have a positive effect on improving students' understanding of mathematical concepts. video media will also help teachers to make it easier to deliver material and create learning situations that are not monotonous and will help make it easier for students to understand the material (kurniawan, kuswandi, & husna, 2018). because the abilities in class vary, videos are designed in such a way that even people who are unfamiliar with mathematics can easily understand the material presented. 3.2.2. design these design aspects include video design, video format, and video content. these three aspects are adjusted to the needs based on the results at the analysis stage. in terms of video design and video format, it involves some software, i.e., powerpoint, geogebra, camtasia recorder 8.0, and camtasia studio 8.4. the process of display design and animation is made using powerpoint. geogebra software is a complement in explaining calculus material, camtasia recorder is used to record videos, and camtasia studio is used to edit videos and convert recordings to mp4 videos. examples of design and video editing stages can be seen in figure 2. figure 2. design and video editing processes volume 8, no 2, september 2019, pp. 209-218 215 the geogebra seen in the video media in figure 2 is used to facilitate the explanation of calculus materials, especially those related to functional materials. the ease of understanding the material explained by using geogebra is a unique attraction for students. this is consistent with the study of trung (2014) which shows that about 79% of students from the total population studied often use geogebra software independently without being instructed by the teacher to recheck their knowledge. according to fitriyani, (2012), geogebra can also increase student activity and learning outcomes. the use of geogebra is arranging so that it does not interfere with the appearance in the video. after going through the editing process, it finally arrived at the final stage. the final stage produces mp4 videos with 720-pixel quality and uploaded to youtube. this video was set so that search engines can not find it on youtube. the reason was that learning videos were distributed to students according to the schedule set by the lecturer. learning videos in this study were necessary materials that must be well understood by students before entering the core material from calculus. we are still developing similar teaching videos for further research. 3.2.3. development the process of developing teaching materials involves several experts, i.e., two material experts and two instructional media experts. as the first learning media expert, mr. kadaruddin, s.pd., m.pd was chosen who was an expert in the field of learning media while the second media expert was mr. sufri mashuri, s.pd., m.pd. he is a calculus lecturer in the mathematics education study program and also experienced in learning media, so he was chosen as a material expert and media expert. other lecturers who are interested in becoming material experts are mr. ansar, s.si., m.sc who is a calculus lecturer in the faculty of engineering university of sembilanbelas november kolaka. the evaluation values of the three experts were input into developing learning videos. there are some suggestions for improvement from media experts and material experts at the first stage of evaluation summarized in table 2. these suggestions are input for researchers to correct some of the shortcomings in the media. after revision, a validation sheet is again given to the material expert and media expert for the final evaluation. the results can be seen in table 3 and table 4. based on table 3, the average value of each aspect both from the first expert and the second expert is not less than four (the scale of one to five). that is, in terms of the feasibility of the video media, it is declared appropriate to be used as a learning media. while in terms of material, the results of the evaluation can be seen in table 4. based on table 4, the average value of each aspect assessed is almost the same as the assessment of media experts. from the evaluation of two material experts, the average score given by each aspect was not less than 4, which meant that the learning videos from the material side were very valid (farman & yusryanto, 2018). thus, because the video has been validated and declared feasible, the learning video can already be used. 3.2.4. implementation the process of implementing media in large class was carried out after the initial test was given. video media is given to students to watch and learn independently. when the lecture time arrives, the teacher needs to ask which part of the video was difficult to understand. sometimes from some material given, only a small portion is poorly understood, so it needs a few minutes of explanation. the learning process in the nasrum & herlina, developing of calculus teaching materials … 216 classroom becomes more active because students are prepared with material that has been studied earlier. another advantage does not require much time to explain the material taught on that day so that the use of teaching time is more efficient. the lecture process like this was done for four weeks, and the final results can be seen in figure 1. comparison of the average results of the pre and post-test was very significant. these results indicate that the use of audiovisual media can influence on improving learning outcomes. it supported with research conducted by asmara (2015) which says that student learning outcomes using audiovisual learning media are better than not using audiovisual. although not measured in detail, from the way to answer the questions given, it appears that understanding the concept of material after the use of the media for the better. it supported by research conducted by utami, (2013) and nurdin et al. (2019) who say that learning by using audiovisual media can improve understanding of material concepts for students. the quality of learning outcomes can be seen from the magnitude of the n-gain value. the value of 0.57 was included in the category of "moderate" improvement. (hake, 1998). 3.2.5. evaluation from the whole series of process of developing teaching materials, starting from designing to the implementation stage, it has been through various types of evaluation stages, starting from evaluating media experts and material experts to evaluating the use of video media itself. finally, an open questionnaire was given to students to see how much they responded to the use of this video media. based on table 5, there are six indicators assessed. first, from the results of research on student responses, 68.18% of students were happy to learn mathematics using audiovisual media, and 31.82% were mediocre. 78.79% of students can quickly receive lessons, 17.42% are mediocre, and 3.79% of students still do not understand sometimes. 63.64% of students became more active in receiving lessons, 18.18% were less active, and the remaining 18.18% were inactive. 68.18% of students are very motivated to follow the lessons and 31.82% are mediocre. the influence of the use of media on learning outcomes can also be seen in table 5. there are about 45.45% of students whose learning outcomes are getting better, 50% of students who have moderate learning outcomes and 4.55% who have still poor learning outcomes. although the data above varies, for the sixth indicator 97.73% of students expressed interest in following the lesson if it were implemented learning using audiovisual learning media like this and only 2.27% or one less interested person. the result from indicator six shows the positive response given by students towards the use of this media. 4. conclusion from the results of the study, several conclusions can be drawn i.e., we have succeeded in making audiovisual-based learning media that have been validated by media experts and material experts in good categories so that the media can be used as learning material both for primary sources and as a complement to textbooks. the use of audiovisual media can be more beneficial in terms of time management because it does not take much time to explain the material in the video. in addition to being efficient, the use of media has an effect on activeness in the classroom and is also very effectively used in improving student learning outcomes. volume 8, no 2, september 2019, pp. 209-218 217 acknowledgements we would like to thank university of sembilanbelas november kolaka that funded this research through the scheme internal "penelitian dosen pemula" 2018. references asmara, a. p. 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(2019). effect of learning using mathematica software toward mathematical abstraction ability, motivation, and independence of students in analytic geometry. infinity, 8(2), 219-228. 1. introduction rapid development of technology for the past two decades has greatly influenced mathematic learning system. higher order thinking skills ability a person is a requirement the main one is able to compete in this 21 st century and mathematics that has an important role in the development of high-order thinking skills. so that technological and mathematical collaboration is needed in answering this challenge. mathematics pre-teacher students are part of a system which is directly influenced by the development of mailto:sutrisnojr@upgris.ac.id murtianto, sutrisno, nizaruddin, & muhtarom, effect of learning using mathematica software … 220 technology. on the other hand the emphasis was on learning mathematics must be in context since learning should be involve the mental processes of students, should be fun, encourage students, and give students the opportunity to construct their learning experience, so that learning become meaningful (nizaruddin, muhtarom & sugiyanti, 2017). furthermore, motivation provides a very important role (rachvelishvili, 2017), in addition to the use of technology in learning mathematics. as it was delivered some researchers have conducted studies that emphasis the view that the success of students’ problem-solving is an important factor in understanding the beliefs of mathematics; students’ beliefs toward solving the problem also depend on the motivation of the belief in mathematic (muhtarom, juniati & siswono, 2017a; 2017b). one of the technology advances in mathematics learning system is the choice variances of mathematics software. the variances are divided into two important parts; dynamic geometry system and computer algebraic system (malinova, 2010). among the mathematical software are maple, mathematica, geometer sketchpad, matlab, and geogebra. a great number of software that can be used by mathematics pre-service teachers in learning requires them to skilfully utilize software they plan to choose (listyani, 2006). taking account to this phenomenon, it is necessary that the students of mathematics education program are provided with computer software utilization skill in order to meet the demands of the workplace. one of mathematic software that can be applied by the students is mathematica software. mathematica is symbol visualization and algebraic manipulation based computer software that was developed by stephen wolfram. it is one of today’s most up-to-date software and this is confirmed by several previous studies by gocheva (2009), malinova (2010) and vosler (2009) which reveal that mathematica software is effective in mathematics learning at university level which investigates concept and finds its connection to other mathematical concepts or its implementation with technology. a more specific research was carried out by kapustina, popyrin, & savina (2015) indicating that visualization concepts of analytic geometry would be easier when presented using this software. the importance of mathematica software in analytic geometry learning is undeniable. this is obvious from the previous studies, two of which were the research sunandar, murtianto & sutrisno (2015) on the development of analytic geometry teaching materials using mathematica software in developing students’ representation, and the research on improving achievement and differential calculus learning independence of mathematics education program students of universitas negeri yogyakarta using mathematica software (listyani, 2006). a number of studies that have been conducted related to software-assisted mathematics learning indicate that the era of modern mathematics learning in the class continues to grow rapidly. the use of software in mathematics learning in classroom should consider the portion and the conformity level to learning objectives. this is so for it can put an effect on the level of abstraction, motivation, and learning independence of students. this thinkable concept can later be used in more complicated and complex level of thinking. the states can raise first abstraction when an individual focuses on the characteristics of objects observed and then label them through a classification process into several groups on the basis of certain categories. motivation in mathematics education is important for it provides energy in learning which can be adapted to bridge (hannula, 2006). meanwhile, motivation is a natural characteristic of a person that can be explored in line with the needs (pintrich, 2003). indeed, motivation cannot be considered directly, but it can be observed from the manifestation of behavior, attitude, and activity of an individual. the general problem is that the average research that has been done previously only emphasizes the volume 8, no 2, september 2019, pp. 219-228 221 cognitive aspects of the dependent variable. research that takes the dependent variable motivation, independence and abstraction ability is usually also carried out separately and not simultaneously. then the purpose of this study is to find out the impact of learning using mathematica on motivation, abstraction ability and independence simultaneously. thus, mathematics learning using mathematica software demands certain motivation to change behavior and attitude through a process of learning, and this is expected to put an effect on the students’ independence. 2. method 2.1. general background of research this research applied a quantitative approach with a quasi-experimental, because in this research it is not possible for researchers all relevant variables. budiyono (2003) stated that research in education is included in quasi-experimental research because educational research often uses intact groups such as classes as experimental groups and classes as groups comparison. this is so for it is impossible for the researcher to control all the relevant variables (budiyono, 2003). some research experts suggest that researches in the field of education are considered quasi-experimental researches since educational researches often make use of intact groups such as classes as experimental class was treated using mathematica software and control class was treated without using them (conventional learning). in this case, randomization is not applied in determining subject assigned to experimental class and control class. the variables in this research were divided into independent and dependent variables. the independent variables were learning media, while the dependent variables were students’ mathematical abstraction, motivation, and independence. multivariate analysis technique, particularly hotelling's t 2 test statistics, was applied for analyzing data since this research only compared two classes (control class and experimental class) and involved three dependent variables, including students’ mathematical abstraction, learning motivation and learning independence. 2.2. sample of research the population of this research is a group of students attending analytic geometry course on third semester that consist of six class in mathematics education department of universitas pgri semarang in the academic year 2018/2019. the sampling of the research using cluster random sampling. the samples of this research consisted of two distinct classes, with one class as the control class and the other is the experimental class. 2.3. instrument and procedures data collection techniques is used in this research are tests and questionnaires. the test technique is used to measure the ability of mathematical abstraction, the questionnaire is used to measure the students' motivation and student’s independence. the mathematical abstraction ability test is used in the form of description consists of two questions, while the questionnaire motivation and student’s independence in the form of a closed questionnaire with four answer options (strongly agree, agree, disagree, and strongly disagree) consisting of 30 items of statement. all such instruments was used to obtain preliminary and final ability data. the student's preliminary ability data was used for the balance test (i.e. univariate normality test, multivariate normality test, homogeneity of variance test, homogeneity of covariance matrices test, and hotelling’s t 2 test), while the student's final ability data was used as the test of the research hypothesis, as in the balance murtianto, sutrisno, nizaruddin, & muhtarom, effect of learning using mathematica software … 222 test. the research was conducted from august to december 2018, while the preliminary ability data was collected prior to the research. 2.4. data analysis multivariate analysis technique, particularly hotelling's t 2 test statistics, was applied for analyzing data since this research only compared two classes (control class and experimental class) and involved three dependent variables, including students’ mathematical abstraction, learning motivation and learning independence. this data analysis technique was used twice, i.e. in balance test for preliminary research data and in hypothesis test for final research data. balance test was intended to determine that both control and experimental classes were in balance before receiving any treatments. this test was carried out to ensure that any changes after treatment provided were resulted from the treatment. before conducting this test statistics, it was necessary to perform prerequisite tests, including multivariate normality test and covariance matrix homogeneity test. mardia test was used to test the data normality, while box’s m was used to test the covariance matrix homogeneity (rencher, 2002). 3. results and discussion 3.1. results preliminary data of abilities in this research were data of students’ mathematical abstraction ability, motivation and independency in learning analytic geometry subject before experiments were conducted. data of mathematical abstraction ability were obtained using written test, while data of learning motivation and independence were obtained using questionnaires. the test was carried out using multivariate technique, particularly test statistics of hotelling’s t 2 . univariate normality test of population obtained in reference to the results of analysis, it was found that both samples constructed test statistics of d ≤ dα and therefore not rejected h0. this was also supported by the pvalue ≥ α = 0.05 for all samples. thus, and the significance level of 5% for both samples was derived from univariate normally-distributed populations. furthermore multivariate normality test of population have been showed that both samples constructed test statistics of b1,p ≤ b1,p,1-α,n and b2,p,α/2,n ≤ b2,p ≤ b2,p,1-(α/2),n. that b1,p is the slope coefficient if it is less than b1,p,1-α,n then it is said to be symmetrical distribution, b2,p is the coefficient of shaking if it is between b2,p,α/2,n and b2,p,1-(α/2),n then the distribution is normal (mesokurtic). this was supported by p-value ≥ α = 0.05 for all samples and therefore not rejected h0. therefore, the significance levels of 5% of both samples were obtained from multivariate normally-distributed populations. homogeneity test of population variance demonstrated that all dependent variables appeared to construct test statistics of and therefore not rejected h0. this was supported by p-value ≥ α = 0.05 for all variables. hence, with the significance levels of 5%, both populations showed homogenous variances for each dependent variable. moreover homogeneity test of population covariance matrices indicated box’s m = 5.359. the value could eventually be interpreted using critical value table of box’s m test in one condition that every cell in factorial design had equal sample size. however, the condition was not fulfilled in this research, and hence box’s m value could not be directly interpreted. for the purpose of interpretation, f approach was employed. for f ≤ fα and therefore not rejected h0. this was supported by p-value ≥ α = 0.05. in conclusion, with 5% significance level, both populations showed homogenous covariance matrices. volume 8, no 2, september 2019, pp. 219-228 223 on the basis of multivariate test using spss, pillai’s trace test resulted in f = 0.214 with p = 0.886; wilk’s lambda test resulted in f = 0.214 with p = 0.886; hotelling’s trace test constructed f = 0.214 with p = 0.886; and roy’s largest root test produced f = 0.214 with p = 0.886. all the tests resulted in p ≥ α = 0.05 and therefore not rejected h0. this research focused more on hotelling’s t 2 test. the results of analysis revealed that statistical test of t 2 ≤ t 2 α was constructed (t 2 = 0.670 and t 2 α = 6.552). statistical test of f ≤ fα was also derived (f = 0.214 and fα = 2.816). this was also supported by p-value ≥ α = 0.05 and therefore not rejected h0. hence, with 5% significance level, both populations had equal and balanced early abilities. all parts that had changed after receiving treatments in experimental class were influenced by the treatments provided. table 1. univariate normality test of population data source dependent variable n d dα p-value result control class mathematical abstraction 26 0.112 0.171 0.200 * not rejected h0 motivation 26 0.101 0.171 0.200 * not rejected h0 independence 26 0.110 0.171 0.200 * not rejected h0 experimental class mathematical abstraction 22 0.089 0.183 0.200 * not rejected h0 motivation 22 0.127 0.183 0.200 * not rejected h0 independence 22 0.074 0.183 0.200 * not rejected h0 research data were data of students’ mathematical abstraction ability, motivation, and learning independence which they obtained after experiment. the data were demon and served as dependent variables to test research hypothesis. the research hypothesis test was carried out using multivariate technique, particularly hotellings t 2 test statistics. the followings are the statistical discussions of the test analysis results. the results of analysis demonstrated at table 1 showed that both samples constructed test statistics of d ≤ dα and therefore not rejected h0. this was supported by pvalue ≥ α = 0.05 for all samples. hence, with the significance level of 5%, both samples were obtained from univariate normally-distributed populations. table 2. multivariat normality test of population of research data data source n test statistics bα p-value result control class 26 b1,p 0.6769 3.780 0.9830 not rejected h0 b2,p 12.0565 lower = 11.440 upper = 17.420 0.1706 experimental class 22 b1,p 1.1482 4.623 0.9374 not rejected h0 b2,p 11.5547 lower = 11.220 upper = 17.280 0.1402 table 2 clearly as showed that both samples appeared to construct test statistics of b1,p ≤ b1,p,1-α,n and b2,p,α/2,n ≤ b2,p ≤ b2,p,1-(α/2),n,. this was supported by p-value ≥ α = 0.05 for murtianto, sutrisno, nizaruddin, & muhtarom, effect of learning using mathematica software … 224 all samples and therefore not rejected h0. hence, with the significance level of 5%, both samples were obtained from multivariate normally-distributed populations. table 3. homogeneity test of population variance of research data dependent variable data source si 2 f fα p-value result mathematical abstraction control class 64.135 1.0083 lower = 0.4378 upper = 2.3558 0.9942 not rejected h0 experimental class 63.610 motivation control class 63.335 1.0235 lower = 0.4245 upper = 2.2840 0.9465 not rejected h0 experimental class 64.824 independence control class 65.433 1.0245 lower = 0.4378 upper = 2.3558 0.9642 not rejected h0 experimental class 63.870 table 3 indicated that all dependent variables appeared to construct test statistics of , and therefore not rejected h0. this was also supported by p-value ≥ α = 0.05 for all variables. hence, with the significance level of 5%, both populations constructed homogenous variances for each dependent variable. table 4 clearly as showed that the revealed box’s m = 3.160. the value could substantively be interpreted with the assistance of critical value table of box’s m test in one condition that each cell in factorial design had equal sample size. however, the condition was not met in this research, and therefore box’s m value could not be interpreted directly. for the purpose of interpretation, f approach was applied. table 4 indicated that all dependent variables appeared to construct test statistics of f ≤ fα and therefore not rejected h0. this is proven by p-value ≥ α = 0.05. hence with the significance level of 5%, both populations had homogenous covariance matrices. table 4. homogeneity test of population covariance matrices of research data data source si box’s m f fα pvalue result control class 64,135 6,895 11, 532 6,895 63, 335 7,188 11, 532 7,188 65, 434              3.160 0.489 2.101 0.817 not rejected h0 experimental class 63, 610 25, 325 3, 541 25, 325 64,825 16, 589 3, 541 16, 589 63,870            volume 8, no 2, september 2019, pp. 219-228 225 table 5. summary of average research data dependent variable class total average control experimental mathematics abstraction (y1) 63.15 77.09 69.54 motivation (y2) 79.85 89.41 84.23 independence (y3) 76.08 85.18 80.25 table 6. summary of multivariate t 2 test of research data source of variance sscp matrices t 2 t 2 α f fα pvalue result treatments 2314.714 1588.344 1512.171 1588.244 1089.776 1037.579 1512.171 1037.579 987.881           h 91.346 6.552 28.538 2.816 0.000 rejected h0 residual, error 2939.203 704.203 362.671 704.203 2944.703 168.671 362.671 168.671 2977.119             e total 5253.917 884.141 1149.500 884.141 4034.479 1206.250 1149.500 1206.250 3965.000           t on the basis of multivariate test through spss, pillai’s trace test resulted in f = 28.538 with p = 0.000; wilk’s lambda test resulted in f = 28.538 with p = 0.000; hotelling’s trace produced f = 28.538 with p = 0,000; and roy’s largest root test produced f = 28.538 with p = 0.000. all tests constructed p < α = 0.05, and hence, h0 was rejected. this research focused more on hotelling’s t 2 test statistics. the summary of analysis is presented in table 6. in reference to results of analysis, test statistics of t 2 > t 2 α was constructed (t 2 = 91.346 and t 2 α = 6,552). this was supported by p-value < α = 0.05. therefore, with significance level of 5%, h0 was rejected. this indicated different effects of conventional learning and learning using mathematica software on students’ mathematical abstraction, motivation, and independence in learning analytic geometry with α = 0.05. in order to find out the differences, further test was carried out using univariate t test on each dependent variable and the summary of analysis is presented in table 7. table 7. summary of univariate t test of research data dependent variable t df αt f α f p-value result mathematical abstraction (y1) 6.019 46 lower = -2.013 upper = 2.013 36.226 4.052 0.000 rejected h0 motivation (y2) 4.126 46 lower = -2.013 upper = 2.013 17.024 4.052 0.000 rejected h0 independence (y3) 3.977 46 lower = -2.013 upper = 2.013 15.264 4.052 0.000 rejected h0 murtianto, sutrisno, nizaruddin, & muhtarom, effect of learning using mathematica software … 226 based on the results of further test on each dependent variable, test statistics of t < t1-(α/2) was constructed, and this resulted in .dkt in addition, test statistics of f > fα was obtained, and this constructed .dkf  this was also proven by p-value < α = 0.05. in conclusion, h0 was rejected in each dependent variable with the significance level of 5%. to derive conclusion related to the different effects, table 5 needs to be observed, particularly on the average of compared cells. with the significance level of 5%, we can conclude that: 1) learning using mathematica software ( was more effective in improving students’ mathematical abstraction than conventional learning ( was in analytic geometry subject; 2) learning using mathematica software ( was more effective in improving students’ motivation on learning than conventional learning ( was in analytic geometry subject; and 3) learning using mathematica software ( was more effective in improving students’ independence than conventional learning ( was in analytic geometry subject. 3.2. discussion thinking process is an activity occurring in human’s brain (muhtarom, murtianto & sutrisno, 2017). the use of software in learning mathematics in classroom has to be related to portion and conformity level with learning objections. this is for the use of software can influence students’ mathematical abstraction, motivation and independence. one of software well-known for mathematics learning, particularly in analytic geometry subject, is mathematica. no one can deny the benefits of this software. mathematica software is one of today’s latest software and this statement is supported by various researches carried out by gocheva (2009) and malinova (2010). malinova (2010) stated that mathematica software is highly effective for learning mathematics at the level of university which examines concept and the relation with other mathematical concepts or implementations with technology. beside that cognitive regulation variable has contributed a greater influence on cognitive variable, than that of cognitive knowledge variable (kapustina et al., 2015; pantiwati & husamah, 2017), indicating that visualization concepts of analytic geometry would be easier when presented using this software. with the use of mathematical software that displays a variety of visualizations and forms of modeling real geometry it will automatically increase student motivation in learning mathematics. with good learning motivation this will have an impact on student independence. simultaneously that mathematical software has a positive impact on mathematical abstraction abilities, motivation and independence of students' mathematics learning. abstraction ability is defined as a process of depicting a particular situation into a thinkable concept through a process of construction. the thinkable concept can later be used in more complicated and complex level of thinking. motivation in mathematics education is important for it provides energy in learning which can be adapted to bridge. motivation related to anxiety and need for achievement (rachvelishvili, 2017), which reflects the manifestation of the behavior, attitudes, and activities of an individual. thus, mathematics learning using mathematica software requires certain motivation to change behavior and attitude through a process of learning, and this is expected to put an effect on the students’ independence. according to listyani (2006), a great number of software that can be used by mathematics pre-service teachers in learning requires them to skillfully utilize software they plan to choose. mathematical software makes it easy to visualize analytic geometry concepts, with varied visualizations produced by mathematical software that will familiarize students in the process of mathematical abstraction. hence, learning volume 8, no 2, september 2019, pp. 219-228 227 analytic geometry using mathematica software is more effective in improving students’ mathematical abstraction ability, motivation, and learning independence than conventional learning. 4. conclusion learning using mathematica software puts an effect on better mathematic abstraction of students compared to conventional learning in analytic geometry subject, learning using mathematica software gives more motivation to students for studying compared to conventional learning in analytic geometry subject and learning using mathematica software is more effective in improving students’s learning independence compared to conventional learning in analytic geometry subject. references budiyono (2003). educational research methodology. surakarta: sebelas maret university press. gocheva (2009). introduction into system mathematica. bulgaria: express gabrovo. hannula, m. s. (2006). motivation in mathematics: goals reflected in emotions. educational studies in mathematics, 63(2), 165-178. kapustina, t. v., popyrin, a. v., & savina, l. n. (2015). computer support of interdisciplinary communication of analytic geometry and algebra. international electronic journal of mathematics education, 10(3), 177-187. listyani, e. (2006). efforts to increase achievement and independence learning differential calculus with mathematica software on mathematics study program students fmipa uny. yogyakarta: fmipa uny. malinova, a. (2010). teaching university-level mathematics using mathematica. bulgaria: plovdiv. muhtarom, m., juniati, d., & siswono, t. y. e. (2017a). exploring beliefs in a problemsolving process of prospective teachers’ with high mathematical ability. global journal of engineering education, 19(2), 130-136. muhtarom, m., juniati, d., & siswono, t. y. (2017b). consistency and inconsistency of prospective teachers’ beliefs in mathematics, teaching, learning and problem solving. in aip conference proceedings, 1868(1), 050014. muhtarom, m., murtianto, y. h., & sutrisno, s. (2017). thinking process of students with high-mathematics ability (a study on qsr nvivo 11-assisted data analysis). international journal of applied engineering research, 12(17), 6934-6940. nizaruddin, n., muhtarom, m., & sugiyanti, s. (2017). improving students’ problemsolving ability in mathematics through game-based learning activities. world transaction on engineering and technolgy eduction, 15(2), 102-107. pintrich, p. r. (2003). a motivational science perspective on the role of student motivation in learning and teaching contexts. journal of educational psychology, 95(4), 667686. https://link.springer.com/article/10.1007/s10649-005-9019-8 https://link.springer.com/article/10.1007/s10649-005-9019-8 https://www.iejme.com/makale_indir/98 https://www.iejme.com/makale_indir/98 https://www.iejme.com/makale_indir/98 http://sci-gems.math.bas.bg:8080/jspui/handle/10525/1410 http://sci-gems.math.bas.bg:8080/jspui/handle/10525/1410 http://www.wiete.com.au/journals/gjee/publish/vol19no2/06-muhtarom.pdf http://www.wiete.com.au/journals/gjee/publish/vol19no2/06-muhtarom.pdf http://www.wiete.com.au/journals/gjee/publish/vol19no2/06-muhtarom.pdf https://aip.scitation.org/doi/abs/10.1063/1.4995141 https://aip.scitation.org/doi/abs/10.1063/1.4995141 https://aip.scitation.org/doi/abs/10.1063/1.4995141 http://www.ripublication.com/ijaer17/ijaerv12n17_84.pdf http://www.ripublication.com/ijaer17/ijaerv12n17_84.pdf http://www.ripublication.com/ijaer17/ijaerv12n17_84.pdf http://www.wiete.com.au/journals/wte&te/pages/vol.15,%20no.2%20(2017)/02-nizaruddin.pdf http://www.wiete.com.au/journals/wte&te/pages/vol.15,%20no.2%20(2017)/02-nizaruddin.pdf http://www.wiete.com.au/journals/wte&te/pages/vol.15,%20no.2%20(2017)/02-nizaruddin.pdf https://psycnet.apa.org/doilanding?doi=10.1037%2f0022-0663.95.4.667 https://psycnet.apa.org/doilanding?doi=10.1037%2f0022-0663.95.4.667 https://psycnet.apa.org/doilanding?doi=10.1037%2f0022-0663.95.4.667 murtianto, sutrisno, nizaruddin, & muhtarom, effect of learning using mathematica software … 228 pantiwati, y., & husamah, h. (2017). self and peer assessments in active learning model to increase metacognitive awareness and cognitive abilities. international journal of instruction, 10(4), 185-202. rachvelishvili, n. (2017). achievement motivation toward learning english language in modern educational context of georgia. problems of education in the 21st century, 75(4), 366-374. rencher, a. c. (2002). methods of multivariate analysis. canada: john willey & sons. inc. publications. sunandar, s., murtianto, y. h., & sutrisno, s. (2015). development of teaching-assisted software mathematica in developing student mathematics representation ability. semarang: universitas pgri semarang. vosler, d. (2009). exploring analytic geometry with mathematica. boston: academic press. https://doi.org/10.12973/iji.2017.10411a https://doi.org/10.12973/iji.2017.10411a https://doi.org/10.12973/iji.2017.10411a http://d.researchbib.com/f/5no2sdnf5hmkdilkw0njafmkzizwnkal80agpgzghjzmp1zqt0al5jmtl.pdf http://d.researchbib.com/f/5no2sdnf5hmkdilkw0njafmkzizwnkal80agpgzghjzmp1zqt0al5jmtl.pdf http://d.researchbib.com/f/5no2sdnf5hmkdilkw0njafmkzizwnkal80agpgzghjzmp1zqt0al5jmtl.pdf sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 8, no. 2, september 2019 e–issn 2460-9285 https://doi.org/10.22460/infinity.v8i2.p229-238 229 the effect of mathematical disposition and learning motivation on problem solving: an analysis masta hutajulu *1 , tommy tanu wijaya 2 , wahyu hidayat 3 1,3 institut keguruan dan ilmu pendidikan siliwangi 2 guangxi normal university article info abstract article history: received july 5, 2019 revised sept 21, 2019 accepted sept 25, 2019 this research was motivated by the low problem solving abilities, mathematical disposition and learning motivation of junior students. this study aims to find and analyze empirically the influence of mathematical dispositions and learning motivation on problem solving abilities. samples were obtained in class vii-2 at smpn 2 cimahi as many as 34 students. study uses correlational quantitative methods. analysis was done by regression method. the data collection was given 2 pieces of study instruments, namely problem solving test instruments and non-test questionnaires in a set of mathematical dispositions and learning motivation. the data was tested for regression and correlation. the results of data analysis that was mathematical disposition and larning motivation were significantly influenced by problem solving ability of junior students, with the regression equation ̂ indicating a positive influence, and the degree of closeness is the pearson correlation coefficient of 0.827 classified in a strong positive interpretation. together, mathematical disposition variables and learning motivation variables can determine the problem solving variable by 68.3%. recommendations from this study, teachers should design learning processes that can improve mathematical disposition and student motivation so that students' problem solving abilities increase. keywords: learning motivation, mathematical disposition, problem solving copyright © 2019 ikip siliwangi. all rights reserved. corresponding author: masta hutajulu, departement of mathematics education, institut keguruan dan ilmu pendidikan siliwangi, jl.terusan jenderal sudirman, cimahi, west java, indonesia. email: masthahutajulu@yahoo.com how to cite: hutajulu, m., wijaya, t. t., & hidayat, w. (2019). the effect of mathematical disposition and learning motivation on problem solving: an analysis. infinity, 8(2), 229-238. 1. introduction problem solving is one of the abilities that need to be owned and developed by every student at the secondary education level. the rationale of the statement includes mathematical problem solving was the ability listed in the curriculum and objectives of the 2006 ktsp mathematics learning and 2013 mathematics curriculum which states that the purpose of mathematics learning was to solve problems that includes the ability to mailto:masthahutajulu@yahoo.com hutajulu, wijaya, & hidayat, the effect of mathematical disposition and learning motivation … 230 understand problems, design mathematical models, solve model, and interpret the solutions obtained (hendriana, rohaeti, & sumarmo, 2017). cooney (hendriana & sumarmo, 2014) suggests that ownership of problem solving ability helps students think analytically in making decisions in daily life and helps improve the ability to think critically in dealing with new situations. thus the mathematical problem solving abilities are very important for students. the importance of ownership of problem solving abilities is reflected in the quote branca (1980) which states that mathematical problem solving is one of the important goals in learning mathematics even the mathematical problem solving process is the heart of mathematics. polya (2004) developed a model, procedure, or heuristic problem solving consisting of steps to solve a problem, namely (1) understanding the problem; (2) devising a plan; (3) carrying out the plan; and (4) looking back. understanding problems refers to identifying facts, concepts, or information needed to solve problems. devising a plan refers to the preparation of mathematical models of known problems. carrying out the plan refers to the completion of the mathematical model that has been compiled. while looking back it relates to examining the suitability or correctness of answers. the stages of problem solving proposed by polya (2004) can be seen as aspects that need to be considered in evaluating problem solving abilities. in other words, mathematical problem solving abilities include the ability to understand problems, make a problem solving plan, implement a problem-solving plan, and examine solutions. based on the description above it is clear that the mathematical problem solving abilities of students need to get attention to be developed. mathematical problem solving ability required to learn and mathematics it self. therefore solving mathematical problems is very important in learning mathematics because it can facilitate students in facing problems in the lives of students today and in the days to come. but the reality in the field shows that the problem solving ability is still low. this is in line with research assesments program for international students (pisa) 2015 (sjøberg, 2015) indicates that student math ability indonesia ranked at 63 out of 71 countries with a score obtained is 386. furthermore, the research results trends in international the 2015 mathematic and science study (timss) shows that ability indonesian mathematics students ranked 44th out of 49 countries with a score obtained is 397. thus, it can be known that mathematical abilities indonesian students are in the low category so that the impact was also wrong one mathematical ability that was a low mathematical problem solving ability (visser, juan, & feza, 2015). many factors can affect solving ability mathematical problems, one of which is the positive attitude of students towards mathematics or mathematical disposition. disposition in a mathematical context relating to how students solve mathematical problems, whether confident, diligent, interested, and thinking flexible to explore various alternative problem solving. disposition mathematically related to how students ask, answer questions, communicate mathematical ideas, work in groups, and solve math problems. disposition mathematically according to nctm (1989) as tendency to think and act positively. in line with nctm, sumarmo (2010) argues that mathematical disposition is desire, awareness, tendency and strong dedication to students to think and do things mathematically in a way that is positive. kilpatrick, swafford, & findell (2001), mathematical disposition is the tendency to view mathematics as something that can be understood, feel mathematics as something useful, believe in diligent effort and resilient in learning mathematics will produce results, do act as an effective learner and the perpetrator of mathematics own. polking (hendriana & sumarmo, 2014), stated that disposition of mathematics shows: (1) confidence in using math, solve problems, give reasons and communicate idea; 2) flexibility in investigating volume 8, no 2, september 2019, pp. 229-238 231 mathematical ideas and trying to find alternative in solving problem; (3) diligently working on the task mathematics; (4) interest, curiosity, and inner meeting power do math assignments; (5) tend to monitor, reflect their performance and reasoning own; (6) assess the application of mathematics to other situations in mathematics and daily experience; (7) appreciation the role of mathematics in culture and value, mathematics as a tool, and as a language. based on explanation of mathematical dispositions at above, it can be concluded that mathematical disposition is a tendency strong for students to get carry out various activities mathematics so that it can complete mathematical problems effectively and efficient. in addition to mathematical dispositions, factors that can influence the ability to solve mathematical problems are learning motivation. this is in line with the opinion of rakhmat (2007) "one of the factors that influence problem solving is motivation". this means that motivation greatly affects the problem solving process. in solving mathematical problems, learning motivation is important elements that must be possessed by students, students who have high learning motivation will be diligent in doing tasks, resilient and never give up in solving various problems and obstacles, interested in the learning process, thinking about solving problems especially those related to mathematical problems. from the opinions above, it can be concluded that learning motivation was thought to improve problem solving abilities. this the authors suspect because of the sliced characteristics (indicators) between learning motivation with the characteristics of problem solving. increasing motivation in solving problems can be through increasing learning motivation and increasing motivation will produce accuracy in problem solving. according to uno (2010) learning motivation indicators can be classified as the following: (a) successful desires and desires; (b) encouragement and needs in study; (c) future hopes and ideals; (d) deep awards learn; (e) interesting activities in learning; and (f) a conducive learning environment, allowing students to learn with well. based on the description above, we can pay attention to the relationship between motivation and mathematical disposition towards problem solving abilities, but this needs to be studied through a study. therefore, the purpose of this research were to find out and examine the correlation of mathematical disposition motivation and learning motivation on problem solving abilities of yunior students. 2. method this study uses correlational quantitative methods. this study includes two independent variables namely mathematical disposition and learning motivation. and one dependent variable is students'problem solving abilities. the independent variable in this study was mathematical disposition and learning motivation, while the dependent variable was problem solving ability. the population of this research all students vii grade at smpn 2 cimahi, to obtain a representative sample the sample been randomly derived class vii-2 at smp 2 cimahi as many as 34 students. the data collection for each student was given 2 pieces of study instruments, namely problem solving test instruments and non-test questionnaires in a set of mathematical dispositions and learning motivation. the problem solving ability instrument in a set of 5 description questions, while the learning motivation questionnaire in a set of 42 statements with 21 positive questions and 21 negative questions and mathematical disposition questionnaire in a set of 44 statements with 22 positive questions and 22 negative questions. data obtained from the questionnaire in the form of ordinal data, is changed by using method successive interval (msi), to become interval data. hutajulu, wijaya, & hidayat, the effect of mathematical disposition and learning motivation … 232 data analysis is quantitative or statistical by using a correlation test that aims to see whether or not there is a relationship between variables. data was collected then processed using multiple linear regression tests and correlation tests, but before the requirements test was carried out as fulfillment of the assumptions needed in multiple regression analysis on things that are very important in practical terms. because the data obtained from tests of problem-solving abilities and questionnaires from disposition and learning motivation have become interval data then test requirements referred to are test (1) normality for the dependent variable, and error, (2) test linearity requirements, (3) multicollinearity requirements test, (4) heteroscedasticity requirements test. based on the method described above, this study uses multiple regression analysis, and various requirements tests including matching tuna tests were also carried out before further analysis. further analysis is carried out by applying multiple regression equations ̂ which is harmonized with research data with various requirements that theoretically have been described in on. the instrument is given in the form of test and non-test, test of problem solving ability, with the indicator identifying the adequacy of the data for trouble shooting, make a mathematical model of situations or everyday problems and complete it, select and implement strategies to solve in mathematic and or outside mathematic, explain or interpret the results according to the origin problem, and the truth of the results or answers. in figure 1, table 1 and table 2 one of the test and non-test instruments (attitude scale) will be presented with mathematical dispositions and learning motivation used in this research: figure 1. one of test instrument for problem solving abilities used in research the following in table 1 presents number of non-test statements mathematical disposition used in research: table 1. instrument lattices of mathematical disposition questionnaire indicator statement responses degree of belief overcomes learning difficulties sa a da sda confidence i feel able to completematerial mathematics assignments around and square area. (+) flexible and try various alternatives in solving problems i feel happy to solve the circumference and square area problems in various different ways. (+) volume 8, no 2, september 2019, pp. 229-238 233 indicator statement responses degree of belief overcomes learning difficulties sa a da sda diligently working on mathematical tasks i study mathematics, when i want to take an exam. (-) interest and curiosity i am afraid to ask the teacher about the material around and the square area that i have not mastered (-) monitor and reflect on performance / learning mathematics during learning i think a lot of other things and don't really listen to what is being discussed in class. (-) assess math applications i study mathematics around and around quadrilateral, useful in solving problems in everyday life. (+) award for the role of mathematics the math lesson is not difficult, provided we diligently study it. (+) description: sa: strongly agree a: agree da: disagree sda: strongly disagree the following in table 2 presents a number of non-test statements motivation to learn are used in research: table 2. instrument lattices of learning motivation questionnaire indicator statement response degree of belief overcomes learning difficulties sa a ds sda the desire and desire succeed i se and completing mathematical tasks circumference and area of quadrilateral material. (+) i always give up when faced with a difficult problem . (-) there is encouragement and need for learning. i always study the material to be learned in class (+) first i never forget the lesson the teacher has conveyed (-) there are hopes or aspirations for the future i feel learning material around and the width of a triangle is useful in everyday life. (+) there is appreciation in learning. i always get low scores on material around the area and square area. (-) there are interesting activities in learning at the time of learning i always keep quiet and copy answers from friends. (-) the existence of a conducive learning environment, allowing students to learn well. i studied in a clean and comfortable classroom. (+) description: sa: strongly agree a: agree da: disagree sda: strongly disagree 3. results and discussion based on the research results, obtained recapitulation of the achievements of students problem solving ability presented in table 3. hutajulu, wijaya, & hidayat, the effect of mathematical disposition and learning motivation … 234 table 3. recapitulation of the average achievement of problem solving ability problem solving indicator average (%) category identify the adequacy of data for problem solving. 65 enough make a mathematical model of everyday situations or problems and solve them 47 less choose and apply strategies to solve mathematical problems and / or outside mathematics 36 less explain or interpret the results according to the origin problem, as well as the truth of the results or answers. 57 enough the problem solving instrument consists of 5 questions with 4 problem solving indicators. based on table 3, the average student can master the completion of the indicator identifying the adequacy of the data for problem solving. 65 % and is the indicator that has the biggest presentation among other indicators. but students still lack the mastery of indicators making mathematical models of everyday situations or problems and completing them also on indicators choosing and applying strategies to solve mathematical problems and / or outside mathematics, with a percentage of 47% and 57%. in addition, 57 % of the indicators explained or interpreted the results according to the original problem and the correct results or answers were sufficiently mastered by the students. the following is presented a table of mathematical disposition results questionnaires with a total of 44 statements consisting of 22 positive statements and 22 negative statements. the results of the learning motivation questionnaire with a total of 42 statements consisting of 21 positive statements and 21 negative statements are as follows (table 4). table 4. results of mathematical disposition and learning motivation questionnaire aspect category total score average (%) mathematical disposition positive statement 1833 59.13 negative statement 1599 51.58 motivation learning positive statement 1795 56.09 negative statement 1561 48.78 table 4 show that mathematical dispositions of sample presentations in answering positive and negative questions, greater presentation of positive questions which is equal to 59.13 % while presentation of the negative questions is 51.58 % from the explanation above, meaning students already have mathematical dispositions although very little difference with students who not yet have a mathematical disposition . furthermore, for the motivation to learn sample presentation in answering positive and negative questions, a greater positive question presentation is equal to 56.09 % while the negative question presentation is 48.78 % from the explanation above, which means that students already have motivation to learn even though there are very few differences with students who do not have learning motivation. volume 8, no 2, september 2019, pp. 229-238 235 after testing various requirements including the match test, further analysis is carried out by applying the multiple regression equation. if the regression will be done by applying multiple regression equations, namely: ̂ . here are presented in table 5, the recapitulation of multiple regression test using spss. table 5. recapitulation of the results of multiple regression tests between mathematical dispositions and learning motivation with problem solving abilities model sum of squares df mean square f sig. 1 regression 51.169 2 25.584 31.298 0.000 b residual 23.706 29 0.817 total 74.875 31 a. dependent variable: score_pm b. predictors: (constant), motivation score, disposing_ score based on table 5, obtained by the sig = 0.000 (<0.05), it can be concluded there are significant mathematical disposition and motivation to learn about problem solving abilities signifikan. a calculation is provided to determine the regression equation (table 6). table 6. multiple regression equation model unstandardized coefficients standardized coefficients t sig. b std. error beta 1 (constant) 1.950 2017 0.967 0.342 disposal_ score 0.121 0.35 0.751 3.481 0.002 motivation score 0.15 0.037 0.86 0.397 0.694 a. dependent variable: score_pm based on table 6, the obtained constant value is 1.95 while the regression coefficient efficient value is 0.121 for mathematical dispositions and 0.015 for learning motivation, so the double regression equation can be made, namely: ̂ , coefficient values are both positive motivation and disposition can be interpreted that the motive a mathematical disposition of the study and a positive influence on solving mathematical ability. to analyze how closely the relationship between mathematical disposition and learning motivation towards problem solving skills , the pearson correlation coefficient values will be determined as shown in table 7. hutajulu, wijaya, & hidayat, the effect of mathematical disposition and learning motivation … 236 table 7. correlation between mathematical dispositions and motivation to learn with problem solving skills motivation score disposal_ score _pm score motivation score pearson correlation 1 0.875 ** 0.742 ** sig. (2-tailed) 0.000 0.000 n 32 32 32 disposal_ score pearson correlation 0.875 ** 1 0.826 ** sig. (2-tailed) 0.000 0.000 n 32 32 32 _pm score pearson correlation 0.742 ** 0.826 ** 1 sig. (2-tailed) 0.000 0.000 n 32 32 32 **. correlation is significant at 0.01 level (2-tailed). based on table 7, pearson correlation coefficients were obtained between mathematical dispositions and problem solving abilities namely 0.875 and pearson correlation coefficients betweenmotivation to learn and problem solving abilities, namely 0.742 this shows that the relationship between mathematical disposition and learning motivation with problem solving abilities is in a very strong classification. positive correlation coefficient shows that between mathematical disposition and learning motivation with problem solving abilities have a positive relationship, meaning that the higher the mathematical disposition and motivation to learn , the greater the ability to solve problems. next to see the correlation between mathematical disposition and motivation to learn together with problem solving skills can be seen in table 8. table 8. correlation between mathematical dispositions and motivation to learn together with problem solving skills model r r square adjusted r square std. error of the estimate 1 0.827 a 0.683 0.662 0.904 a. predictors: (constant), score_disposition, score_motivation based on table 8, the correlation coefficient between mathematical disposition and learning motivation together with problem solving ability is 0.827, meaning that the higher the mathematical disposition and motivation to learn , the greater the ability to solve problems. in table 8 it can also be seen that the determination value of the correlation coefficient is 68.3 %, this can be interpreted that the mathematical disposition and motivation to learn together affect the problem solving ability by 68.3% while the remaining 31.7% is influenced by factors other than mathematical disposition and learning motivation. based on the results of data analysis it was concluded that mathematical disposition and student learning motivation had a significant influence on problem solving abilities, it could see from the double regression equation: ̂ . this is in line with the research of darmawati (2017), fadila, septiana, amelia, & wahyuni (2019), kusmaryono, suyitno, dwijanto, & dwidayati (2019) and taiyeb & mukhlisa (2015), that there were a relationship between mathematical disposition, learning motivation and learning outcomes. likewise, it is also in line with the research of huda (2016) and ningsih & rohana (2016) that mathematical dispositions and student learning motivation are mainly students' activeness in aspects: working together to solve problems, volume 8, no 2, september 2019, pp. 229-238 237 giving opinions when there are group friends who have not understood, resolved dissent, and communicated with friends and teachers during the learning process in the classroom has increased. therefore teachers need to instill students' learning motivation in each lesson (suprihatin, 2015). to embed a mathematical disposition and students' motivation is high, then the teacher needs to create a fun learning environment, enable and develop selfconfidence and always provide good motivation (hidayat & sariningsih, 2018; subaidi, 2016). according to cleopatra (2015) and rosyana, afrilianto, & senjayawati (2018), learning in a structured and meaningful manner can also increase learning motivation. with high confidence and motivation, the students' ability to convey ideas or mathematical ideas will be better. 4. conclusion based on the results and discussion, the conclusion of this study is that problem solving abilities are influenced by mathematical dispositions and learning motivation. as well as mathematical disposition and learning motivation both individually and jointly have a positive effect on students' problem solving abilities, meaning that the higher the mathematical disposition and learning motivationstudents, the higher the problem solving ability of students, the further the correlation coefficient is classified into a very strong classification. based on the results of this study also, the authors recommend that the level of problem solving abilities of students is influenced by mathematical disposition factors and learning motivation, so as to improve mathematical disposition and motivation to learn students also need to pay attention to learning that must be designed as well as possible. acknowledgements place furthermore, we would like to thank the ikip siliwangi who has given full support so that this paper can be realized. also, we thank to smpn 2 cimahi, the place of research. references branca, n. a. (1980). problem solving as a goal, process, and basic skill. problem solving in school mathematics, 1, 3–8. cleopatra, m. (2015). pengaruh gaya hidup dan motivasi belajar terhadap prestasi belajar matematika. formatif: jurnal ilmiah pendidikan mipa, 5(2), 168-181. darmawati, j. (2017). pengaruh motivasi belajar dan gaya belajar terhadap prestasi belajar ekonomi siswa sma negeri di kota tuban. jurnal ekonomi pendidikan dan kewirausahaan, 1(1), 79–90. fadila, a., septiana, a., amelia, v., & wahyuni, t. (2019). the influence of group investigation learning implementation judging from learning motivation against students’ mathematical problem solving ability. journal of physics: conference series, 1155(1), 12098. hendriana, h., rohaeti, e. e., & sumarmo, u. (2017). hard skills dan soft skills matematik siswa. bandung: refika aditama. hendriana, h., & sumarmo, u. 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(2015). home and school resources as predictors of mathematics performance in south africa. south african journal of education, 35(1), 1-10. http://jurnal.unswagati.ac.id/index.php/jnpm/article/view/1027 http://jurnal.unswagati.ac.id/index.php/jnpm/article/view/1027 http://jurnal.unswagati.ac.id/index.php/jnpm/article/view/1027 http://e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/view/187 http://e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/view/187 http://e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/view/187 https://eric.ed.gov/?id=ej1201186 https://eric.ed.gov/?id=ej1201186 https://eric.ed.gov/?id=ej1201186 https://eric.ed.gov/?id=ej1201186 http://www.e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/view/214 http://www.e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/view/214 https://books.google.co.id/books?hl=id&lr=&id=z_hsbu9kyqqc&oi=fnd&pg=pp2&dq=polya,+g.+(2004).+how+to+solve+it:+a+new+aspect+of+mathematical+method.+princeton+university+press.&ots=oypgpnkyt4&sig=w0zq2_f-ee9_hvospsq6sqiejt0&redir_esc=y#v=onepage&q=polya%2c%20g.%20(2004).%20how%20to%20solve%20it%3a%20a%20new%20aspect%20of%20mathematical%20method.%20princeton%20university%20press.&f=false https://books.google.co.id/books?hl=id&lr=&id=z_hsbu9kyqqc&oi=fnd&pg=pp2&dq=polya,+g.+(2004).+how+to+solve+it:+a+new+aspect+of+mathematical+method.+princeton+university+press.&ots=oypgpnkyt4&sig=w0zq2_f-ee9_hvospsq6sqiejt0&redir_esc=y#v=onepage&q=polya%2c%20g.%20(2004).%20how%20to%20solve%20it%3a%20a%20new%20aspect%20of%20mathematical%20method.%20princeton%20university%20press.&f=false http://e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/view/286 http://e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/view/286 http://e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/view/286 http://e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/view/286 https://www.taylorfrancis.com/books/e/9781315708713/chapters/10.4324/9781315708713-14 https://www.taylorfrancis.com/books/e/9781315708713/chapters/10.4324/9781315708713-14 ejournal.unira.ac.id/index.php/jurnal_sigma/article/view/68 ejournal.unira.ac.id/index.php/jurnal_sigma/article/view/68 http://ojs.fkip.ummetro.ac.id/index.php/ekonomi/article/view/144 http://ojs.fkip.ummetro.ac.id/index.php/ekonomi/article/view/144 https://ojs.unm.ac.id/bionature/article/view/1563 https://ojs.unm.ac.id/bionature/article/view/1563 https://ojs.unm.ac.id/bionature/article/view/1563 https://www.ajol.info/index.php/saje/article/view/113801 https://www.ajol.info/index.php/saje/article/view/113801 https://www.ajol.info/index.php/saje/article/view/113801 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 9, no. 2, september 2020 e–issn 2460-9285 https://doi.org/10.22460/infinity.v9i2.p173-182 173 comparison of algebra learning outcomes using realistic mathematics education (rme), team assisted individualization (tai) and conventional learning models in junior high school 1 masohi anderson leonardo palinussa universitas pattimura, indonesia article info abstract article history: received jul 9, 2020 revised sep 5, 2020 accepted sep 6, 2020 the study aims to examine the application of the realistic mathematics education (rme), the cooperative learning model team assited individualization (tai) type and conventional learning models on algebra. the population in this study were all eighth grade smpn 1 masohi. the type of this study is an experimental research design with quasi experimental research. instruments in this study using the test results, analyzed using anova test and further tests using tukey's hsd test. from the analysis of these study obtained data: (1) based on the normality test results obtained sig. x1 (rme learning model) of 0.976, x2 (cooperative learning model tai type) of 0.889 and x3 (conventional learning model) of 0.906. (2) based on the one-way anova calculation with the spss 20.0 program, obtained a significance value of 0.003. (3) there are significant differences in algebra learning outcomes between classes using the rme learning model, the cooperative learning model tai type and conventional learning model, and (4) the algebra learning outcomes of students used the rme learning model are higher than the students that are used cooperative learning models tai type and the students that used conventional learning model. keywords: learning outcomes, realistic mathematics education, team assitsed individualization, conventional, algebra copyright © 2020 ikip siliwangi. all rights reserved. corresponding author: anderson leonardo palinussa, department of mathematics education, universitas pattimura jl. ir. m. putuhena, poka, tlk. ambon, maluku 97233, indonesia email: apalinussa@yahoo.com how to cite: palinussa, a. l. (2020). comparison of algebra learning outcomes using realistic mathematics education (rme), team assisted individualization (tai) and conventional learning models in junior high school 1 masohi. infinity, 9(2), 173-182. 1. introduction the world of education at the lowest level up to the highest level is basically played by mathematics as a complementary science in all disciplines. in addition, mathematics is very useful to be applied in terms of life, so it becomes a provision that must be required by students. https://doi.org/10.22460/infinity.v9i2.p173-182 palinussa, comparison of algebra learning outcomes using realistic mathematics education … 174 the difficulty of students in working on mathematical problems is inseparable from the teacher's role. according to clarke & roche (2017) teachers have an important role in the learning process. the low number of indonesian students in the 2015 pisa results reflects that learning by teachers still emphasizes the ability to read, write and count. in fact, although mathematics is a subject that plays an important role in education, there are still students who do not master mathematics. because students continue to be used as learning objects in a series of learning activities, while the teacher becomes the center of learning. ratumanan (2015) says that student activities in class are not involved in teaching mathematics. because the role of the teacher is made more dominant to learn material that is not the teacher's job. this causes students to be less active in learning, so understanding concepts about student mathematics is very lacking and poor students learning outcomes. the process of learning mathematics in the classroom found a variety of problems including, the teacher still dominates the learning process and when the teacher explains that only some students pay attention well, while other students are busy telling stories and when given questions students only apply the formula given and student activity is not yet visible in the learning process so the learning becomes meaningless. in addition, teachers only use conventional learning models, so learning in the classroom tends to be monotonous which causes students to be bored and lazy to learn, and result in weak understanding of student material, especially for material that is considered difficult. this resulted in decreased student learning outcomes. to overcome the problems that have been raised, it is necessary to choose an appropriate learning model and can be a solution to improve the quality of learning. the realistic mathematics education (rme) learning model and the team assisted individualization (tai) type of cooperative learning model can be applied to increase understanding and increase student creativity. the realistic mathematics education (rme) learning model is one of a series of classroom learning programs designed with the aim of building students' ability to know things that have not been learned through student activities. mathematical concepts become the basis for students to find them in learning mathematics guided by the teacher. problem solving in the form of contextual problems becomes the principle of students discovering the mathematical concept itself. formal mathematical knowledge is obtained by students by modeling the contextual problems they face while learning. in addition, everyday human activities become mathematics learning materials that are designed with the aim of achieving the goals of mathematics learning (gravemeijer, 1994). one of the cooperative learning models that can be used is the team assisted individualization (tai) type. tai has the meaning that students in groups or teams formed heterogeneously when they have a goal to understand the material provided by the teacher must be assisted by individuals who have good learning abilities. meanwhile, according to (siregar, budiyono, & slamet, 2018) tai has a rationale that is to achieve the ability and achievement of students to adapt to differences in individual abilities. the tai type of cooperative learning model is a learning model designed to solve problems in teaching programs, for example in terms of student learning difficulties individually and can help students be more active in the classroom because students will work together between groups in solving the given problems, students also interact with each other , help each other and complement each other. thus every student who has a low ability when assisted by students who have high abilities have the hope to improve their abilities. with this learning model, the key to success in achieving the mathematics learning goals to be achieved is to adapt students to one another. based on the background above, the problems to be investigated and discussed in this study are (1) is there a difference in student learning outcomes taught with the rme volume 9, no 2, september 2020, pp. 173-182 175 learning model, the tai type of cooperative learning model, and the conventional model on the algebraic arithmetic operations material. (2) which learning model is superior to rme learning model, tai type cooperative learning model and conventional learning models on algebraic arithmetic operations material. 2. method the type of this research used the experimental research. the research design is quasi experimental research because the researcher cannot control the variables outside the research that the researcher did not expect. the variables contained in this study are x1: student learning outcomes in mathematics taught with the rme learning model, x2: student learning outcomes in mathematics taught with cooperative learning model tai type and x3: student learning outcomes in mathematics taught with conventional learning models. the learning tools in this study are in the form of learning implementation plan (rpp), student worksheets (lks), and learning materials. determine the population to be the beginning of this study and choose a sample of the existing population. the population in this study were all students of eighth grade of junior high school 1 masohi, central maluku district. the sample selection is done by purposive sampling technique, which is the technique of determining the sample with certain considerations (bidgood, hunt, & jolliffe, 2010). there are three classes chosen by researchers as research samples and obtained the first class as an experimental class 1 using the rme learning model, the second class as an experimental class 2 using a tai type of cooperative learning model, and the third class as a control class using a conventional learning model. data obtained from the results of research in the form of quantitative data. the quantitative data then tested to answer the hypotheses that have been formulated by researchers in accordance with established test procedures. quantitative data were obtained from even semester test results and post test results. data analysis of the results of even semester tests using microsoft excel 2013 software was carried out to find out that the three experimental classes had almost the same average values. the aim is to ensure that at least there is no difference in the initial capabilities of the three groups. while the post test data analysis uses spss (statistical product and service sulation) version 20. for windows in order to find out accept h0/h1. 3. results and discussion 3.1. results this study began by using the results of the even semester tests to determine the experimental class 1, experimental class 2 and the control class and to determine differences in learning outcomes used the post test. after comparing it turns out that even semester 2018/2019 test results between classes eighth grade-1, eighth grade-6, and eighth grade-7 are relatively the same as shown in figure 1. palinussa, comparison of algebra learning outcomes using realistic mathematics education … 176 figure 1. average daily repeat value from the average semester test scores (figure 1), the experimental class 1 is eighth grade-7 with an average of 71.6154, experimental class 2 is eighth grade-1 with an average of 71.8333, and the control class is eighth grade-6 with an average 72.333. data normality and homogeneity of data were tested before using the anova test. the prerequisite test which includes the normality test uses the chi-square test and homogeneity test using the f test. to find out whether the data is normal or not normal, a chi-square calculation is done for the control class and the experimental classes and the results are as shown in table 1. table 1. normality test results class sig. α experiment 1 (rme) (x1) 0.976 0.05 experiment 2 (tai) (x2) 0.889 control (conventional learning) (x3) 0.906 data decision making is normal if asymp sig. (2-tailed) is greater than the level of significance. based on table 1 obtained sig. x1 = 0.976, x2 = 0.889 and x3 = 0.906 which is greater than the significance level of 5% (0.05), so it can be stated that all data are normal. then the variance homogeneity test is performed. to find out that the ability of students in a homogeneous population, two or more variances were used in common using the levene test (see table 2). table 2. homogeneous variance test class sig. α experiment 1 (rme) (x1) 0.654 0.05 experiment 2 (tai) (x2) control (conventional learning) (x3) average std dev volume 9, no 2, september 2020, pp. 173-182 177 table 2 show that calculation of the similarity of two or more variances using the levene test shows the value of sig. greater than 5% (0.05) is 0.654 > 0.05, from the test criteria for the levene test is accept h0 if fcount < ftable and reject h0 if fcount > ftable, it can be concluded that the variance of the three data groups is experimental 1, experimental 2 and control class is homogeneous because h0 is accepted which is 0.95 < 3.12. from the test scores of learning outcomes and calculations of the mean, standard deviation, one-way anova, for the experimental 1, experimental 2 and control class the following results were obtained (see table 3). table 3. anova calculation source of variation df sum of squares mk fcount ftable decision total 74 18286.207 6.347 3.12 fcount > ftable between groups 2 2740.756 1370.378 in group 72 15545.451 215.909 based on the anova one way calculation used spss 20.0 program, a significance value of (0.003) was obtained, meaning that the value of sig. is less than 5% (0.05), it can be concluded that there are differences in learning outcomes of the three learning models. table 3 show that fcount > ftable is obtained (6.347 > 3.12) then h0 is rejected or there are differences in the learning outcomes of eighth grade students of junior high school 1 masohi who are taught using the realistic mathematics education (rme) learning model, the team assisted individualization (tai) of cooperative learning model and the conventional learning model in the operations of algebra. to determine a better learning model among the three learning models used, the average value of student learning outcomes from the three learning models can be considered which can be presented as follows in figure 2. figure 2. the average value of the three groups after treatment was given figure 2 show that the average value of the highest student learning outcomes is the class taught by the realistic mathematics education (rme) learning model (72.1332). then the cooperative learning model team assisted individualization (tai) type (65.2020) and the lowest is the conventional learning model (57.3356). furthermore, to find out a better learning model among the three learning models used, then using a follow-up test or socalled after anova analysis using tukey's hsd (see table 4). palinussa, comparison of algebra learning outcomes using realistic mathematics education … 178 table 4. average differences between groups x1 x2 x3 x1 6.9312 7.8664 x2 6.9312 7.6904 x3 14.7976 7.8664 interpret hsd values by comparing the average differences between groups with the results of hsd calculations. based on the tuckey's hsd test results obtained the value of hsd = 9.9926. test the difference x1 and x2 = 7.4537. obtained from the difference between the average x1 and x2 ie (72.1332 57.3356) then x1 = x2 because 6.9312 < 9.9926, test the difference x1 and x3 = 14.7976. obtained from the difference between the average x1 and x3 ie (72.1332 57.3356) then x1 ≠ y because 14.7976> 9.9926, test the difference x2 and x3 = 7.8684 obtained from the difference between the average x2 and x3 ie (65202 57.3356) then x2 = x3 because 7.8664 <9.9926. based on tuckey's hsd calculation (see table 4), the average value of the three classes is experimental 1 (x1) which has a higher average number so it can be stated that the learning model that is superior among the three learning models is the realistic mathematics education (rme) learning model. 3.2. discussion in the class taught by the realistic mathematics education (rme) learning model, at the beginning of the learning the teacher provides stimulus in the form of material using contextual examples, so that students can better understand the material provided through these examples. and then by following the steps in the rme learning model the teacher guides students to be able to understand the steps of learning. although initially the students still looked confused, with the teacher's guidance the students were then able to understand the steps in the rme learning model well. after students get an explanation of what rme is and the steps of the rme learning model, students who have been sitting in groups begin to look busy with the material to be completed in the group. rme has superior potential compared to conventional and tai learning models in improving mathematics learning outcomes. in rme students are trained to develop reasoning and logical abilities. mathematics learning through rme is very relevant to students in dealing with daily problems so that students can interact with the teacher continuously to solve problems. various studies with rme in indonesia explore the extent to which rme can be utilized and stimulate improved learning process (sembiring, hadi, & dolk, 2008). during the learning process takes place students are also required to better understand the material by solving questions in the worksheet in groups. this causes a sense of responsibility, mutual respect and mutual assistance in the group during the learning process. the rme learning model itself is a learning model that can structure the level of student understanding so that students can relate information that has just been obtained with existing material with the cognitive structure they have. according to gravemeijer (1994) and afriansyah (2016), there are three main principles in rme, namely: (a) guided reinvention and progressive mathematization); (b) didactical phenomenology; and (c) a selfdeveloped model. the first phase guided reinvention, which students should be given the volume 9, no 2, september 2020, pp. 173-182 179 opportunity as a society to find a process similar to the process in which mathematics is found. during the learning process, students independently have the opportunity to build their own mathematical knowledge. in the second stage of didactic phenomenology, a situation that is relevant to the topic of mathematics is created so that it can be applied to be investigated in learning. therefore, it is also necessary to balance the types of applications or methods that must be anticipated in learning by the teacher. the aim of the phenomenological inquiry is to find problem situations in which a specific approach can be generalized. another aim is to find situations that give rise to a paradigmatic solution procedure. the third stage is a self-developed model. self-developed models play an important role in bridging the gap between limited informal knowledge and formal mathematical knowledge. this model was developed by the students themselves. through mathematical generalization and formalization, this model is developed by students to aid mathematical reasoning (sumirattana, makanong, & thipkong, 2017). the results of this study are relevant to the results of research (batlolona et al., 2019) which found that rme has very good effect on improving the mathematics learning outcomes of junior high school students. rme allows teachers and students to connect the context of abstract learning material to be concrete. it is easier to solve contextual problems that students encounter in their daily lives with rme. therefore, rme assists teachers in designing learning that is relevant to the needs of students in real-life contexts. reality concept is a context of known children's knowledge in their lives, and then becomes components of thinking scheme. the scheme components connect various mathematical contexts and concepts. related to this situation, creative thinking can involve various dimensions of knowledge in every stage of cognitive thinking process. thus, reality and intertwinement as rme principles can be used to encourage someone's learning outcomes. the real learning concept is the context of the child's knowledge that is known in his life, then becomes a component schema of thought. schema components connect various mathematical contexts and concepts. associated with in this situation, thinking process can involve various dimensions of knowledge in every stage of thinking process. thus, reality and linkages as the principles of rme can be used to encourage thought processes so that learning outcomes increase (muhtarom, nizaruddin, nursyahidah, & happy, 2019; nuraida & amam, 2019; sitorus & masrayati, 2016; umbara & nuraeni, 2019). student learning outcomes are much improved with rme compared to stad and conventional learning due to an increase in learning activities as well. learning that is real and in accordance with real-world conditions, encourages students to increase learning activities (arsaythamby & zubainur, 2014). this happens because students become curious about the topic they are studying when it is related to real conditions. students arouse curiosity to reveal how the solution to the problems they face. in addition, students experience learning on their own, so they feel the importance of learning and understand that rme helps them in learning. on the other hand, rme can make learning memorized meaningful because students try to connect information that is already in their minds with information that will be obtained so as to enhance student understanding because it contains a summary of concepts and material relationships in the cognitive structure of students (clarke & roche, 2017). this awareness is very motivating for an increase in learning outcomes compared to tai and conventional learning. in the class taught by the tai type of cooperative learning model the teacher only works as a facilitator who is ready to help groups or individuals who need help. the results of individual work will be brought into their respective groups to be discussed and discussed in groups. all group members are responsible for the entire answer that is done. in this learning model there is no competition between students in groups because students work together to complete the given task and students also respect each other's different ways of palinussa, comparison of algebra learning outcomes using realistic mathematics education … 180 thinking, students not only expect help from the teacher, but also motivated to learn accurately fast on all material. the results of group learning are compared with other groups to get awards in the form of praise from the teacher. this type of tai cooperative learning places more emphasis on group appreciation. of the five groups in this tai class, the fourth group was given credit for their work as the super group or the best group while the first, second, third and fifth groups were given credit for their work as a good group. then each student in the group is given an evaluation in the form of a quiz (fact test). in the other hand, the selection of the tai model as a learning model is felt to be accordance with the existing problems. the use of tai is the use of a very simple learning model and is able to provide understanding concepts to students so easily that it becomes a solution for students in learning difficult material. in tai learning, students are required to actively solve problems given by the teacher individually or in groups. the groups formed in the learning of tai consist of students who have high, medium and low abilities making it easier for students to discuss. students who lack understanding can ask students who understand better, especially the group leader (ikhsanudin, 2014). alimuddin (2017) state that the tai model had a significant influence on the mathematics learning outcomes of seventh grade students at bungap satoro middle school by 13.7%. from the results of the research conducted above it can be concluded that the team assisted individualization model can improve learning outcomes and motivation. in classes taught by conventional learning models, at the beginning of learning the teacher conveys the material to be learned and conveys the learning objectives. after that, during the learning process takes place the teacher dominates the learning process while the students only pay attention and record what is explained by the teacher. the teacher explains the material in stages, then gives examples of questions, after that gives the opportunity for students to ask questions and respond back to what students are asking. conventional learning is more oriented towards achieving curriculum goals so that it ignores efforts to instill concepts that are deep and relevant to student needs (leasa & corebima, 2017). however, if there are no questions from students, the teacher will continue the material. then the teacher provides a summary and assignments to complete. in addition, during the learning process only certain students pay attention, while other students don't pay attention to what the teacher says. this is because the learning model used is more centered on the teacher, so students only accept what is conveyed by the teacher which results in a less active learning process. in line with that aziz & hossain (2010) argues that the conventional learning model or lecture method that focuses students' full attention on the teacher so that only teachers are active here, while students are only subject to listening to the explanation presented by the teacher. 4. conclusion based on research that has been done and discussion of research results, it can be concluded that there is a difference in the learning outcomes of eighth grade students of junior high school 1 masohi who are taught using the rme learning model, the cooperative learning model team assisted individualization (tai) type and the conventional learning model. other than that, the superior model used to teach algebraic operations is the rme learning model. rme has a positive impact on student learning outcomes when compared team assisted individualization (tai) and the conventional learning model. volume 9, no 2, september 2020, pp. 173-182 181 references afriansyah, e. a. 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(2018). team assisted individualization (tai) in mathematics learning viewed from multiple intelligences. journal of physics: conference series, 1108(1), 012073. https://doi.org/10.1088/17426596/1108/1/012073 sitorus, j., & masrayati, m. (2016). title page students ’ creative thinking process stages : implementation of realistic mathematics education. thinking skills and creativity, 22, 111-120. https://doi.org/10.1016/j.tsc.2016.09.007 sumirattana, s., makanong, a., & thipkong, s. (2017). using realistic mathematics education and the dapic problem-solving process to enhance secondary school students ’ mathematical literacy. kasetsart journal of social sciences, 38(3), 307– 315. https://doi.org/10.1016/j.kjss.2016.06.001 umbara, u., & nuraeni, z. (2019). implementation of realistic mathematics education based on adobe flash professional cs6 to improve mathematical literacy. infinity journal, 8(2), 167-178. https://doi.org/10.22460/infinity.v8i2.p167-178 https://doi.org/10.1007/s11858-008-0125-9 https://doi.org/10.1088/1742-6596/1108/1/012073 https://doi.org/10.1088/1742-6596/1108/1/012073 https://doi.org/10.1016/j.tsc.2016.09.007 https://doi.org/10.1016/j.kjss.2016.06.001 https://doi.org/10.22460/infinity.v8i2.p167-178 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 8, no. 1, february 2019 e–issn 2460-9285 https://doi.org/10.22460/infinity.v8i1.p87-98 87 design of learning materials on circle based on mathematical communication cita dwi rosita 1 , tri nopriana *2 , isna silvia 3 1,2,3 universitas swadaya gunung djati article info abstract article history: received dec 15, 2018 revised jan 26, 2019 accepted jan 28, 2019 mathematical communication skills is an important role in mathematics learning. however, the importance of mathematical communication skills has not been fully realized in learning, especially circle material. design a learning material based on mathematical communication is one way to develop this ability. the preliminary study produced the findings of an epistemological learning obstacle so that students' mathematical communication skills were still in the low category. this study aimed to analyze learning obstacle and designing learning materials based on the material mathematical communication circle. this study is design research that contained two stages of didactical design research (ddr), didactic situation and metapedadidactional stage. research result obtained are students difficulties in relating the material defining elements of the circle with their own language, identifying circle elements that were known and explaining through pictures, calculating the circumference and distance of circular objects based on problems, calculating the surface area of circular objects based on the problems, and rearrange the formula which states the relationship of circle elements. to solve that learning obstacle, we recommend some learning trajectory in a circle that useful for teachers. this design of learning material is valid and practical to implement in the classroom. keywords: didactical design research circle learning obstacle mathematical communication copyright © 2019 ikip siliwangi. all rights reserved. corresponding author: tri nopriana, departement of mathematics education, universitas swadaya gunung djati, jl. pemuda no.32, cirebon, indonesia email: trinopriana@unswagati.ac.id how to cite: rosita, c. d., nopriana, t., & silvia, i. (2019). design of learning materials on circle based on mathematical communications. infinity, 8(1), 87-98. 1. introduction mathematical communication skills are one of five abilities recommended by the national council of teachers of mathematics (hiebert, 2003). this is in line with baroody's (1993), there are two important reasons why mathematical communication is one of the focuses on mathematics learning. first, mathematics is basically a language for mathematics itself. second, learning and teaching mathematics are social activities that involve at least two parties, namely teachers and students. in addition, it was also strengthened by minister of education and culture regulation no.58 at 2014 which states mailto:trinopriana@unswagati.ac.id rosita, nopriana, & silvia, design of learning materials on circle … 88 that the purpose of mathematics learning is to communicate ideas, reasoning, and be able to compile mathematical evidence by using complete sentences, symbols, tables, diagrams or other media to clarify the situation or problem. according to greenes & schulman (1996), mathematical communication is (1) a central force for students in formulating concepts and strategies; (2) capital of success for students towards approaches and solutions in mathematical exploration and investigation; (3) a forum for students to communicate with their friends to obtain information, share thoughts and discoveries, brainstorm, assess and sharpen ideas to convince others. based on the explanation, it can be said that mathematical communication skills are mathematical abilities that must be realized in mathematics learning. geometry is a branch of mathematics in the scope of learning material in schools. in our environtment, geometry can be found on objects in the form of spheres, tubes, boxes, lines, circles and so on. according to bobango (abdussakir, 2012) states that the purpose of geometry learning is students gain confidence about their mathematical abilities, become good problem solvers, can communicate mathematically, and can reason mathematically. in line with that, walle & jhon (2001) suggested the reason for the importance of studying geometry including geometry being able to provide more complete knowledge about the world and play an important role in learning other concepts in mathematics learning. based on the description above, it can be concluded that geometry is very important to learn, to foster the ability, and to communicate a mathematical idea. in connection with that, one of the materials in the scope of geometry in the eighth grade of junior high school that needs attention is the topic of the circle. the basic competencies that must be achieved by the eighth grade students on the topic of circle are students required to be able to express a description of the circle material that has been studied using their own language, explain the concept of broad and circumferential circles with real objects or images, connect a real situation about the circle into a mathematical model, and formulate definitions and generalizations of the relation of the center angle, bow length, and the area of the circle’s section. however, the importance of mathematical communication skills has not been fully realized in mathematics learning. based on horizon research center, inc. (tiffani, surya, panjaitan, & syahputra, 2017) suggests that at the junior high school level, student achievement related to problem-solving abilities, reasoning abilities, and communication skills in helping students to think mathematically is only 30%. this is in line also as expressed by munawaroh, rohaeti, & aripin (2018) the percentage of student error in solving the problem of mathematical communication is equal to 38% at inappropriate data category, 34% at inappropriate procedure category, and 26% at omitted data category. based on some of these explanations, it shows that mathematical communication skills have not been realized in the learning of mathematics, including in circle material. one of the causes is due to the learning barriers experienced by students. students find it difficult to explain a mathematical idea related to circles with pictures, construct conjectures, and relevant generalizations of the circle’s concepts. learning barriers here are learning barriers commonly known as the epistemological learning obstacle sulistiawati, suryadi, & fatimah (2015) explained the cause of the epistemological learning obstacle is due to a lack of conformity of teaching materials presented to students with the condition of students in learning mathematics material. one way that is thought to be able to overcome the epistemological learning obstacle is by designing a learning materials. this is in line with rosita (2016), who argued that educators should provide and develop learning materials that are in accordance with the characteristics and social environment of students. in this study, the learning materials that will be designed are printed learning materials in the form of modules. learning materials that are designed in the form of volume 8, no 1, february 2019, pp. 87-98 89 modules can help students to understand mathematical concepts independently with minimal assistance from teachers, because the material is arranged based on student’s learning obstacle. the design of learning materials is thought to be a solution for building students' mathematical communication skills in mathematics learning. the research that supports this solution is the research conducted by rosita, nopriana, & dewi (2017), arguing that a learning material design can complete the ability of mathematical understanding both classical and individual. noto, pramuditya, & fiqri (2018) stated that the limit learning material for algebraic functions based on mathematical understanding can minimize learning obstacle after being implemented. the previous research shows that students' mathematical abilities can be built with the didactical design in the form of learning materials arranged by the teacher. therefore, the purpose of this study is to design circle learning materials that develop mathematical communication skills and learning trajectories to understand circle material. 2. method this study uses a qualitative method in the form of didactical design research. didactical design research (ddr) which consists of three phases, namely the didactic situation analysis before learning, metapedadidactic analysis, and retrospective analysis (suryadi, 2013). the stages carried out in this research are the didactic situation analysis stage before learning and the metapedadidactic analysis phase. didactical situation analysis phase before learning in the form of extracting information about learning obstacle material circles and formulating anticipatory didactical pedagogical (adp) as a framework for learning materials. meanwhile, the metapedadidactic phase is the implementation of learning materials and the preparation of learning trajectories related to circle material. subjects in this study were 47 students of majalengka 6th junior high school which was divided into two groups, namely the subject for extracting information about learning obstacle, circle material and subject for the implementation of learning materials. information gathering about learning obstacle was carried out for grade ix students who had already received circle material and the implementation of learning materials was done for class viii students who had not studied circle material. data collection techniques used in this study are triangulation techniques. the combination of techniques used in this study is tests, interviews, and questionnaires. the instrument tests used was a mathematical communication ability test questions for learning circle material learning obstacle information, interviews are used to track data that is not obtained through tests. module validation questionnaire, and module practical questionnaire for teachers and students given to test the validity and practicality of modules that have been made used. 3. results and discussion 3.1. learning obstacle and didactical situation related to circle material the stage of didactical situation analysis before learning are students’ learning obstacle analysis on circle related to their mathematical communication. grouped learning obstacle then find a solution to overcome the learning obstacle. the solution is to design learning materials based on learning obstacle related to the material in the eighth grade of junior high school which will be included in the learning materials using the following rosita, nopriana, & silvia, design of learning materials on circle … 90 didactical situations. the results of the analysis of the learning obstacle and didactical situation were explained at table 1, table 2, and table 3. table 1. learning obstacle related to circle element number didactical situation didactic anticipation 1 a student divides the area in a circle using 6 bowstrings. how many areas can the student make? draw the circle area in question! a student divides the area in a circle using 6 bowstrings. how many areas can the student make? draw the circle area in question like the description of the image shown below. the maximum area of 1 bowstring is 2 area. 2 in the picture below, the point o is the center point of the circle, points c, d, e, f, g, i and j lie on the circle and the point h lies inside the circle. cd and ij line segments are circle diameters, ef line segments and gh are not circular diameters. based on the description, write in your own language what is meant by the center and diameter of the circle! observe the following picture. the picture below is a picture of a bullet-shaped game forming a circle based on the description, write in your own language what is meant by the center and diameter of the circle! in question number 1, students still have difficulty in describing the ideas specified in the problem because they do not understand well about the concept of bowstring and areas that can be drawn and model images that are suitable for getting relevant solutions. in problem number 2, students still have difficulty in writing down the definitions of elements that have been identified by their own language. the way to overcome this learning obstacle is to provide a stimulus in the form of questions/statements true/false to students so that students can be directed to define themselves about the elements of the circle. the existence of a "definition column" in the module to provide opportunities for students to redefine the elements of the circle that have been learned using their own language and discuss with friends to share with each other the definitions that have been prepared by each student. in addition, a "creation column" is also provided in the module for students to train students in communicating various possibilities from an explanation of an idea and provide opportunities for students to present their ideas, as well as the teacher's direction to determine the relevant solution of a circle problem through discussion small group. volume 8, no 1, february 2019, pp. 87-98 91 table 2. learning obstacle related to circumference and area of the circle number didactical situation didactic anticipation 3 a bicycle wheel has a radius of 21 cm. when the bicycle is paddled, the wheel rotates 50 times. determine the circumference and distance traveled by the bicycle wheel! a bicycle wheel has a radius of 21 cm. when the bicycle is paddled, the wheel rotates 50 times. determine the distance traveled by the bicycle wheel using the circumfeence formula relationship! 4 a pool is known as a circle. if the distance of a pole that is right in the middle of the pond to the edge of the pool is 14 meters, determine the surface area of the circle-shaped pond! a pool is known as a circle. if the distance of a pole that is right in the middle of the pond to the edge of the pool is 14 meters as illustrated in the sketch below. determine the area of the pool based on the situation! in problem number 3 above, students still have difficulty in connecting the real situation to calculate the distance traveled by the wheel based on the circumference that has been calculated previously. so there are some students who are only able to answer around the wheel without the distance from the wheel based on the given situation. in problem number 4, students still have difficulty in identifying the known elements in real situations, namely the error in setting the radius in diameter based on the real situation given. the way to overcome these various learning obstacles is to remind them of the concept of distance and circumference in daily life through question and answer. the teacher also gives direction to students to link concepts that are known to the real situation through questions and answers and a series of materials in the module. the existence of giving some pictures of the real form of the elements of the circle in the module. the teacher also provides a variety of real situations in the form of drill exercises on a series of module materials. table 3. learning obstacle related to determine the relationship of angle at circle number didactical situation didactic anticipation 5 shown ab=15 cm. calculate the arc length by completing the following fields. ... dan ... , then the cd arc length can be calculated using the shown aob=〖30〗^°, cod=〖120〗^°, ab=15 cm. calculate the arc length by completing the following fields. ... dan ... , then the cd arc length can be calculated using the arc length relationship with ................., namely as follows. rosita, nopriana, & silvia, design of learning materials on circle … 92 number didactical situation didactic anticipation arc length relationship with ................., namely as follows. so that, . . . is . . . so, the relationship between the central angle and the arc length can generally be written as sehingga, is . . . cm so, the relationship between the central angle and the arc length can generally be written as in problem above, students still have difficulty in compiling arguments to determine the relationship of the center angle with the arc length, and determine the generalization of the relationship of the center angle and the length of the circle arc based on the steps of the previous settlement. the way to overcome these various learning obstacles is to provide guidance to students to develop generalizations from the concept of a circle through discovery guided by the "let's find" activity and help students to establish relevant generalizations through discussions between students regarding the results of the generalization that has been done. 3.2. result validation of learning materials on circle based on mathematical communication one way to find out whether a module that is designed to be feasible or not to use is to do a validation test by the validator. the indicators used in this module validation cover several aspects, namely aspects of relevance, adequacy, completeness of presentation, systematics of presentation, student-centered orientation, linguistics, bruner's learning theory, and mathematical communication. below is presented the validation results of the module by the validator in table 4. table 4. result of validation expert validator percentage validation criteria validation validator 1 96 % very valid validator 2 78 % valid enough validator 3 90 % very valid validator 4 93 % very valid average 89 % very valid based on the results of the validation of the four experts, the average percentage of 89% with the validation level is very valid so the circle module based on mathematical communication is appropriate to be used in mathematics learning with small revisions. the volume 8, no 1, february 2019, pp. 87-98 93 suggestions for improvement of the validator for the module are described in the following explanation. validator 1, the criteria for learning materials are very valid and provide suggestions for presenting more creative questions in the module. validator 2, it is obtained that the criteria for learning materials are quite valid and provide suggestions for multiplying practice questions per sub-chapter, presenting real pictures related to the active phase, and completing indicators of mathematical communication skills in all exercises and questions in the module. validator 3, the criteria for learning materials are very valid and provide suggestions to correct some errors in the use of words in the module. furthermore, validator 4, the criteria for learning materials are very valid and provide suggestions for adding non-routine questions to sample questions and exercises and updating illustrations that are not clear. 3.3. result validation of learning materials on circle based on mathematical communication after the module is revised based on advice from experts, then the circle module based on mathematical communication is tested for practicality. aspects used in the module practicality test include aspects of ease, aspects of time efficiency, and aspects of benefits. the module practicality test was carried out by a junior high school mathematics teacher and 15 students from majalengka 6 state middle school. the following module practicality results are presented in table 5. table 5. result of validation expert subject percentage practicality criteria practicality average practicality by teachers 93 % very practical average practicality by students 89 % very practical based on the calculation of the percentage of module practicality test by the teacher and students, the average percentage is 93% and 89% so that the practicality of the module is very practical. calculation of the percentage of the practicality of learning materials for teachers in each aspect and obtained a result of 95% in terms of convenience, 100% in the aspect of time efficiency, and 83% in aspects of benefits. thus, facilitation aspects are very practical criteria, time efficiency aspects are very practical criteria and aspects of benefits are very practical criteria. while the calculation of the percentage of practicality for students in each aspect and obtained a result of 91% in the convenience aspect, 82% in the aspect of time efficiency, and 88% in aspects of benefits. thus, facilitation aspects are very practical criteria, time efficiency aspects are very practical criteria, and benefits aspects are very practical criteria. 3.4. learning trajectory of circle material based on the analysis of learning obstacle in the circle material, the learning trajectory design (learning trajectory) needs to be done as a reference in learning circle material. trajectory learning is a certain learning path that is facilitated through a series of learning activities according to students' abilities. the preparation of learning trajectory has the potential to bring up an alternative presentation of learning materials that are more in line with the needs of students because they have considered the various thinking processes of students (dedy & sumiaty, 2017). through this approach, the didactic concept of the circle concept is arranged in the hope that students can understand the concept as a whole in order to minimize the learning obstacle that occurs when students go through the learning trajectory. in the preparation of the learning trajectory, there is the term main rosita, nopriana, & silvia, design of learning materials on circle … 94 concept and pressure point. the main concept shows a common thread of concepts in circle material. while the pressure point is an important point of the main concept that makes the flow of learning flow or does not cause jumping thinking. this is so that the learning material presented is in line with a series of didactic situations, namely the pattern of student-material relations through the help of teacher presentations developed on students' learning trajectory. trajectory learning of circle material is grouped into three types, namely learning trajectory material of circle elements, learning trajectory of material around an area of the circle, and learning trajectory of the material relation between center angle, arc length, and circle area of the circle which are presented in the following figure. figure 1. learning trajectory related circle element learning trajectory to understand the elements of a circle begins by giving students the opportunity to observe the surrounding environment related to the shape of a circle. next, students express their own language about the definition of a circle in a section accompanied by several reasons for their observations. when students are able to define themselves appropriately, students identify similarities and differences from circular and non-circular objects so that circle characteristics and circle elements can be found. students learn to find forms of relationships between elements of circles based on their own observations. volume 8, no 1, february 2019, pp. 87-98 95 figure 2. learning trajectory related circumference and area of circle in this learning trajectory the process of understanding students towards the concept of circumference and the area of a circle is built through discovery activities that are associated with the concept of comparative values and the area of rectangles. figure 3. learning trajectory related relation of center angle, bow length, rosita, nopriana, & silvia, design of learning materials on circle … 96 the student learning trajectory in understanding the concept of the relationship between central angles, arc length, and circle circle area is carried out through the process of discovery by involving students' understanding of the concept of comparable worth as prerequisite material. the three learning trajectories that are built in understanding students in circle material are based on constructivism and brunner learning theories. the effort was made to create a learning community for students through the process of rediscovering. based on the results of the study of johar, patahuddin, & widjaja (2017) that contextual problems may be used to examine students' interest in problems and motivating students to work on it. this is in line with the opinion of hwang et al. (2007) that learning activities in which there are problem solving, discussing each other and providing responses among fellow students, can improve the ability to express mathematical ideas with various forms of representation. linking the prerequisite material to the concepts students will learn is in line with hung (1997) who states that in learning, students need to be motivated and guided by instructors to construct their own ideas, concepts, and understandings based on the prior knowledge they already have. martin, et al. (2005) emphasize that a set of mathematical understandings is an understanding obtained when a group of students work together in completing mathematical tasks. development of knowledge through observation and discovery is intended to add to the learning experience of students. jonassen (2010) explains, one of the factors that influence students' ability to solve problems is prior experience. the prior experience role for a problem solver as a basis for interpreting the problem, provides signs about what should be avoided and predicts the consequences of decisions or actions taken. this is in line with the meaning of full learning according to von glasersfeld & steffe (1991) that meaningful learning will not be realized only by listening to lectures from the instructor, meaningful learning experiences for students can be given one of them through teaching assignments that are more oriented to students' thinking abilities, and students who also do the thinking process. 4. conclusion based on the results of the analysis that has been done, it can be concluded that at the stage of didactic situation analysis before learning produces a learning obstacle experienced by students is an epistemological type of learning obstacle. the learning obstacle that occurs in the circle material is the related learning obstacle, defining the elements of the circle with their own language. based on the results of the validation of the four experts, the validation level is very valid so the circle module based on mathematical communication is appropriate to be used in mathematics learning with small revisions. meanwhile, at the metapedadidactic stage, the results of the module practicality test obtained by the teacher and students obtained very practical module criteria, so that the module is easy to use, useful, and the time used becomes more efficient in mathematics learning. researchers also compiled learning trajectories related to circle material including learning trajectory material circle elements, learning trajectory material around and wide circle, as well as learning trajectory material relationship between center angle, arc length, and circle circumference area. this trajectory learning can be used as a reference in studying circle material to facilitate the diversity of student learning trajectories. volume 8, no 1, february 2019, pp. 87-98 97 references abdussakir, a. 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(2007). multiple representation skills and creativity effects on mathematical problem solving using a multimedia whiteboard system. journal of educational technology & society, 10(2), 191-212. johar, r., patahuddin, s. m., & widjaja, w. (2017). linking pre-service teachers’ questioning and students’ strategies in solving contextual problems: a case study in indonesia and the netherlands. the mathematics enthusiast, 14(1), 101-128. jonassen, d. h. (2010). learning to solve problems: a handbook for designing problemsolving learning environments. routledge. martin, t. s., mccrone, s. m. s., bower, m. l. w., & dindyal, j. (2005). the interplay of teacher and student actions in the teaching and learning of geometric proof. educational studies in mathematics, 60(1), 95-124. munawaroh, n., rohaeti, e. e., & aripin, u. (2018). analisis kesalahan siswa berdasarkan kategori kesalahan menurut watson dalam menyelesaikan soal komunikasi matematis siwa smp. jpmi (jurnal pembelajaran matematika inovatif), 1(5), 993-1004. noto, m. s., pramuditya, s. a., & fiqri, y. m. (2018). design of learning materials on limit function based mathematical understanding. infinity journal, 7(1), 61-68. rosita, c. d. (2016). the development of courseware based on mathematical representations and arguments in number theory courses. infinity journal, 5(2), 131-140. rosita, c. d., nopriana, t., & dewi, i. l. k. (2017). bahan ajar aljabar linear berbasis kemampuan pemahaman matematis. unnes journal of mathematics education research, 6(2), 266-272. sulistiawati, s., suryadi, d., & fatimah, s. (2015). desain didaktis penalaran matematis untuk mengatasi kesulitan belajar siswa smp pada luas dan volume limas. kreano, jurnal matematika kreatif-inovatif, 6(2), 135-146. tiffani, f., surya, e., panjaitan, a., & syahputra, e. (2017). analysis mathematical communication skills student at the grade ix junior high school. ijariie-issn (o)-2395-4396, 3. rosita, nopriana, & silvia, design of learning materials on circle … 98 suryadi, d. (2013). didactical design research (ddr) dalam pengembangan pembelajaran matematika. in prosiding seminar nasional matematika dan pendidikan matematika, 3-12. von glasersfeld, e., & steffe, l. p. (1991). conceptual models in educational research and practice. the journal of educational thought (jet)/revue de la pensée educative, 91-103. walle, j. a., & jhon, a. (2001). geometric thinking and geometric concepts. elementary and middle school. mathematics: teaching developmentally, 4th ed. boston: allyn and bacon. sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 9, no. 2, september 2020 e–issn 2460-9285 https://doi.org/10.22460/infinity.v9i2.p263-274 263 the common errors in the learning of the simultaneous equations pg. mohammad adib ridaddudin pg. johari1, masitah shahrill*2 1maktab sains paduka seri begawan sultan, ministry of education, brunei darussalam 2sultan hassanal bolkiah institute of education, universiti brunei darussalam, brunei darussalam article info abstract article history: received sep 12, 2020 revised sep 20, 2020 accepted sep 28, 2020 the purpose of this study is to understand the causes of common errors and misconceptions in the learning attainment of simultaneous equations, specifically on linear and non-linear equations with two unknowns. the participants consisted of 30 year 9 students in one of the elite government schools in brunei darussalam. further analyses of their work led to the categorisation of four factors derived from the recurring patterns and occurrences. these four factors are complicating the subject, wrong substitution of the subject, mathematical error and irrational error in solving the question. these factors usually cause participants to make errors or simply misconceptions that usually led them to errors in solving simultaneous equations. keywords: simultaneous equations, errors, misconceptions, secondary mathematics, brunei darussalam copyright © 2020 ikip siliwangi. all rights reserved. corresponding author: masitah shahrill, sultan hassanal bolkiah institute of education, universiti brunei darussalam, tungku link road, gadong, bandar seri begawan, brunei darussalam. email: masitah.shahrill@ubd.edu.bn how to cite: pg. johari, p. m. a. r., & shahrill, m. (2020). the common errors in the learning of the simultaneous equations. infinity, 9(2), 263-274. 1. introduction simultaneous equation is often perceived as a difficult and demanding topic to deal with requiring a lot of algebraic processes to find the solution (ugboduma, 2012). the nature of it being heterogeneous and often vigorous is why most participants have little to no interest in studying or even attempting the question during their test or examination (ugboduma, 2006). this is particularly true in brunei darussalam (hereinafter, referred to as brunei) where rote memorisation has normally been the common way of teaching and learning mathematics (khalid, 2006), only to be used for passing certain tests or examinations (shahrill, 2009, 2018; salam & shahrill, 2014; shahrill & clarke, 2014, 2019; zakir, 2018). this prevents participants to utilise and relate any lessons learned from the class to the real-life situation. moreover, the lack of understanding in learning mathematics due to rote memorisation usually led participants to forget most of the knowledge taught after going through their said tests or examinations, which usually daunts them once they have to go through it again, due to the repeating nature of mathematics (matzin et al., 2013; https://doi.org/10.22460/infinity.v9i2.p263-274 pg. johari & shahrill, the common errors in the learning of … 264 shahrill et al., 2013). this is why for most students, they have negative attitude towards mathematics rendering it as one of the most challenging subjects for students in brunei generally (chua, et al., 2016; khoo et al., 2016). hence, an intervention to alleviate this negative trend is required. although there are some literature studies that investigate the matter of simultaneous equations (ugboduma, 2006, 2012; yunus et al., 2016; nordin et al., 2017), this study in particular focuses on linear and non-linear equations in two unknowns. this makes the investigation of this material to be more significant, at least in the opinion of the researchers. this is because simultaneous equations is an integral part of algebra which is needed in most mathematical topics or even other learning area of the 21st century such as computer, sciences or even engineering to name a few. nevertheless, simultaneous equations are usually one of the challenging topics to be taught in school as participants usually struggle to understand the concepts and just prefer to memorise steps and methods for the sake of getting through tests or exams. accordingly, this really creates a question whether the current method of teaching is ineffective and should a different method of teaching be required as an alternative of teaching simultaneous equations, particularly of linear and non-linear equations in two unknowns in brunei. yunus et al. (2016) also pointed out that most teachers in brunei teaches simultaneous equation by telling which only provide participants with instrumental understanding in applying the rules of algebra in solving simultaneous equations, neglecting the relational understanding which is more helpful in participants’ understanding when also present. yunus et al. (2016) then further mentioned that, because of this, participants usually interpret teacher’s instruction wrongly due to failure in understanding participants’ thought processing mechanism. therefore, a learner-centred approach is recommended in order to minimise any misconceptions that might arise. this is in-line with the thoughts from ugboduma (2006, 2012) that mentioned good methodologies are required to help stimulate participants in enhancing their understanding of simultaneous equations. he further stated that a carefully designed methodology that is adopted by an adept teacher is a key factor for participants to improve their learning. jaggi (2006) clearly impart that a statement of equality is defined as an equation. we call it as an identity when the statement of equality is true for all the unknown values involved, denoted by the symbol ≡, and we call it as conditional equation using the symbol =, when the statement of equality is only true for certain values of the unknown qualities. häggström (2008) defined an act of equaling by which a state is being equal as an equation. this formal statement of equivalence in terms of mathematical logical expressions is often denoted by the symbol of equal sign, =. a mathematical statement that has two same values is an equation. for example, 2+1=4−1. häggström (2008) later explained that when two events are done, occurring or happening at the same time, it is then called simultaneous. therefore as stated by ugboduma (2012), if we have two or more equations that are true at one end, satisfying the same values of involved unknowns, then we can call it as simultaneous equations. for a straight-line equation that has two variables, the number of solutions will be infinite. if we denote the first variable as 𝑥 and the other variable as 𝑦, then any one of the solutions for 𝑥 can be substituted into the straight-line equation giving its corresponding 𝑦 value. however, if two of such equations are simultaneously calculated together then there might be only one set of solution of 𝑥 and 𝑦 that satisfy both equation simultaneously (ugboduma, 2012). for simultaneous equations of linear and non-linear equations in two unknowns, this amount of solution that can satisfy both equations simultaneously increase depending on the degree of the non-linear equations. for instance, if the non-linear part of volume 9, no 2, september 2020, pp. 263-274 265 the equation is a quadratic equation, then the solutions should come in two sets or one repeating solution. as mentioned by yahya and shahrill (2015), it should be easier to improve participants’ understanding in their future endeavours in solving algebraic problems, which is crucial for simultaneous equations, if the reasons of their workings can be identified. consequently the purpose of this present study is to understand the causes of common errors and misconceptions made by participants in their attainment of simultaneous equations, particularly of linear and non-linear equations in two unknowns. this is so that an alternative method of teaching can be proposed to minimise these misconceptions and errors as much as possible by way of analysing and thinking. another reason is to investigate the causes of common errors and misconceptions that participants keep on committing in attaining the learning of simultaneous equations of linear and non-linear equations in two unknowns, especially for mid to low level ability participants. although there are a lot of studies that cover on types common errors and misconceptions (sarwadi & shahrill, 2014), it is hoped that in identifying the causes of it may help participants in preventing in committing those common errors and misconceptions so participants can have a better understanding, attitude and mindset in the process of learning the topic. importantly, with the formation of this study, we hope that further contribution can be made on the literature concerning how simultaneous equation is taught in brunei. the authors also feel the necessity of the study since upon reviewing literature, particularly in simultaneous equations of linear and non-linear equations in two unknowns, almost none surfaced. its instant existence in literature can be used as a doorway to pave for future studies in providing an alternative way of teaching simultaneous equations in mathematics lessons, particularly of linear and non-linear equations with two unknowns. as such, this present study is guided by the research question “what are the common errors and misconceptions made by participants in their learning of the simultaneous equations?” 2. method a total of 30 participants participated for this study taken from two year 9 classes in one of the elite government schools in brunei. the level of ability of both classes ranges from medium to low ability, mostly being medium. both classes have the required algebraic and arithmetic skills to do simultaneous equations of linear and non-linear equations with two unknowns, such as linear equation manipulation and solving quadratic equations. a test was administered to the participants that contained three item questions chosen from a pool of questions (refer to table 1) validated by experienced mathematics teachers. the questions chosen should test participants in various ways on solving simultaneous equation of linear and non-linear equations in two unknowns, such as choosing a proper subject to be used for the substitution method or how they can avoid complications of simultaneous equations by simplifying equations further before solving. the validity was assessed through judgmental methods collected from comments and opinions of experienced mathematics teachers from the school mathematics department. it was also assessed to a specification method using the first four levels of blooms’ taxonomy namely remembering, understanding, applying and analysing. pg. johari & shahrill, the common errors in the learning of … 266 table 1. list of questions for the test with item number item number questions 1 𝑦 = 𝑥𝑦 + 𝑥2 − 9 𝑦 = 3𝑥 − 1 2 4𝑥 + 𝑦 = −8 𝑥2 + 𝑥 − 𝑦 = 2 3 𝑥 3 − 𝑦 2 + 3 = 0 3 𝑥 + 2 𝑦 − 1 2 = 0 3. results and discussion 3.1. results the nature of item 1 (𝑦 = 𝑥𝑦 + 𝑥2 − 9, 𝑦 = 3𝑥 − 1) consisting of one simple linear equation and a quadratic equation is quite straightforward in relative to the other items. for the linear equation, the variable 𝑦 has already been arranged as the subject. both equations are not in a fraction form making it easier for algebraic manipulations. ideally this should be a straightforward task of substitution, expansions, simplifications and quadratic equation solving, skills that all participants already acquired. there are two common errors that were made most by participants for this item. the first one is where participants try to make 𝑥 as the subject from the linear equation. while this is actually not a form of error in any ways, making 𝑥 as the subject in this case will give a fractional subject of 𝑥 = 𝑦+1 3 which usually will result in an error due to complication that it will produce. typically, a lot of errors were usually made when the subject is made into a complicated fraction form (low et al., 2020). figure 1 exhibits a sample of a student 1’s work dealing with said fractional subject. this unnecessary step causes the question to become more complicated in a form of fractions, expanding fractions, and fractional algebra manipulation, to name a few. these unnecessary complications usually increase the risk of participants being careless as shown by this participant’s work, where he did not expand ( 𝑦2+1 3 ) × 3 3 correctly which then leads him to get the wrong final quadratic equation. one can assume that this is just an overlooked error made by the participant since the other mathematical part of his workings was done quite well. one mark was given for his correct although unnecessary substitution of subject 𝑥, and another one mark is given for his valid attempt in solving the final quadratic equations. volume 9, no 2, september 2020, pp. 263-274 267 figure 1. sample of student 1’s work for item 1 secondly, there are quite a number of participants who made an error of failing to substitute their subject 𝑦 = 3𝑥 − 1 into both side of the quadratic equation 𝑦 = 𝑥𝑦 + 𝑥2 − 9. this will make their equation impossible to solve since both variable 𝑥 and 𝑦 still exist, defeating the purpose of substitution, which is to eliminate one out of the two variables. from the sample work by one participant shown in the figure 2, the participant only substituted 𝑦 = 3𝑥 − 1 into the right-hand side of 𝑦 = 𝑥𝑦 + 𝑥2 − 9 which in the end gives her the final equation of 𝑦 = 4𝑥2 − 𝑥 + 9. student 2 then forces her way through in solving the final quadratic equation even though both variables still exist. this then resulted a wrong answer with no marks, since there were no opportunities for the marker to give one throughout the workings. pg. johari & shahrill, the common errors in the learning of … 268 figure 2. sample of student 2’s work for item 1 for item 2 (4𝑥 + 𝑦 = −8, 𝑥2 + 𝑥 − 𝑦 = 2), almost half of the participants managed to get full marks, reflecting the easier nature of the question. the common error made by participants, who mostly scored 2 marks for this item, is very similar to the error made in item 1. it is using the fractional subject for substitution, which as mentioned before is not an actual error, but usually leads to mathematical errors since it complicates workings. figure 3 below shows another working of a participant where he makes the variable 𝑥 as the subject, i.e. 𝑥 = −8−𝑦 4 . this subject is not only fractional in nature but also contains a lot of negatives sign, which usually can cause carelessness that leads to complications. however, the error made by student 3 is the expansion of ( −8−𝑦 4 ) 2 , where the denominator 4 is not expanded. this can be due to a simple misstep or lack of indices skills or knowledge. one can assume that these two factors can be easily eliminated if variable 𝑦 was made as the subject, since the participant will then have a fraction-less subject leading to a straightforward expansion. this error then leads to a wrong solution. student 3 was awarded with 2 marks for a correct substitution and a valid attempt on solving the final quadratic equation. figure 3. sample of student 3’s work for item 2 volume 9, no 2, september 2020, pp. 263-274 269 for item 3 ( 𝑥 3 − 𝑦 2 + 3 = 0, 3 𝑥 + 2 𝑦 − 1 2 = 0), although unanimously, all of the participants were unable to score more than 1 mark, some attempts can be seen to have the correct idea in generally solving the simultaneous equations. however, most participants lack the skills in manipulating algebraic fractions that led to errors that hindered them to get the required final quadratic equations, resulting in the severe loss of marks. this also caused a lot of participants to quit trying after their working seems to get very complicated. the sample work of student 4 in figure 4 reflects on this. after choosing the subject 𝑥 = 3𝑦 2 − 9, a correct substitution into the second equation yield her 1 mark. she then proceeds to simplify the equations by trying to get rid of the fraction. in doing so, she made an error by dividing the whole equation with 2 instead of multiplying. as the equation goes peculiar, she then stops trying. it can also be observed that she failed to see 12𝑦 2 as 6𝑦, which can then make her equation simpler. one can perceive from this that lack of critical thinking was present when attempting the question. figure 4. sample of student 4’s work for item 3 then some attempts, especially from participants who managed to score 1 mark, were quite decent relative to the challenging nature of the question. figure 5 shows an example of this. student 5 can be seen to have a very good algebraic manipulation skills but made an error in expanding (2 − 1 2 𝑦)(−18 + 3𝑦) which then made him lose 4 marks. the 1 mark was given for a valid attempt to find the solution from his wrong working. errors were generally made when the subject is made into a complicated fraction form, which seems to be the case here. once again one can assume that student 5 may obtain more than 1 mark if the error can be avoided by getting the fraction in the first instance. item 3 can be categorised as a challenging due to the fact that both are in a fraction state of form. however, the difficulty can be lowered if participants can change the fraction nature to whole number by multiplying it with the lcm of the denominator. from there the question will then be on par as items 1 and 2. pg. johari & shahrill, the common errors in the learning of … 270 figure 5. sample of student 5’s work for item 3 to achieve in-depth insights of the students’ work for further analysis, the following four categories of factors were derived from the recurring patterns and occurrences, which affects the students’ work. these factors usually cause participants to make errors or simply misconceptions that usually led them to errors. these four factors are: complicating the subject (cs), wrong substitution of the subject (ws), mathematical error (me) and irrational error in solving the question (i). briefly, (cs) is a factor when a student complicates a simple subject that then may lead to producing errors. for example, in item 1, instead of using the simple subject 𝑦 = 3𝑥 − 1, the student might complicate it by using 𝑥 = 𝑦+1 3 instead. this may cause errors further in their workings. (ws) is a factor when participant error in substituting their subject into another equation. this can be either literally substituting their subject wrongly or only substituting their subject partially, which this factor will focus on solely. for example, substituting 𝑦 = 3𝑥 − 1 into the right-hand side of 𝑦 = 𝑥𝑦 + 𝑥2 − 9 only, will not make the elimination of variable 𝑦 complete, since there will still be variable 𝑦 on the left-side of the equation. hence, making it impossible to solve the simultaneous equation. (me) is self-explanatory where participants made simple mathematical errors such as expanding, rearranging, changing signs or algebraic manipulations, to name a few. it can be due to carelessness of the participant or lack of mathematical skills. (i) is when participants have no understanding about the question and in solving it. usually this can be seen when participant tend to give unreasonable solution or answering it as a different topic such as solving both equations from the simultaneous equations volume 9, no 2, september 2020, pp. 263-274 271 independently or solving it as another topic, for example using 𝑏2 − 4𝑎𝑐 from the topic discriminant of intersections. figure 6. factors contributing to participants’ marks on the test the bar graph from figure 6 shows that for item 1, a large number of 12 participants changed their subject from 𝑦 = 3𝑥 − 1 into 𝑥 = 𝑦+1 3 . out of these 12 participants who committed cs, 9 of them yield 0 mark. this can tell us that indeed complicating the initial subject usually leads to errors and an effort to prevent participant from doing cs might improve their marks. then 6 participants committed the ws where most of them failed to substitute the subject properly. only 2 of these participants scored 0 mark while others had a good attempt acquiring 1 or 2 marks. a small number of irrational errors tell us that most participants have the general idea on solving the question even though the topic has not been covered with them. for item 2, there is still a moderate fraction of participants committing the cs, although only 2 out of these 8 participants scored 0 marks indicating a good attempt. this might be due to the simpler nature of the algebraic equation. no ws was recorded since the equation was designed for a one-sided substitution only, unlike item 1. most participants were able to score well on this question, but there is an interesting case where a participant who scored full mark on item 1 and item 2 committed a cs on item 2 but not on item 1. the participant choose variable 𝑥 as the subject regardless how difficult it can be. this can tell us that although his mathematical skills are very high, a critical thinking might be lacking. one can assume that the reason 𝑥 is used as the subject on both occasions might be because he is used to it from his previous lower level education, where 𝑥 is always used as the starting subjects in classroom or exams. finally, item 3 shows that most participants committed the me, understandably due to the complicated nature of the fraction form. this though can be avoided since the question is designed in such a way that the fraction can be get rid of and changed into a much simpler fraction-less equation by a simple algebraic manipulation, which all of the participants should already possess the skill to by now. 3.2. discussion based on the in-depth analysis of the repeating pattern found in the participants’ work, four main factors were detected in affecting participants’ test as mentioned earlier. the three major factors were complicating the subject needed for substitution method (cs), 12 6 7 3 8 0 8 2 0 0 18 6 0 5 10 15 20 cs ws me i item 1 item 2 item 3 pg. johari & shahrill, the common errors in the learning of … 272 making error while substituting their subject into the other equation (ws) and simple mathematical error (me). the first factor, while mathematically correct, was committed by a total of 20 participants for both items 1 and 2 of the test, which mostly led participants in making mathematical error for their subsequent workings, scoring them a very low mark in average. the second factor was mostly found in item 1, where six participants failed to substitute their subject of 𝑦 = 3𝑥 − 1 to the both side of 𝑦 = 𝑥𝑦 + 𝑥2 − 9 rendering their following workings wrong. both of these factors were perceived by the researchers as misconceptions believed due to the lack of understanding on the meaning of the mathematical process in solving the simultaneous equations, which may have resulted them to be rigidly stuck in their sole method, regardless of how difficult it was for them. the third factor comprises the highest frequency count out of the other factors (33 total for all items), where participants committed the mathematical errors. although this result is understandable due to the fact that most participants have the mathematical ability of lower to medium, the mathematical part of the question was designed and allowed to be simpler if certain mathematical skills were to be applied such as simplification, changing fractions to whole numbers or changing negative coefficient of quadratic equations to positive before solving it. failure in doing it usually leads to participants having to deal with complicated equations or forcing them to commit errors due to carelessness. these three factors are believed to contribute to the poor results obtained by almost all participants during the test, where 28 out of the 30 them only managed to score marks of below average out of the total 15 marks, where 2 marks being the mode of the result. consequently, rohmah and sutiarso (2018) mentioned that a weak prior knowledge is one of the major problems in solving simultaneous equations. however, the participants of both classes, who are mostly of medium ability participants, managed to score above average marks if not excellent, even though they were not taught on how to solve the simultaneous equations. 4. conclusion simultaneous equations, especially linear equation versus non-linear equation, with its vigorous and heterogeneous nature always intimidate participants in learning it wholeheartedly. they perceive it as a subject that is very difficult to follow rather than something that is yet to be fully understood. this incomplete understanding usually leads them to make misconceptions and common errors along the line that further hinder their study. one of the major factors that resulted from this study was misconception in making only 𝑥 as the main subject regardless how difficult it can render their subsequent workings, although other variable as subject can offer much simpler workings. another factor is failing to use their understanding in simplifying equations to achieve simpler mathematical workings in avoiding complications and careless mistakes. it is imperative that we understand the causes of common errors and misconceptions made by participants in their attainment of simultaneous equations, particularly of linear and non-linear equations in two unknowns. this way we may be able to minimise these misconceptions and errors as much as possible and to analyse and reason on every steps taken in calculating that leads to the attainable correct answer. volume 9, no 2, september 2020, pp. 263-274 273 references chua, g. l. l., shahrill, m., & tan, a. 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(2015). the strategies used in solving algebra by secondary school repeating students. procedia – social behavioural and sciences, 186, 1192-1200. https://doi.org/10.1016/j.sbspro.2015.04.168 yunus, d. h. r. p. h., shahrill, m., & abdullah, n. a., & tan, a. (2016). teaching by telling: investigating the teaching and learning of solving simultaneous linear equations. advanced science letters, 22(5/6), 1551-1555. https://doi.org/10.1166/asl.2016.6676 zakir, n. (2018). the impact of educational change processes in brunei preschools: an interpretive study. unpublished doctoral dissertation, university of sheffield, united kingdom. https://doi.org/10.34044/j.kjss.2019.40.2.06 https://doi.org/10.5539/ies.v6n10p39 https://www.globalacademicgroup.com/journals/knowledge%20review/ugboduma.pdf https://www.globalacademicgroup.com/journals/knowledge%20review/ugboduma.pdf https://doi.org/10.4314/gjedr.v11i2.8 https://doi.org/10.1016/j.sbspro.2015.04.168 https://doi.org/10.1166/asl.2016.6676 http://etheses.whiterose.ac.uk/21197/ http://etheses.whiterose.ac.uk/21197/ http://etheses.whiterose.ac.uk/21197/ sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 11, no. 1, february 2022 e–issn 2460-9285 https://doi.org/10.22460/infinity.v11i1.p133-144 133 the development of online learning game on linear program courses zainnur wijayanto, dafid slamet setiana, betty kusumaningrum* universitas sarjanawiyata tamansiswa, yogyakarta, indonesia article info abstract article history: received dec 19, 2020 revised jul 14, 2021 accepted jul 16, 2021 this study aims to produce online learning games on linear program subjects for 3rd-semester students that are valid, practical, efective and can increase student learning motivation. students are less interested in linear program subject because it requires high analysis skill and feel boring. this research and development model consisting of the stages of define (literature study and field survey), design (early product design activities), develop (expert validation, product revisions, and development testing), and disseminate (final product revision) with descriptive analysis techniques qualitatively and quantitatively. qualitative descriptive analysis techniques are used to describe the stages of development that describe the results of observations of the implementation and effectiveness of online learning games that have been developed in the field. quantitative descriptive analysis techniques are used at the development stages. this study has achieved the expected goal: producing online learning games for linear program subjects that are valid (very good category), practical (very good category), and effective (85.71% of students had achieve a minimum score of c). keywords: learning games, linear programs, online this is an open access article under the cc by-sa license. corresponding author: betty kusumaningrum, department of mathematics education, universitas sarjanawiyata tamansiswa, yogyakarta jl. batikan, tahunan, umbulharjo, daerah istimewa yogyakarta 55167, indonesia email: betty.kusumaningrum@ustjogja.ac.id how to cite: wijayanto, z., setiana, d. s., & kusumaningrum, b. (2022). the development of online learning game on linear program courses. infinity, 11(1), 133-144. 1. introduction the development of science and technology encourages the learning process to be more applicable and attractive as an effort to improve the quality of education (hughes, 2004). appropriate teaching methods will help the students understanding process, so students can apply the knowledge gained in everyday life (ganyaupfu, 2013; kalyani & rajasekaran, 2018) . one of the ways to encourage the achievement of effective learning, is to use learning aids or what are commonly called media (wahid et al., 2020; wardani et al., 2018). one of the media that can be used in learning is a game (wahyudi et al., 2019). games can be used as learning media (becker, 2007). one of the effective learning methods https://doi.org/10.22460/infinity.v11i1.p133-144 https://creativecommons.org/licenses/by-sa/4.0/ wijayanto, setiana, & kusumaningrum, the development of online learning game … 134 to achieve learning goals is to use games, or the learning process through gaming (aleksić et al., 2016; ding et al., 2017). gaming is one of the main methods in the learning process for adults (hidayat, 2018). therefore the role of the media in the learning process is important because it will make the learning process more varied and less boring (pivec & kearney, 2007; wijaya, 2020). the use of games as learning media can be applied to technologies that are widely used today, such as mobile phones (ekanayake & wishart, 2014). a mobile phone is a communication tool that can be used to make calls or send text messages. mobile phones that are currently developing have supporting features, including internet, game applications, and others. this mobile phone can be used as a device to play mobile games (godwin-jones, 2011). implementation of games on mobile phones and internet networks as learning media at the higher education are not fully used yet (yu & conway, 2012). therefore, it is necessary to design online learning games as an innovation in mathematics learning that can increase motivation to learn mathematics in the subject that are considered difficult by students, one ofthem is a linear program. liner program requires analysis and long processing steps (ariawan, 2015) and also requires high reasoning and communication skills (saparwadi & aini, 2016). it can be seen in the final exam, there were still many students who get c+ (17.85%), c (14.28%), and d (25%) grades. by using online games, it is expected to increase student motivation which can improve student learning outcomes.the results of this study are expected to be used as a reference in developing learning media that is suitable for internet generation learning. in addition, learning games that have been designed can be used by educational institutions as a basis for improving the quality of the process and student learning outcomes. the need for more urgent references is associated with the lack of references that discuss online game development in mathematics learning at the higher education. 2. method 2.1. research design the procedure for developing a linear program online learning game consists of define, design, develop, and disseminate stages.the define stage includes literature study and field surveys to identify problems and analyse needs; the design stage includes early product design activities; the develop stage includes expert validation, product revisions, and development testing, while the dissemination stage includes final product revision. the development procedure are presented in figure 1. figure 1. the development procedure volume 11, no 1, february 2022, pp. 133-144 135 2.2. participants research subjects are grouped based on two activities: product development and product development testing. at the product development stage, research subjects consisted of 2 expertswhile at the product development testing stage, the research subjects were 28 students. 2.3. data collection in the define stage, data was collected by observation, interviews, and literature studies to obtain information about the use of technology and the internet in learning among students; (2) the design stage: data was collected by literature study to produce linear program questions as material for making online learning games; (3) the development stage: data was collected by instrument validation (at the early product development stage), a questionnaire (at the development testing and the experiment testing) and student learning outcomes. 2.4. data analysis the data were analysed by descriptive qualitative and quantitative. qualitative descriptive analysis was used to describe the development implementation of linear program online learning game, and describe the effectiveness of linear program online learning games that have been developed in the field. quantitative data analysis was used at the development stage. the data analysis approach used was: (1) the implementation and results of the online learning game development linear program and the validity of the linear program questions described in the form of a data presentation, then analyzed qualitatively and quantitatively; (2) at the development testing, the test results of the application of the linear program online learning game were analyzed by a quantitative approach; (3) experiment testing using a quantitative analysis approach. the following were the steps that used to determine the quality criteria for the developed game-based learning media products: (1) data in the form of expert scores obtained through the validation sheet are added up; (2) the actual total score was obtained converted into qualitative data on a scale of four shown in table 1. table 1. conversion of quantitative data to qualitative data of scale 5 interval category x > mi + 1.5 sbi verry good mi + 0.5 sbi < x ≤ mi + 1.5 sbi good mi 0.5 sbi < m ≤ mi + 0.5 sbi enough mi 1.5 sbi < m ≤ mi 0.5 sbi less x ≤ mi 1.5 sbi verry less the analysis technique for measuring validity was to provide the instruments that would be validated to the expert deemed appropriate to provide an assessment. the aspects that were assessed in term of material/content, construction, and language. the criterion used to decide that an instrument has an adequate degree of validity is if the mean (x) of the results of the assessment for all minimum aspects is in the "valid" category. if this is not the case, it is necessary to revise it based on the suggestions of the validators or by looking back at the aspects that are lacking, re-validated then re-analyzed. and so on until it meets the minimum average value in the valid category. wijayanto, setiana, & kusumaningrum, the development of online learning game … 136 linear program online learning game are considered practical if the results of student assessments for all minimal aspects are in the "good" category. these results indicate that the online games developed are practical and can be applied at universities, while it can be said effective if it meets the effectiveness indicator: the achievement of student competence classically reaches the minimum category c (passed). the data analysis steps on the effectiveness of the linear program online learning game in terms of achieving student learning competencies were: (1) recapitulating the scores that appear automatically at the end of the game (2) calculating the (number) of students who reach the specified level of learning outcomes: minimum c; and (3) determine the achievement of the objectives or classical learning outcomes (all students in one class): minimum 75% of students get a c grade. 3. results and discussion 3.1. results the result of this research was a product in the form of an online learning game “kahoot” in the linear program subject. before developing a product, a needs analysis must be carried out first. needs analysis was carried out to obtain information about linear program learning of 3rd semester mathematics education students and the use of technology and internet in mathematics learning among the students. the needs analysis obtain in this research process are linear program learning has taken advantage of technology by using lindo software (linear interactive discreat optimizer). this software is used to solve linear program problems easily, quickly, and accurately. however, in linear program learning, internet-based technology has not been utilized, such as the use of online game-based applications that encourage motivation and interest in learning linear program. online game applications using kahoot have never been used in linear program subject. kahoot is a free online game-based learning platform that can be accessed via a web browser or kahoot application using a computer or gadget that is easily accessible to students. after conducting a needs analysis, the next step was design. the first design stage in this research was a literature study that used for making questions about linear program in online learning games. the next stage was make an online learning game using kahoot. the questions were made in 2 forms, 5 multiple choice questions and 5 true and false questions. multiple choice and true-false questions are selected based on their ability to cover a wide range of subjects in an exam. before making the questions, the researcher determined the question lattices first, so that the questions were in accordance with the indicators of cognitive ability to be measured. the grid of questions is presented in table 2. table 2. the grid of questions indicators number form of problem can determine the area of the set of solutions of a known system of two-variable linear inequalities 1, 2 multiple choice can determine a two-variable linear inequality system from the set area of known solutions in the problem 3,4,5 multiple choice can determine the area of the set of solutions of a known system of two-variable linear inequalities 6,7 true-false can determine the minimum value of a function if the area of the set of solutions is known 8 true-false volume 11, no 1, february 2022, pp. 133-144 137 indicators number form of problem can determine the maximum revenue from a sale if the area of the set of solutions is known 9 true-false can determine the intersection point between two lines 10 true-false the questions that have been made then validated. the purpose of validation was to find out whether the instrument could be measuring what is desired. validation was carried out by 2 lecturers. the validation process was validating ten linear program questions in the kahoot. the results of the question validation for each component can be seen in table 3. table 3. results of validation no components v1 v2 a. content 1 problems in accordance with the measured cognitive domain 5 5 2 there is only one correct answer 5 5 total 10 10 average 10 b. construction 1. problem is clearly formulated 5 4 2. the question provides no clues to the answer 5 5 3. the images/graphs/diagrams are presented clearly 4 5 4. the item does not depend on the answer to the previous question 5 5 5. problem does not contain double negative statements 5 5 total 24 24 average 24 c. language 1. the language used is in accordance with indonesian rules 5 5 2. communicative language 5 5 3. no local language is spoken 5 5 total 15 15 average 15 the criteria and limit values for content were determined (see table 4). table 4. the criteria and limit values of content content the criteria and limit values of content the max score of each item: 5 the min score of each item: 1 number of item: 2 ideal average = 6 2 210 = + standard deviation = 3 4 6 210 = − =1.3 very good x > 7.95 good 6.65 < x ≤ 7.95 enough 5.35 < x ≤ 6.65 less 4.05 < x ≤ 5.35 very less x ≤ 4.05 average : 10 (very good) the criteria and limit values for construction were determined (see table 5). wijayanto, setiana, & kusumaningrum, the development of online learning game … 138 table 5. the criteria and limit values of construction construction the criteria and limit values of construction the max score of each item: 5 the min score of each item: 1 number of item: 5 ideal average = 15 2 525 = + standard deviation = 6 525 − = 3.3 very good x > 19.95 good 16.65 < x ≤ 19.95 enough 13.35 < x ≤ 16.65 less 10.05 < x ≤ 13.35 very less x ≤ 10.05 average : 24 (very good) the criteria and limit values for language were determined (see table 6). table 6. the criteria and limit values of language language the criteria and limit values of language the max score of each item: 5 the min score of each item: 1 number of item: 3 ideal average = 9 2 315 = + standard deviation = 6 315 − = 2 very good x > 12 good 10 < x ≤ 12 enough 8 < x ≤ 10 less 6 < x ≤ 8 very less x ≤ 6 average : 15 (very good) the overall results of test validation were very good (see table 7), so the linear program test proper to use in the kahoot. the validator also provides suggestion: questions are formulated more clearly and the pictures/graphs are presented more clearly. the questions that have been validated are then used in the kahoot learning game. table 7. summary of test validation results no component average criteria 1 content 10 very good 2 construction 24 very good 3 language 15 very good development testing the subjects in this stage were 5 students of the mathematics education study program who have been taking linear program lectures. the students were asked to become a player in the online learning game kahoot. the researcher simulated by showing the game using a projector and the five students were asked to take part in the game until finish using their smartphones. then, students filled out a questionnaire and provide a suggestion on the linear program online learning game that has been made. the results of the questionnaire can be seen on table 8. table 8. development testing result components respondents total 1 2 3 4 5 game online 1 increase interest on linear programming 5 5 5 5 5 25 2 increase motivation to learn 5 5 5 5 5 25 volume 11, no 1, february 2022, pp. 133-144 139 components respondents total 1 2 3 4 5 3 improve communication to exchange information among studens 5 5 5 5 5 25 4 the set time duration can increase the speed and accuracy in answering questions 5 5 5 5 5 25 5 easy to use 4 5 4 4 5 22 average 24.4 appearance 1 easy to read 5 5 5 5 5 25 2 images/graphics are presented clearly 5 4 4 5 5 23 3 the order of the questions is adjusted to the difficulty level of the questions 5 5 5 5 5 25 4 the duration of answering the questions is sufficient 5 5 5 5 5 25 5 music can support competition and concentration 5 5 5 5 5 25 average 24.6 the criteria and limit values of development testing were determined (see table 9). table 9. the criteria and limit values of development testing development testing the criteria and limit values of language the max score of each item: 5 the min score of each item: 1 number of item: 5 ideal average = 15 2 525 = + standard deviation = 6 525 − = 3.3 very good x > 19.95 good 16.65 < x ≤ 19.95 enough 13.35 < x ≤ 16.65 less 10.05 < x ≤ 13.35 very less x ≤ 10.05 overall, the result of development testing gots very good criteria (see table 10). however, there was a less than optimal score on the “easy to use” component, because the ability to access the internet varies depending on the cellular internet provider of each student. in addition, the weakness of this linear program online game was the graphics were not clearly visible. table 10. summary of development testing results no components average criteria 1 game online 24.4 very good 2 appearance 24.6 very good experiment testing after the kahoot is implemented, students then filled out 30 statements on a questionnaire to find out their responses to the kahoot online learning game that has been developed. this questionnaire aims to determine the practicality of kahoot online learning games. the questionnaire results are presented in table 11. wijayanto, setiana, & kusumaningrum, the development of online learning game … 140 table 11. student questionnaire results no aspect item practicality grade x category 1 content 1-8 very good x > 67.35 good 65.18 < x ≤ 67.35 enough 63.01 < x ≤ 65.18 less 60.84 < x ≤ 63.01 very less x ≤ 60.84 68.3 very good 2 learning 9-14 very good x > 72.83 good 65.83 < x ≤ 72.83 enough 58.83 < x ≤ 65.83 less 51.83 < x ≤ 58.83 very less x ≤ 51.83 72.85 very good 3 technical 15-21 very good x > 69.18 good 63.63 < x ≤ 69.18 enough 58.08 < x ≤ 63.63 less 52.53 < x ≤ 58.08 very less x ≤ 52.53 69.8 very good 4 overall evaluation 22-30 very good x > 67.27 good 63.54 < x ≤ 67.27 enough 59.8 < x ≤ 63.54 less 56.06 < x ≤ 59.8 very less x ≤ 56.06 67.32 very good all aspects of the assessment were “very good” category, it can be concluded that the online learning game is practical for use in learning. media can be accessed and used by students easily without expensive costs. after the students have finished working on 10 questions on the kahoot, a summary of the student's work can be seen immediately. from the results of the summary analysis, the level of difficulty of each question item can be determined (see table 12). table 12. results of test analysis number the number of students who answered correctly percentage of students who answered correctly test difficulty level 1 18 64.29 easy 2 13 46.43 easy 3 18 64.29 easy 4 15 53.57 moderate 5 14 50 moderate 6 21 75 easy 7 14 50 moderate 8 8 25 difficult 9 10 35.71 difficult 10 22 75 easy the scores obtained by the students were then converted into letter grades according to the university's academic guidelines (see table 13). volume 11, no 1, february 2022, pp. 133-144 141 table 13. conversion of learning outcomes interval class letter grades score category 90 – 100 a 4.00 very excellent 80 – 89 a3.80 excellent 75 – 79 b+ 3.30 very good 68 – 74 b 3.00 good 64 – 67 b2.80 pretty good 60 – 63 c+ 2.30 enough 56 – 59 c 2.00 not enough 40 – 55 d 1.00 less 0 – 39 e 0 very less student scores obtained from the application of the kahoot online learning game are shown in table 14. table 14. student score no name correct score letter grades no name correct score letter grades 1 a 9 90 a 15 o 7 70 b 2 b 9 90 a 16 p 7 70 b 3 c 9 90 a 17 q 7 70 b 4 d 9 90 a 18 r 7 70 b 5 e 8 80 a 19 s 7 70 b 6 f 8 80 a 20 t 7 70 b 7 g 8 80 a 21 u 6 60 c+ 8 h 8 80 a 22 v 6 60 c+ 9 i 8 80 a 23 w 6 60 c+ 10 j 8 80 a 24 x 6 60 c+ 11 k 8 80 a 25 y 5 50 d 12 l 7 70 b 26 z 5 50 d 13 m 7 70 b 27 aa 4 40 d 14 n 7 70 b 28 ab 4 40 d 3.2. discussion the teaching-learning process is an important element in education, it includes the planning, implementation and assessment processes. assessment refers to the process of observing the changes in the lives of the people (çalışkan & kaşıkçı, 2010). during a pandemic, the right way to assess is to do a digital assessment. digital assessments provide instant feedback and can be used to conduct individual or group assessments in a competitive environment (yilmaz & baydas, 2017). so, digital assessment in education is important in terms of feedback and control of learning. one of the digital assessments that can be used in learning, especially in learning mathematics is kahoot!. the kahoot! is a free online game application that can be used in every learning session to increase student participation and can be used as a formative assessment. based on the results of development testing, it was concluded that kahoot! easy to apply in learning because it does not require special training for students and can be easily accessed via a smartphone or pc (plump & larosa, 2017). the set time duration can increase the speed and accuracy in answering questions. the points earned by students are wijayanto, setiana, & kusumaningrum, the development of online learning game … 142 determined by how quickly students respond to questions as well as to answer question correctly. kahoot! can be used to increase students' concentration during the course, especially when their concentration starts to decrease after the first ten minutes. in this study, kahoot! proven to increase student interest in linear program lectures. they are motivated to attend lectures by communicating with others to exchange information about the subject. in terms of appearance, kahoot! can attract students' attention because of kahoot! equipped with features that support the learning process. during the quiz, there is a music feature that can increase the enthusiasm of students in competing. in each quiz, kahoot comes with customizable response times. when the time was up, a voice sounded and the names of the top 5 students were displayed on the board (bawa, 2019; çeti̇n, 2018). quiz featured on kahoot! can vary, it can be in the form of quizzes, discussions or questionnaire, so that students do not get bored easily with the monotonous form of questions. in this study, the researcher used multiple choice questions and true-false questions with a sequence of questions adjusted to the level of difficulty. based on the results of the test analysis, it is known that students who use kahoot! in learning activities achieve good grades in exams. it means that the kahoot! application had the potential to improve and develop the high scores in exams. our outcomes show that kahoot! motivated students to be engaged the knowledge and encourage interaction in the classroom. student stated that kahoot! had a positive impact on their knowledge and skills. features on kahoot! which can increase attention and student involvement really supports students in learning. 4. conclusion this study has achieved the expected goal: producing valid, practical, and effective online learning games for linear program subjects. validity is seen from the results of expert validation. overall from the results of expert validation, it can be said that this product was very good or feasible to use. practicality of this product is seen from the results of development testing and experiment testing. it show that the student's assessment of the product being developed was also very good or practical for use in learning. effectiveness is obtained from student scores at the end of the game. students who achieve a minimum score of c were 85.71%. the linear program online learning game is said to be effective if the overall score obtained by students who reaches a minimum value of c is at least 75%. it can be concluded that the linear program online learning game was effectively used in learning (apsari & rizki, 2018; ariawan et al., 2017). based on the results of the study it can be concluded that the development of kahoot! meet the criteria of validity, practicality, and effectiveness. by the results of the validity test, the development of kahoot! it has very good criteria in terms of content, construction, and language. kahoot! also meet practical requirements in terms of content, technical learning, and overall evaluation. it means that kahoot! easy to read, can present pictures/graphics clearly, enough time for students to answer the questions, the music features of kahoot! can support competition and concentration, and the form of the questions presented is appropriate and adjusted to the level of difficulty of the questions. application of kahoot! also able to support students to achieve good scores on tests. based on the results of the study, it is recommended that teachers can use creative learning media that utilize technology so that students become accustomed to using computers or laptops and smartphone not only to play game but also enrich their insights. the use of educational games in the classroom can also minimize interference, so as to improve the quality of learning. volume 11, no 1, february 2022, pp. 133-144 143 references aleksić, v., ivanović, m., budimac, z., & popescu, e. 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(2019). development of web game learning materials for primary school students. infinity journal, 8(2), 199-208. https://doi.org/10.22460/infinity.v8i2.p199-208 wardani, d. k., martono, t., pratomo, l. c., rusydi, d. s., & kusuma, d. h. (2018). online learning in higher education to encourage critical thinking skills in the 21st century. international journal of educational research review, 4(2), 146-153. https://doi.org/10.24331/ijere.517973 wijaya, t. t. (2020). how chinese students learn mathematics during the coronavirus pandemic. ijeri: international journal of educational research and innovation, 15, 1-16. https://doi.org/10.46661/ijeri.4950 yilmaz, r. m., & baydas, o. (2017). an examination of undergraduates’ metacognitive strategies in pre-class asynchronous activity in a flipped classroom. educational technology research and development, 65(6), 1547-1567. https://doi.org/10.1007/s11423-017-9534-1 yu, f., & conway, a. (2012). mobile/smartphone use in higher education. proceedings of the 2012 southwest decision sciences institute, 831-839. https://doi.org/10.1177/2379298116689783 https://doi.org/10.20414/jtq.v14i1.20 https://doi.org/10.1088/1742-6596/1594/1/012047 https://doi.org/10.1088/1742-6596/1594/1/012047 https://doi.org/10.22460/infinity.v8i2.p199-208 https://doi.org/10.24331/ijere.517973 https://doi.org/10.46661/ijeri.4950 https://doi.org/10.1007/s11423-017-9534-1 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 9, no. 2, september 2020 e–issn 2460-9285 https://doi.org/10.22460/infinity.v9i2.p213-222 213 relationship between misconception and mathematical abstraction of geometry at junior high school gida kadarisma*, nelly fitriani, risma amelia insititut keguruan dan ilmu pendidikan siliwangi, indonesia article info abstract article history: received aug 21, 2020 revised sep 20, 2020 accepted sep 22, 2012 this study aims to examine the misconceptions that often occur in junior high school students on the concept of geometry based on abstraction level. the research method is qualitative with a case study design. subjects in this study are 27 students of the 3rd grade of junior high school students, who had to learn all the concepts that will be appeared on the test. material that will be given on the test of this research is the concept of triangle, quadrilateral, flat side geometry and curved side geometry. this research takes a place at one of the junior high schools in cimahi. the instrument in this study is a diagnostic test (to find out the types of students’ misconception), mathematical abstraction tests (to determine the level of abstraction) and interview rubrics. misconceptions produced by students are closely related to students’ mathematical abstractions, the higher the level of abstraction ability, the more students away from misconceptions. the topic taken in this study is the topic of basic geometry, the results can be a source of information about the types of misconception that often occur in students, and how the solution so that these misconception do not re-occur. keywords: abstraction, geometry, misconception copyright © 2019 ikip siliwangi. all rights reserved. corresponding author: gida kadarisma, departement of mathematics education, institut keguruan dan ilmu pendidikan siliwangi, jl. terusan jenderal sudirman, cimahi, west java 40526, indonesia. email: gidakadarisma@ikipsiliwangi.ac.id how to cite: kadarisma, g., fitriani, n., & amelia, r. (2020). relationship between misconception and mathematical abstraction of geometry at junior high school. infinity, 9(2), 213-222. 1. introduction geometry is a part of mathematics, geometry has an important role to several things, for instance by studying geometry, it will increase logical thinking and the ability to make proper generalizations; better understanding on arithmetic, algebra , and calculus; getting a further learning; accelerating the mental development of students (novita et al., 2018). but unfortunately, geometry is one the topic of mathematical which experiencing problems. the performance of students in geometry reportedly very bad and is already supposed to be a concern for teachers of mathematics, the parents and the government (adolphus, 2011). poor performance is indicated by the wrong answers that are often made by students. the types of error that are often made by students are very important to know, classify and examine the causes, so that learning can be more effective. based on this , https://doi.org/10.22460/infinity.v9i2.p213-222 kadarisma, fitriani, & amelia, relationship between misconception and mathematical … 214 researchers want to identify the type of error that made the students of junior high school and to investigate the possibility of the cause of the error, the reliable hypothesis emerge that the misconceptions is associated with the process of students’ abstraction. misconceptions is a mistake in understanding the concepts or errors in interpreting the concept meaning (ay, 2017). misconception can also be interpreted by the cognitive structure inherent in a person but deviates from the actual conception. misconceptions experienced by a person in learning mathematics will have a long impact on the subsequent understanding of mathematics. because concepts in mathematics are not solitary, but are interrelated with one another. one basic concept of mistake, will lead someone to make other mistakes (kadarisma, 2016). when someone is having misconception, it is different with what we called as "nescience". when a student experiences a misconception , in fact he has gone through the process of processing the information, only the way that might be wrong, some are memorizing immediately or some are wrong in interpreting so it leads to misconception. if the misconceptions happen during process of constructing the concept / structuring the cognitive experience , then the concept that is accepted will not be completely perfect and continuation for other concepts will be hampered. if it is not corrected immediately, it will become a serious problem. the process of constructing the concepts is a process of mathematical abstraction. so between these two things certainly have a close relationship. it can be concluded that if a person experiences a misconception, there is a problem in the abstraction process experiences problems or even does not have this ability. so as to avoid misconceptions happening to students, the abstraction process conducted by students must be improved/ developed. the ability of abstraction are in different levels from one to another or even there is student who does not have the ability. fitriani (2018) modifies the levels of abstraction and indicators based on research that has been done by (battista, 2007; goodson-espy, 1998; hong & kim, 2016; nurhasanah, 2018), among which are: perceptual abstraction/ level 1 (getting to know the properties of mathematical objects based on the use of physical objects, recognizing previous experiences related to the problem being faced); internalization/ level 2 (representing the results of thought in the form of mathematical symbols, words, pictures, or diagrams; interiorization/ level 3 (organizing (collecting, compiling, developing, and coordinating) concepts into new understanding or new knowledge), and second level of interiorization/ level 4 (generalizig new knowledge in a different context). based on this theory, students experiencing misconceptions do not have the ability to mathematical abstraction or perhaps at the level of beginner/ pre levels of abstraction. when that happens, students have a tendency to solve problems with routine procedures (hendriana, prahmana, & hidayat, 2018), so perhaps a teacher/ teaching materials do not facilitate students to do so, but tend to directly provide formulas and do not coordinate the concepts with one to another. misconceptions include understanding or thinking which is not based on true information (kusmaryono et al., 2020). according to dayanti, sugiatno, & nursangaji (2019), there are three types of misconceptions commonly done by students; classificational misconception, correlational misconceptions and theoretical misconceptions. researchers are interested in analyzing the extent of misconceptions experienced by students in terms of the level of abstraction. according to this, researchers can recommend things that are considered capable to avoid students from misconceptions. volume 9, no 2, september 2020, pp. 213-222 215 2. method the research method of this research is qualitative with a case study design. the research subjects in this study are 27 students of 3rd grade of junior high school who had learned all the concepts that would be presented in the test, namely the concept of triangles, quadrilateral, flat side geometry and curved side geometry. the location in this study is in one of the junior high schools in cimahi. the instrument in this study is set of question of diagnostic tests (to find out the types of difficulties that faced by students), mathematical abstraction tests (to determine the level of abstraction) and interview rubrics (as a form of data triangulation). the research procedures are: 1) students are given a test of mathematical abstraction (aims to find out the basic level of the students), 2) students are given a special diagnostic test on the topic of geometry that has been explain previously (aims to find out the types of misconceptions / errors that are faced by students) and conduct interviews with some students who experiencing misconceptions. data processing procedures: 1) analyzing the abstraction level of students, 2) examining the misconceptions of the students, 3) in depth analysis on the relation between the levels of abstraction and misconceptions done by students, 4) concluding the phenomenon. 3. results and discussion 3.1. results in this study, we obtained some data to be analyzed, including the percentage of students experiencing misconceptions based on their level of abstraction, (see table 1). table 1. level abstraction and types of misconceptions that are produced mathematical abstraction level misconception type (%) theoretical classification correlational level 1 (19 people) 55.56 62.96 70.37 level 2 (5 people) 7.41 3.70 level 3 (2 people) level 4 (1 person) based on table 1, it appears that the subjects in this study are divided into several levels of abstraction ability, ranging from level 1 to level 4. there are 4 students at level 3 and 1 student at level 4. these two level show a limited number of students; it happens because the characteristics of students taken are from students with a basic to average level of ability. students at levels 3 and 4 did not experience any misconception (see table 1). they managed to answer the diagnostic test well. students at levels 3 and 4 discover no errors in determining the elements in building space or getting up flat, they are also capable determine the relationship between concepts (between flat and shape geometry), and they are able to explain problems such as height in a triangle. in contrast to students at level 1, 55.56% of students experiencing theoretical misconception, 62.96% experiencing classificational misconception and the largest is 70.37% in a correlational misconception. we can say that, students at that level experienced a lot of misconceptions. while at level 2 there are those who experience misconceptions but kadarisma, fitriani, & amelia, relationship between misconception and mathematical … 216 the percentage is not significant. there is a suspicion that the higher level of students’ abstraction, the bigger possibility they will avoid any kind of misconception (see table 1). furthermore, the students’ error during the diagnostic test. researchers try to analyze several possible reasons for errors, the result of the analysis leads to the low ability of mathematical abstraction (see table 2). table 2. types of misconceptions and forms of errors committed by students types of misconceptions mistake made possible reason theoretical error in determining the formula for surface area and volume of space do not understanding the concepts of area and volume, students only memorizing the formulas. error in understanding some formulas for solid geometry confusion using formulas because they do not understand the concept of volume, do not understand the relationship between shapes, students only memorizing the formulas error determining height in triangle students do not understand high definition well and lack of mastery of prerequisite material mistakenly determined edge on brsl does not have well understanding on the definition of edge, has weak spatial ability mistakenly determine the diagonal plane and the diagonal plane on the cube has weak spatial ability classification student error in classifying the types of triangles incomplete understanding of the concept correlational error in determining the relationship between the concept of prism with the concept of a cube, cuboid, or cylinder low ability to visualize, low ability to construct mathematical ideas error in determining the relationship between the concept of the pyramid with the concept of cones low ability to visualize, low ability construct mathematical ideas error in determining the relationship between quadrilateral shapes low able to visualize the following will examine some of the results of errors that have been made by students. first is classificational misconception, it happens first because students are not volume 9, no 2, september 2020, pp. 213-222 217 able to classify the types of triangles. if they being asked the types of triangles, students were only able to answer the isosceles triangle, right triangle, equilateral triangle, and scalene triangle. as shown in the sample of student’s answers in figure 1. figure 1. sample of student’s answers figure 1 show that an example of the answers of students who experience classificational misconceptions. students cannot answer the types of triangles thoroughly. when teaching concepts about triangles, both the teacher and the textbook convey the concepts separately. begin with the concept of equilateral triangle, isosceles triangle and scalene triangles, then focus on formulas to find area and circumference. after that, the review a little about the triangle based on the angle is given. this has become less balanced. everything is given directly by the teacher and textbooks, not through the use of physical objects, and students are not given the opportunity to represent their observasion. so that the form of coordination between concepts is definitely not happening. students do not experience a process of abstraction in finding the concept and experiencing a classificational misconception. furthermore, in the term of theoretical conception, students experience confusion in determining the height of a triangle if they are asked about the area of a triangle, as in figure 2. figure 2. sample of student’s answers students experience misconceptions when working on these problems. generally, they know that the concept of height in the triangle is a vertical line from the top to the base, there they do not understand the definition of height in depth (see figure 2). if student examines the diagnostic problem that is given well, then the number shown will be triple phytagoras, so that between the shortest sides forming an angle of 900 means that there is a concept of base and height to determine the area of a triangle. students experiencing other theoretical misconceptions and correlational misconceptions, this includes errors in explaining mathematical facts and also connecting concepts with one another (see figure 3). kadarisma, fitriani, & amelia, relationship between misconception and mathematical … 218 figure 3. sample of student’s answers figure 3 show that students experience confusion in using the formula between the area of surface and the volume of solid geometry. in addition, students also feeling confuse in using the formulas of volume of solid geometry in solving a given problem. they have difficulty in memorizing all of these formulas, the demands given require students to memorize everything (not to understand it). this is reinforced by the results of the interview with one of the students (s1), following the interview excerpts conducted. .............................................. t : can you solve the problem? s1 : sure ma'am, it just sometimes i forgot the formula, hehehe ... t : why is that? s1 : there are so many formulas, sometimes it is like being switched, even i already memorizing it. .............................................. students do this is caused by several factors, one of which is that teachers teach concepts directly and the target of their learning is students must be able to work on the problems given. the books are used is also have a similar objective, the books contain a formula that ends with exercises. both the teacher and the book that were designed, were only oriented towards the final results/ final test, and paid little attention to the occurrence of the concept formation. in addition, the material conveyed tends to stand solitarily, not connected one to another, students do not recognize that the cube, cuboid, even the cylinder is included in the prism. pyramid and cone was never be related one another. when students are asked whether a square is a rectangle, whether a rectangle is a parallelogram, whether the rhombus is a parallelogram, students generally answer no. this has triggered the emergence of correlational misconceptions. students' understanding that they all stand alone (have each formula which is different and not related to each other (not have interconnected concepts). this is reinforced by the results of interviews with other students who experienced misconceptions (s2), following is part the interview: .............................................. t : why do you think that formulas of volume of the shape are many? s2 : yes there are indeed many, there are cube volumes, there are cuboid volumes, there are prism bolts, not to mention area of the square, the area of rhombus and others, it make me dizzy, it is too many and it so hard to memorize t : do the shapes you mentioned earlier have different formulas? s2 : obviously different, ma'am, so i have difficulty in memorizing it t : is there no relation between formula one and the other formula? s2 : there is no ma'am volume 9, no 2, september 2020, pp. 213-222 219 t : are there the same properties between one shape and another, for example a square with rectangle? s2 : (students just being quite and look confused ...) .............................................. 3.2. discussion the results showed that there were students from various levels of abstraction who experienced different misunderstandings (see table 1 and table 2). as the level rises, students generally do not experience significant misconceptions. these results are in line with research conducted by fitriani, suryadi, & darhim (2018) that the low mathematical abstraction ability of junior high school students is highly correlated with the level of mathematical ability that is indeed in the lower category, so that the tendency when the level of abstraction is medium or low, they more often experience mathematical misconceptions. furthermore, researchers have described several types of errors that have been made by students when working on diagnostic test. the types of error made are categorized based on the types of misconceptions that have been mentioned previously, the errors generated are in line with the results of research conducted by ozerem (2012). based on the diagnostic tests, it turns out students at the low level of abstraction experience these 3 types of misconceptions; theoretical, correlational, and classificational misconceptions. first is classificational misconception, this misconception happen because students are not able to classify the types of triangles. generally, students answer the teacher's question about the types of triangles, but the answers they give are less comprehensive. these results are in line with research that has been done by sanapiah & juliangkary (2017), that the understanding of the concept of a triangle of students have not fulfilled in the stages of classifying the types of triangles. after analyzing the textbooks and conducting the classroom observations, it turns out that learning designs that happen is not using a physical objects, and students are not given the opportunity to represent themselves about what they observed, then the material structure is not proportional. so that the form of coordination between concepts is definitely not happening. students do not experience an abstraction process in discovering the concept and experience a classificational misconception. then students experience theoretical misconceptions, they experience confusion when determining the height of a triangle when being asked about the area of a triangle. the results of these students' answers are in line with the results of research conducted by hutagalung, mulyana, & pangaribuan (2020). this misconception occurs to students, because in general they are usually given examples of routine problems. students are never got a good definition, they are never get the opportunity to construct a definition. students are only given an explanation, which includes the height or base of a triangle through basic examples. submission of concepts is very much avoided from the process of abstraction, students are not invited to recall previous experiences relating to the concept of phytagoras and their properties which can further strengthen the concept of the base and height of the triangle, the instructional process avoids direct physical observation, students are not directed to represent what is observed in a geometrical drawing, and at the end, students are not able to coordinate the concept of phytagoras with the height / base of the triangle so that they experience a classificational misconception to solve the area of the triangle. students experience other theoretical misconceptions and correlational misconceptions, this includes errors in explaining mathematical facts and also connecting kadarisma, fitriani, & amelia, relationship between misconception and mathematical … 220 concepts with one another. students experience misconceptions because they have to memorize all formula of geometry. there are several incorrect orientations. the process of abstraction in geometry is not happen. according to syahbana (2013), the volume of a geometry can be recognized by tracing the shape of the base. in essence, a geometrical structure derives from the broad structure of the base which forms the height of the geometric structure. if there are other irregular spaces, try to form a sketch so that the shape of the base can be recognized. assuming that this geometry has undergone a transformation in form from its normal form, it is necessary to trace which shape is the base and determine which height. with this process of abstraction, the learning to convey the concept of the volume of geometry will avoid misconceptions. the material conveyed by the teacher regarding rectangular also about geometry should be designed to be interconnected, when the teacher designs learning well, the learning objectives will be achieved (kadarisma et al., 2019), so students do not experience confusion in constructing concepts, and the coordination between concepts will be built up, the abstraction process is very instrumental in it. if this is applied, the students of geometry ability will be better and students will not face misconceptions. from the analysis, we can see some factors that ultimately make students experience misconceptions. based on this, it appears that students are very isolaeded from the process of abstraction. to overcome this, students should be directed to be able to recognize the properties of geometry by using physical objects or discover it directly, then students must re-know previous experiences related to the concept being faced (for example when studying space construction, review back to the concept of a flat build, the concept of congruence, the concept of alignment, etc.), do not let the students have limited understanding about the prerequisite material. furthermore, students must be able to represent the results of their thoughts / observations in the form of drawings (specifically geometry), lest students only see, without being able to pour what they see, as a form of analysis carried out on the results of their observations. when drawing, students indirectly do mathematical modeling, students feel which parts of the structure are congruent and analyze the properties of the observations as outlined. next, students is asked to construct the concept of construction process (put it in the student worksheet), then direct students to be able to develop what they have captured (can be by giving other cases or open ended cases), and coordinating other concepts that similar so that they become a new understanding or new knowledge that is more comprehensive. based on the data obtained, it appears that students who experience misconceptions are students who come from the lowest level of abstraction. for students with high levels of abstraction, they generally do not experience misconceptions. visible relationship between the two, then it becomes a recommendation for researchers so that the process of abstraction occurs to students, thus avoiding students from misconceptions. in order for students to have good mathematical skills, the mathematics teacher as a supporting factor must also have good mathematical skills (hidayat, 2017). in addition, this abstraction process is closely related to the level of students’ geometrical thinking, the abstraction process that is sharpened makes students develop a level of geometrical thinking so students are expected to have a higher level of knowledge in geometry and certainly avoid misconceptions. 4. conclusion based on research that has been done, it can be concluded that students experience various types of misconceptions. having analyzed that occur on student misconceptions are closely linked to the ability of abstraction that is owned by the students where the better the volume 9, no 2, september 2020, pp. 213-222 221 ability of abstraction, the more students are protected from misconception. the topic taken in this research is the topic of basic geometry, the results can be a source of information for middle school teachers about the types of errors that often occur in students. references adolphus, t. 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(2020). ontological misconception in mathematics teaching in elementary schools. infinity journal, 9(1), 15–30. https://doi.org/10.22460/infinity.v9i1.p15-30 novita, r., prahmana, r. c. i., fajri, n., & putra, m. (2018). penyebab kesulitan belajar geometri dimensi tiga. jurnal riset pendidikan matematika, 5(1), 18-29. https://doi.org/10.21831/jrpm.v5i1.16836 nurhasanah, f. (2018). mathematical abstraction of pre-service mathematics teachers in learning non-conventional mathematics concepts. bandung: universitas pendidikan indonesia. ozerem, a. (2012). misconceptions in geometry and suggested solutions for seventh grade students. procedia social and behavioral sciences, 55, 720–729. https://doi.org/10.1016/j.sbspro.2012.09.557 sanapiah, & juliangkary, e. (2017). profil pemahaman konsep mahasiswa ditinjau berdasarkan pengalaman belajar segitiga. elpsa conference, 1(1), 96–105. syahbana, a. (2013). alternatif pemahaman konsep umum volume suatu bangun ruang. edumatica, 3(2), 1-7. https://doi.org/10.22460/infinity.v9i1.p15-30 https://doi.org/10.21831/jrpm.v5i1.16836 http://repository.upi.edu/49513/ http://repository.upi.edu/49513/ http://repository.upi.edu/49513/ https://doi.org/10.1016/j.sbspro.2012.09.557 http://elpsa.org/proceeding/index.php/ec17/article/view/10 http://elpsa.org/proceeding/index.php/ec17/article/view/10 https://online-journal.unja.ac.id/edumatica/article/view/2662 https://online-journal.unja.ac.id/edumatica/article/view/2662 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 10, no. 1, february 2021 e–issn 2460-9285 https://doi.org/10.22460/infinity.v10i1.p81-92 81 fraction cipher: a way to enhance student ability in addition and subtraction fraction mohd afifi bahurudin setambah1*, anis norma jaafar1, mohammad ikhwan mat saad1, mohd faiz mohd yaakob2 1sultan idris education university, tanjong malim, perak, malaysia 2universiti utara malaysia university, sintok, kedah, malaysia article info abstract article history: received jan 7, 2021 revised jan 15, 2021 accepted jan 16, 2021 learning the concept of fractions can be one of the most difficult skills to master for primary school students. fractions are also seen to affect other mathematical knowledge, such as algebra. researchers have introduced an innovation called fraction cipher to help students learn fractions. fraction cipher is an innovation in the arena of education that involves learning the malay language and mathematics. design research is used as the research method to solve this problem consisting of three phases: preliminary design, teaching experiment, and retrospective analysis. the instruments used are fraction cipher, fraction test, and observation checklist. the results of the pair's comparative study by controlling the type i error using the bonferroni method show that the mean values of the mathematical achievement of the experimental group and the control group are significantly different. the results show that fraction cipher impacts students to understand and master the concept of fractional addition and fraction subtraction operations. this research also explains the "sake-beda" strategy to make it easier for students to solve fractional operation problems. besides, this study also shows the change in students' attitudes from negative to more positive. thus, students understand and are more motivated to learn the concept of fractions. keywords: design research, fraction, fraction addition, fraction subtraction, mathematics education copyright © 2021 ikip siliwangi. all rights reserved. corresponding author: mohd afifi bahurudin setambah, faculty of human development sultan idris education university, 35900 tanjong malim, perak, malaysia email: mohdafifi@fpm.upsi.edu.my how to cite: setambah, m. a. b., jaafar, a. n., saad, m. i. m., & yaakob, m. f. m. (2021). fraction cipher: a way to enhance student ability in addition and subtraction fraction. infinity, 10(1), 81-92. 1. introduction mathematics is an appropriate instrument used to develop individual intellectual proficiency. among the aspects that need to be developed are logical reasoning, spatial visualization, analysis and abstract thinking of students. this can be done when they learn numeracy, reasoning, thinking and problem solving skills through learning mathematics (malaysia education ministry, 2014). there are various mathematical topics that students learn from year 1 to year 6. these topics form the basis of their future mathematical development. among the topics they studied were numbers and operations, measurements and geometry, relationships and algebra, statistics and algebra (malaysia education https://doi.org/10.22460/infinity.v10i1.p81-92 setambah, jaafar, saad, & yaakob, fraction cipher: a way to enhance student ability … 82 ministry, 2014). within those topics, there are smaller subtopics. for example the topics of numbers and operations contain smaller subtopics such as whole numbers, fractions, decimals, percentages and money. therefore, this study only focuses on fractions. fractions have been seen as numbers that have unique properties compared to whole numbers that students have learned before. the uniqueness of its nature has made it difficult to understand (braithwaite et al., 2018). this topic often occurs, there are four things that students often do when answering addition and subtraction fraction operation questions, namely systematic errors, random errors, negligence errors and not knowing how to answer fraction questions (braithwaite et al., 2018; loc et al., 2017; purnomo et al., 2019; salleh et al., 2013; saparwadi et al., 2017; tian & siegler, 2017). learning the concept of fractions can be one of the most difficult skills to master for elementary school students (gaetano, 2014; nurhani et al., 2018). fractions are also seen to affect other mathematical knowledge such as algebra. this in turn will affect mathematic achievement (siegler & lortie-forgues, 2015). if viewed over a long period of time, such knowledge will also affect their mathematical ability in high school (siegler & pyke, 2013). this is necessary and can be overcome through the teaching and learning process. one of the aspects that can improve students' understanding is through the use of effective teaching aids (noh et al., 2016; rohaeti et al., 2020). therefore, innovation and transformation must be done through the development and construction of teaching aids. the use of teaching aids is very important so that teachers can explain things more accurately and clearly compared to oral explanations only. this can ensure that the delivery of teaching and learning can be implemented more effectively (noh et al., 2016; rohaeti et al., 2020). the need to develop these teaching aids is very significant as described by jones et al. (2011) and mcneil and jarvin (2007). the use of aids can change the teaching and learning methods of the teacher for the better and give internal motivation to students to learn something (gaetano, 2014). there are several teaching methods of teachers that are often practiced by mathematics teachers in order to cultivate effective teaching and learning practices. among them are lecture methods (oral teaching and presentation of materials), discussions, inquiry methods, problem based methods, cooperative learning, project methods (idris, 2005; mok, 1993; setambah, 2017). however, teachers still maintain teaching practice with the method of reviewing training answers, lectures and individual exercises while conducting math classes. this is because they are more focused on improving academic achievement (koh et al., 2008; mariani & ismail, 2013). teachers are also said to still practice teacher-centered methods as informants and demonstrators, while students as observers and recipients of knowledge (bahuruddin et al., 2016). for the teaching and learning of mathematics, there are seven frequently used math teacher teaching practices. two of the seven practices are practiced by most teachers, namely the emphasis on understanding the concept and use of the polya model in teaching and learning. in addition, teachers also often use appropriate examples when explaining a mathematical topic. the use of easy-to-understand mathematical terms as well as existing materials has become commonplace by mathematics teachers. there are also teachers who use mind maps such as i-think and heuristic models during their teaching and learning sessions. some of them also take into account the factors of students' abilities when planning their teaching and learning sessions. according to idris (2005), there are several factors that hinder the learning of mathematics namely mind set (mind set), less effective drills, memorization before comprehension, less active student involvement, undiagnostic student doubts and unchallenged training. this has become the practice of mathematics teachers and has been identified by him while conducting research. in conclusion, the researcher would like to emphasize that the teaching practices presented are based on several surveys conducted by researchers, especially the teaching and volume 10, no 1, february 2021, pp. 81-92 83 learning practices of mathematics. therefore, teachers are expected to make transformations and reforms in order to practice teaching and learning practices that cultivate skills and increase the added value of human capital. this can be started by building the right teaching and learning materials. innovative materials are able to give a better effect. the effect of the material being built should be tested for its effectiveness. therefore, this study aims to identify the effects of fraction cipher (fc) to improve mathematical achievement for fraction topics. fraction cipher (fc) (figure 1) is an innovation in the arena of education that involves learning the malay language and mathematics. this absorption element is an incentive proposed by the ministry of education malaysia. fc is a combination of fraction and cipher words. the fraction is a topic chosen for improvement. cipher is a key code used by a person for the purpose of conveying information in secret (yeoh et al., 2015). the combination of these two words forms fc. the integration is carried out so that the concept of numerical mathematics familiar with malay. it can improve students' vocabulary related to malay although fc is specially developed for fractions in math. this is very well done because it can combine two subjects in one material. in other words, fc is a teaching aid that takes into account cross-curricular elements as recommended (malaysia education ministry, 2014). fc is a teaching aid in the form of board that contains the hidden words. each board contains a specific theme. students are required to find the hidden words in the fc board. next the word is converted into fraction number form as in the given guide. students are required to solve the fraction question using the concept of "sake beda". the group that successfully completes all the questions will move on to the next station. fraction reinforcement process for repeated fc use by station until students successfully complete all fc themes. this teaching process begins with forming a group of students. the concept of adventure-based teaching (explore race) is used where students will move according to the checkpoint. for example; figure 1. fraction cipher fc needs to be practiced using a fun learning method in order to further enhance its effectiveness through the application of the concept of gamification. gamification is meant to combine teaching and learning fractions in math operations and the strengthening of malay vocabulary through crossword puzzle game version of the cryptographic code. j a l a n setambah, jaafar, saad, & yaakob, fraction cipher: a way to enhance student ability … 84 according to huang and soman (2013), gamification is a craft that produces the fun and addictive elements found in games and uses them for everyday life activities. this will help teachers attract the interest and attention of students towards the teaching and learning sessions delivered. gamification refers to the application of game design elements to nongame activities and has been used for a variety of contexts including education (nah et al., 2014). fc holds that the concept of learning mathematics should involve fun activities, interest in things enjoyed, students be actively involved, and involve daily life. four of the six elements suggested by bahuruddin et al. (2016) and setambah et al. (2019) were applied during the construction of fc. this concept of gamification was chosen because of its good effect on improving student learning (pradhana & latifah, 2013) in particular the improvement of vocabulary and fraction knowledge of students. apart from that, fc also uses a fun learning method which is adventure based learning (abl). through a review of the literature that has been made, this method is rarely carried out for the purpose of learning the malay language and mathematics. this abl method was selected based on proven impact based on studies that can produce a student who is competitive, able to lead, improve communication skills, and help strengthen students' critical thinking skills. this method also coincides with 21st century learning methods (bahuruddin et al., 2016). this innovation also emphasizes the concept of "sake beda". the word sake refers to "sama=equal means permanent" while the word beda refers to "beza=difference mean multiply". this technique is a very important element in solving the problem of fractional basic operations among primary school students. in addition, students will also be able to add english vocabulary through this game indirectly. for example, among the words supplied such as transitive verbs are buy, give and many more. the word supplied refers to the theme of each game set. it is thus able to improve students' knowledge of the malay language. in conclusion, fc is a teaching aid development project that emphasizes some important elements. first, it involves a combination of mathematics and the malay language. second, applying the concept of gamification in order to increase the interest of students. third, use the abl method during teaching and learning. fc provides a more engaging learning environment when it incorporates two curriculum elements. fc also provides unique game learning methods that form a deep interest and motivate students. fc also forms a collaboration between students to think to complete assignments. fc emphasizes the concept of adherence to time while learning as well as emphasizing the element of discipline during learning. finally, emphasize the concept of "sake beda" while performing fraction addition and subtraction operations. therefore, it is hoped that fc will be able to give implications to students in order to improve the addition and subtraction operations for fraction topics. fc is expected to be able to impact the human capital aspects of students, especially thinking skills and leadership skills. however, this study focuses on mathematical achievement for fraction topics only. 2. method design research is used as a research method. the design research consists of three main phases namely experimental preparation, design experimental, and retrospective analysis (aris et al., 2017; gravemeijer & cobb, 2006). there are two important aspects related to design research namely hypothetical learning trajectory (hlt) and local instruction theory (lit). learning activities as a learning path taken by students in learning activities they must have hlt and lit. hlt consists of three components (hendriana et al., 2019). volume 10, no 1, february 2021, pp. 81-92 85 in the first phase, the researcher conducted a content analysis for fraction topics. in addition, the researcher also set the objectives and purpose of teaching fractions. then, determine the material to be used, concepts to be applied, teaching methods to be used and discuss the development of interventions to solve problems. besides that, researchers also review the results of student training, teacher teaching sessions, and assessments instrument used by teachers. researchers have also interviewed teachers to help with problems that arise. after identifying all of these, a fc was developed for use in the second phase. in the second phase, the researchers tested the fraction cipher with the help of a teacher and 8 students. a run test was performed as required by the researcher. the running test involves the process of improving the fc, the teaching period to be carried out, the method chosen during the use of fc. the results of the first round test were used for the purpose of improvement in the second round experiment. researchers have found that teaching takes a long time because students are slow to find words on fc. second, the concept of the fraction cannot be properly applied. third, the process of teaching and learning journeys seems unsystematic during activities. this has been overcome by setting the time of each fraction cipher and more marks are given if students can give the most and fastest answers. researchers also introduced the concept of "sake-beda" to facilitate students to implement the process of addition and subtraction of fractions. sake means “sama-kekal refer to equal value of the denominator value”, so that the value of the denominator is permanent. beda mean “beza=darab different denominator value”, so student needs to multiply each other or make the denominator to equal value. next, the researchers have arranged the student movement system according to a predetermined fc theme. linear and rotation systems are used during student movement. for example, fc a will change to fc b, fc b will change to fc c, fc c will change to fc d. eventually fc d will change to fc a. this system can help launch teaching and learning sessions using fc. after improvements were made, the second experiment was carried out smoothly. in the third phase, all data implemented during the experimental process were collected and analyzed. analysis using descriptive statistics and inferences using statistical package for the social sciences (spss) software. thus, the findings can answer the research questions and fulfill the purpose of the study that has been formed. the intervention (figure 2) was carried out on 30 students in which 2 groups were formed namely 15 experimental groups and 15 control groups. the experimental group was given a fraction cipher while the treatment group was given a conventional learning method. students are selected based on using cluster techniques based on the following procedures: (a) write the name of the class on a piece of paper; (b) the paper is put in a box; (c) one paper is randomly drawn; (d) the class name listed is used as a sample; (e) students who are in the class are used as a study sample. there are the differences between the fraction cipher learning method and the conventional method are as follows: (a) teaching and learning across the curriculum for mathematics and malay language for the experimental group, while the control group only learning math; (b) learning uses fc teaching aids for experimental groups, while conventional groups do not involve fc; (c) using adventure-based learning methods (bahuruddin et al., 2016) for experimental group, control group using lecture, drill and teacher-centered methods. setambah, jaafar, saad, & yaakob, fraction cipher: a way to enhance student ability … 86 figure 2. implementation of fraction cipher intervention pre-tests were given before the intervention and post-tests were given after the intervention. observation sessions were also conducted before and after the intervention. students for the experimental group were divided into four groups. each group is given a different fc theme. students are given 15 minutes to find the hidden words on fc board. when they have finished finding the word, students need to decipher the word based on color. each color found in fc represents a fractional value. for example, the color yellow represents value ½. red represents value 0. students are then asked to sum up or subtract fractions depending on the decipher they do. the concept of "sake beda" is used during the process of addition and fraction breakdown. students are given marks based on the number of hidden words found and the implementation of correct and accurate addition and subtraction operations. this intervention process was carried out repeatedly using fc for 4 weeks. this means that students are given interventions during that period. 3. results and discussion the learning that is implemented is to overcome the problem of students who have problems in addition and subtraction of fractions. the study began with a review and observation of the students. when investigated the main cause of their errors is lack of understanding of the process involved, difficulty in subtracting fractions, difficulty converting fractions to the same denominator, errors in calculations, difficulty converting volume 10, no 1, february 2021, pp. 81-92 87 improper fractions to mixed numbers and using incorrect processes. students' errors in the process of adding fractions are shown through figure 3. this occurs when misconceptions occur from one concept to another. students found to have brought the concept of operations of addition of whole numbers to the addition topic fraction. this can be seen through the answers to questions 1, 2, 3, 4, 6, 7 and 8 that students provide. they were found to add numerators and numerators, as well as denominators and denominators. this clearly shows that a misconception has happened to them. the same thing happens when researchers review student exercises in subtraction operation. this review is similar to the study that has been conducted by salleh et al. (2013). the results should include the rationale or design of the experiments as well as the results of the experiments. results can be presented in figures, tables, and text. figure 3. student error on the process of addition of fractions when the researchers reflect back, the researchers also found that the methods that the researchers implemented during the teaching and learning sessions did not have a positive impact on them. researchers simply use examples and write step-by-step operations of addition and subtraction fractions without the help of teaching aids. this can be seen in the effect when researchers often find that students always complain of misunderstanding, re-ask the process of addition and subtraction of fractions this can be recorded through the expression of their words such as "i do not understand the teacher", "then how is the teacher", "ouch, why cannot be like that teacher". this proves that they often rely on the teacher’s answers and no longer understand the concepts that have been taught by their teacher. findings show that students have an improvement in their learning for the topic of addition and subtraction of fractions. these findings can be seen through figure 4. significant improvement can be seen through students 4, students 5, students 7, students 8 and students 15. this shows that fc is able to have a good impact on students. the findings setambah, jaafar, saad, & yaakob, fraction cipher: a way to enhance student ability … 88 of this study are in line with the study aris et al. (2017) that the intervention process enhances student interest is able to have a positive impact on student mathematical achievement. figure 4. differences of pre-test and post-test of experimental group comparisons between the experimental group and the control group were also performed through t-test. the findings show that there is a significant difference [f(1,28)=4.61, p<0.05] with large effect size based on value partial eta square = 0.141 (cohen et al., 2007). the mean of the experimental group was higher than that of the control group. the results of the comparative analysis of the pair by controlling the type i error using the bonferroni method show that the mean values of the mathematical achievement of the experimental group and the control group are significantly different (mean difference = 4.2, p<0.05). the results of this study further strengthen the findings of the study of noh et al. (2016) which shows that innovative teaching aids can have an impact on student achievement. observation findings also indicate a change in good behavior. this study coincides with the study of jones et al. (2011) and mcneil and jarvin (2007) when fc had a positive impact on student attitudes. before the intervention is performed. students were found to exhibit negative behaviors such as (1) talking unrelated to the topic, (2) thinking elsewhere (chestnuts), (3) walking from one place to another, (4) doing other work, (5) interrupting other students physically, (6) try to attract attention, (7) sharpen a pencil and (8) leave the classroom. after the intervention is implemented, negative behavior can be reduced from 40% to 10%. this can be seen more clearly through the observation table made by the researcher. table 1 shows the observations that were made before the intervention was performed. for example, student 1, negative behavior is reduced to 10%. student 2 reduced by 20%. volume 10, no 1, february 2021, pp. 81-92 89 table 1. observation of student behavior student observation percentage 1 2 3 4 5 6 7 8 9 10 1 3 4 3 8 40% 2 2 2 2 30% 3 2 1 4 4 40% 4 1 1 4 4 40% 5 7 4 4 30% 6 6 10% 7 5 10% 8 1 5 5 30% 9 1 1 1 1 8 1 60% 10 1 10% 11 3 7 2 30% 12 1 2 2 30% 13 3 3 5 30% 14 1 10% 15 2 3 20% researchers also conducted interviews on teachers who had been exposed to fc (figure 5). figure 5. discussion with mathematics teacher the results of interviews with teachers found that fc has attracted their interest. they think that fc is a good innovation. they also stated that fc is able to give them a difference in terms of teaching and learning. fc changed the teacher-centered approach to the student setambah, jaafar, saad, & yaakob, fraction cipher: a way to enhance student ability … 90 centered approach. they feel excited and want to use fc in their teaching and learning. teaching aids give a good impact on teaching methods. thus, fc gives a good perception on teachers and students. fc is seen to have a good impact on students (noh et al., 2016). 4. conclusion learning operations of addition and subtraction of fractions using the fc have a positive impact on students in terms of understanding, interest and motivation. this study also proves that the construction of mathematical concepts is not seen as something that needs to be moved passively, but rather needs to be built by students actively through concrete experience. in general, this study successfully solves the problem of student learning from the aspect of fractions, especially in addition and subtraction operations. through this fc-based learning, it is hoped that the six mistakes that students often make while completing the addition and subtraction operations of fractions can also be reduced. such errors are such as lack of understanding of the process involved, difficulty in converting to the same denominator before performing addition operations, errors in calculation, and difficulty in converting improper fractions to mixed numbers. fc is expected to have positive implications on the mission and aspirations of malaysian education. fc is seen to have other potentials such as providing more enjoyable teaching and learning methods for teachers, providing useful experiences to students, enhancing student cooperation during group activities, improving student concentration style to find words, changing student character to be punctual and disciplined according to game rules and improve thinking skills through reasoning. future studies can be conducted to determine these various aspects. references aris, r. m., putri, r. i. i., & susanti, e. 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(2015). aplikasi matematik. bangi: pelangi professional publishing sdn. bhd. https://doi.org/10.33474/jpm.v3i2.715 https://doi.org/10.1037/edu0000025 https://doi.org/10.1037/a0031200 https://doi.org/10.1177/0022219416662032 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 10, no. 1, february 2021 e–issn 2460-9285 https://doi.org/10.22460/infinity.v10i1.p109-120 109 pre service teachers’ perception on the implementation of project based learning in mathematic class marah doly nasution1, ahmad*2, zulkifley mohamed3 1universitas muhammadiyah sumatera utara, indonesia 2universitas muhammadiyah purwokerto, indonesia 3sultan idris education university, malaysia article info abstract article history: received nov 6, 2020 revised jan 16, 2021 accepted jan 18, 2021 project-based learning is one of the 21st-century methods that can increase the students' ability to have useful competence in their knowledge, especially in learning mathematic. hence, the teachers' perception of the implementation of pbl is essential to know. the purpose of this study was to determine student perceptions about the application of project-based learning models. this research is a survey research with a quantitative descriptive approach. the samples used in this study amounted to 63 students of the sixth semester in the department of mathematical education, muhammadiyah university north sumatra. the data collection technique used a questionnaire. the data analysis technique consists of quantitative analysis techniques with a statistical approach. the results of this study indicate that: (1) the students' perceptions of the interaction aspects of students and teachers are in the very good category with a mean score of 85.32%. (2) students' perceptions of motivation / increasing student interest in learning are in the very high category, with an average score of 85.53%. (3) students' perceptions on the competency aspect of understanding subject matter are in the very good category with an average score of 85.48%. (4) students' perceptions of the competency aspects of critical, effective, and efficient thinking are in the category of strongly agree with a mean score of 82.62%. (5) students' perceptions of good time management competence are in the good category with an average score of 79.10%. (6) students' perceptions of good student learning outcomes are in the very good category, with a mean score of 82.67%. (7) students' perceptions of the learning model's conformity aspect with subject characteristics are in the very high category with a mean score of 84.05%. keywords: mathematics education, pre service teacher, project based learning copyright © 2021 ikip siliwangi. all rights reserved. corresponding author: ahmad, department of mathematics education universitas muhammadiyah purwokerto, jl. kh. ahmad dahlan, kembaran, banyumas, central java 53182, indonesia email: ahmad@ump.ac.id how to cite: nasution, m. d., ahmad, a., & mohamed, z. (2021). pre service teachers’ perception on the implementation of project based learning in mathematic class. infinity, 10(1), 109-120. 1. introduction teachers are expected to be able to choose and use learning strategies in accordance with the material to be delivered (english & kitsantas, 2013). every learning strategy has https://doi.org/10.22460/infinity.v10i1.p109-120 nasution, ahmad, & mohamed, pre service teachers’ perception on the implementation … 110 strengths and weaknesses seen from various angles, but in essence any learning strategies, method or model used must have clear objectives to be achieved (kurzel & rath, 2007). because students have very heterogeneous interests, ideally a teacher should use a multimethod, that is, varying the use of the learning model used in the classroom. this is intended to avoid boredom experienced by students (tamim & grant, 2013). in this process, students use all their basic abilities and knowledges to obtain information and the learning outcomes they get. students try to find out and solve solutions to any existing problems (amamou & cheniti-belcadhi, 2018). so that students get experience and knowledge that are truly meaningful, not only learning outcomes in terms of values. project-based learning (pbl) is a learning model that is conceptualized on a process, timed, problem-focused, meaningful learning unit by integrating concepts from a number of components of knowledge, discipline and collaborative learning activities. so that in its implementation the teachers act as a facilitator whose task is to help provide experience for students in designing problem solving related to the subject matter (efstratia, 2014). students are expected to be able to interact with teachers and study groups to find solutions of the problems (van rooij, 2009). pbl contains project-based complex tasks based on the questions and problems that are very challenging, and requires students to design, solve problems, make decisions, carry out investigative activities, well as provide the opportunity for students to work independently. the goal is that students have independence in completing the tasks they face (barron et al., 1998). in the implementation of learning, pbl teachers pose problems in the form of sheets student activities then students carry out activities to complete problems and teachers oversee student performance (amamou & cheniti-belcadhi, 2018). when finished, one of the students representing the group presented the results of the discussion in front of the group then asked each other questions. the teacher leads the class discussion. this shows that with the pbl model students can develop conceptual understanding, procedural skills, ways of thinking of launching a related problem so that they can understand the problem setting and find out the next steps to take through discussion (sart, 2014). as a result of the discussion, students will become more skilled at using ideas and techniques that produce experiences of the problems at hand (anazifa & djukri, 2017). this research tried to explore more deeply the teachers’ perception about using pbl. the deep analysis by exploring the previous research and the current literature review enrich the novelty of this research. the reasons in conducting this research know the teacher’s perception on pbl model will give a new paradigm on how to use pbl in teaching and learning process, especially in learning mathematic, thus the possession of this research is very important for futher research the same topic. based on the considerations of the thoughts and problems, the researcher took the title "pre service teachers’ perception on the implementation of project based learning in mathematic class”. 2. method the type of research used is a survey with a quantitative descriptive approach, where the phenomena to be studied are events that have passed or are ongoing (design-based research collective, 2003). the procedure of the research follows the scientific model of descriptive analysis in which it is conducted using some stages, namely: deciding the best model of research, selecting the suitable respondents, creating and validating the instrument and doing the scientific analysis methods to guarantee the output of this research. this type selected for this study intends to reveal how the process of applying and perceptions of students about the model of project-based learning (project-based learning) in mathematics volume 10, no 1, february 2021, pp. 109-120 111 samples used in this study amounted to 63 respondents student 6th semester mathematics education, university of muhammadiyah sumatra utara. in collecting information about student perceptions, researchers used a questionnaire in the form of a closed questionnaire with alternative answers given to the indicators, namely strongly agree, agree, disagree), and strongly disagree. there are 7 indicators used to measure student perceptions with a total of 30 questions (see table 1). table 1. research instrument grid of project-based learning in mathematics indicator item number total number 1. interaction aspects students and teachers 1, 2, 3, 4, 5 5 2. ability to motivate / increase interest student learning 6, 7, 8, 9 4 3. understanding the subject matter 10, 11, 12, 13, 14 5 4. emerging think critically, effectively and efficiently 15, 16, 17,18, 19 5 5. effective time management 20, 21, 22 3 6. student learning outcomes 23, 24, 25 3 7. the suitability of the application of the learning model with subject characteristics 26, 27, 28, 29, 30 5 number of questions / statements 30 descriptive statistical analysis, including mean price, standard deviation, median value, mode, range, highest score, lowest score and frequency distribution were used for each research variable / indicator. 3. results and discussion in this research, there are 7 indicators that can measure the success of implementing the project-based learning model. the following is an analysis of the results of research on student perceptions about the application of project-based learning in subjects (see table 2). table 2. results of analysis of students' perceptions indicator percentage category student perceptions in terms of student and teachers interaction aspects 85.32% very good student perceptions in terms of motivation / increase student learning interest 83.53% very good perception of subject matter 85.48% very high student perceptions are reviewed from critical, effective and efficient thinking competencies 82.62% very good nasution, ahmad, & mohamed, pre service teachers’ perception on the implementation … 112 indicator percentage category perception of students judging from good time management competence 79.10% good perception of students judging from results good student learning 82.67% very good student perceptions about the suitability of the application of learning models with subject characteristics 84.05% very high table 2 shows that: (1) students' perceptions of the aspects of student and teachers’ interaction are in the very good category with an average score of 85.32%; (2) students' perceptions on the aspect of motivation / increasing student interest in learning are in the very high category with an average score of 85.53%; (3) students' perceptions on the competency aspect of understanding subject matter are in the very good category with an average score of 85.48%; (4) students' perceptions of the competency aspects of critical, effective and efficient thinking are in the category of strongly agree with a mean score of 82.62%; (5) students' perceptions of the aspects of good time management competence are in the good category with an average score of 79.10%; (6) students' perceptions on aspects of good student learning outcomes are in the very good category with a mean score of 82.67%; (7) students' perceptions on the conformity aspect of the learning model with subject characteristics are in the very high category with a mean score of 84.05%. 3.1. student’ perception in terms of student and teachers’ interaction the results of data analysis on student perceptions about project-based learning models on the indicators of student and teachers’ interaction aspects can be seen in the table 3. table 3. student perception of student and teachers’ interaction ideal score interval frequency % category > 16.25 35 55.56 very good 12.5 to 16.25 28 44.44 good 8.75 to 12.5 0 0 bad < 8.75 0 0 very bad table 3 shows that there are 35 students (55.56%) who are in the very good category, 28 students (44.44%) are in the good category and there are no students who are in the sufficient and very bad category. from the analysis of each question item of the indicators of student and teachers’ interaction aspects which consist of 5 questions. the lowest mean score was 3.32, which is in question item number 1 with the question: "i feel more active in working on drawing assignments with a project-based learning model". about 5 the questions raised, only item number 1 has the lowest mean, but that does not mean intercourse students and faculty are located in the poor category. this is evidenced by the interaction between students and teachers on question items 2-5 still going very good. so that it can support the deficiencies in item number 1. volume 10, no 1, february 2021, pp. 109-120 113 data obtained from questionnaires given to 63 respondents on indicators of the interaction of students and professors showed that the tendency of the average score (mean) of 17.06 (85.32%) lies in the class interval > 16.25 in the excellent category. from the findings that have been explained, that students strongly agree with the application of the project-based learning model on the aspects of student and teachers’ interaction (mills & treagust, 2003). this is in accordance with the objectives of implementing the project-based learning model, namely to create a more active condition of student and teachers’ interaction (condliffe et al., 2017), so that in dealing with problems in carrying out assignments and subject matter can run smoothly. the teachers as a facilitator in this learning model can play a role, namely by knowing the progress of the learning activities that students carry out from the interaction process. it is stated that the learning method is a method used by teachers to establish relationships / interactions with students. 3.2. students’ perception of the term motivation and learning interest the results of the data analysis, perceptions of students about project-based learning model on indicators of motivation / growing interest in learning of students (see table 4). table 4. students’ perception in the term of motivation and learning interest ideal score interval frequency % category > 13 32 50.79 very high 10 to 13 31 49.21 high 7 to 10 0 0 moderate < 7 0 0 low table 4 shows that there are 32 students (50.79%) in the very high category, 31 students (49.21%) in the high category and no students who are in the medium and low categories. from the analysis of each question item of this indicator it can be seen that the lowest mean score was 3.21, which is in question item 9 with the question: "i don't feel tired in doing every assignment given by the teachers ". with these findings, this statement implies that students still feel tired in doing their very bad on work. this is influenced by the length of the meeting duration for each one-time meeting. and the number of each very bad on competency that must be achieved. however, of the 4 question items, there are weaknesses in question number 9 that can be overcome with questionable items 6-8, that students remain motivated, increase interest in learning and are enthusiastic in implementing project-based learning models in mathematics subjects. data obtained from questionnaires given to 63 respondents on indicators of motivation interest to learn the students showed that the tendency of the average score (mean) of 13.37 (83.53%) lies in the class interval > 13 in the category are very high. from the findings that have been explained, that students strongly agree with the application of the project-based learning model in mathematics in the aspect of motivation / increasing student interest in learning. this indicator itself is a development of the analysis of student characteristics in the planning process of the learning model. so that in its application, it can be known or can be determined by the learning model used which can motivate / increase student interest in learning. and with this project-based learning model, it has been proven that students can be motivated / increase their interest in learning. nasution, ahmad, & mohamed, pre service teachers’ perception on the implementation … 114 3.3. students’ perception of the term of understanding subject matter the results of data analysis on students' perceptions about project-based learning models on the competency indicators of understanding the subject matter (see table 5). table 5. students’ perception understanding subject matter ideal score interval frequency % category > 16.25 37 58.73 very good 12.5 to 16.25 24 38.10 good 8.75 to 12.5 2 3.17 bad < 8.75 0 0 very bad table 5 show that, there are 37 students (58.73%) who are in the very good category, 24 students (38.10%) are in the good category and there are no students who are in the sufficient and poor category. from the analysis of each question item of the competency indicator in understanding the subject matter which consists of 5 questions. obtained the lowest average score (mean) of 3.32, which is in question item number 13 with the question: "from the application of the project-based learning model, i have come to understand the meaning of each line in the mathematical picture". this question item has a role as a form of deepening students in understanding the material from mathematics subjects. overall, the existing data on the indicators of material understanding, students can be said to understand and understand the content of mathematical subject matter by applying the mathematics learning model. this is supported by data analysis on this indicator, there are no students who disagree and disagree with the application of the project-based learning model in mathematics. data obtained from questionnaires given to 63 respondents to the indicators of competence to understand the subject matter shows that the propensity score average (mean) of 17.10 (83.48%) lies in the class interval > 16.25 excellent category. from the findings that have been explained, that students strongly agree with the application of the project-based learning model in mathematics in the aspects of understanding the subject matter. this indicator is intended to measure the extent to which students understand understanding of the material considering the purpose of implementing a project-based learning model is to provide a memorable learning experience for students. as the definition stated that project based learning is a method that foster abstract, intellectual tasks to explore complex issues (alacapinar, 2008). pbl is a learning approach that pays attention to understanding the subject matter. so that students are required to explore, assess, interpret and synthesize learning information in meaningful ways (mcdonald, 2008). 3.4. students’ perception of the term of critical, effective and efficient thinking competencies the results of data analysis on students' perceptions about project-based learning models on the indicators of competency in critical thinking, effective and efficient (see table 6). volume 10, no 1, february 2021, pp. 109-120 115 table 6. student perception in terms of critical, effective and efficient thinking competencies ideal score interval frequency % category > 16.25 31 49.21 very good 12.5 to 16.25 32 50.79 good 8.75 to 12.5 0 0 bad < 8.75 0 0 very bad table 6 shows that there are 31 students (49.21%) who are in the very good category, 32 students (50.79%) are in the good category and there are no students who are in the sufficient and poor category. from the analysis of each question item of the competency indicator to think critically, effectively and efficiently which consists of 5 questions. obtained the lowest average score (mean) of 3.11, which is in the item question number 19 with the question: "the project-based learning model made me find new ideas to work on math picture assignments ". this statement means that students have not been able to find renewable ideas by doing math assignments. even though the project-based learning model in its application requires students to develop student ideas to find new knowledge in dealing with the work they face. however, the other four statements have shown good results, namely students are able to think creatively, can find solutions to any existing problems, can apply their drawing assignments into existing assignment exercises and can explore the potential that exists in students. data obtained from questionnaires given to 63 respondents to the indicators of competence critical thinking, effective and efficient show that the propensity score average (mean) of 16.52 (82.62%) lies in the class interval > 16.25 in the excellent category. from the findings that have been explained, that students strongly agree with the application of the project-based learning model in mathematics subjects in the competency aspects of critical, effective and efficient thinking. so that in its application, the projectbased learning model has achieved self-development potential. this shows that the problems given by educators as a source of learning can train students to think and develop their potential and personality (harisman et al., 2020; hidayat & sariningsih, 2020; putra et al., 2020; widodo et al., 2020). 3.5. students’ perception of the term of time management the results of data analysis on student perceptions about project-based learning models on indicators of time management competence are good (see table 7). table 7. student perceptions in terms of time management ideal score interval frequency % category > 9.75 35 55.56 very good 7.5 to 9.75 19 30.16 good 5.25 to 7.5 9 14.29 bad < 5.25 0 0 very bad nasution, ahmad, & mohamed, pre service teachers’ perception on the implementation … 116 table 7 shows that there are 35 students (55.56%) who are in the very good category, 19 students (30.16%) are in the good category, 9 students (14.29%) are in the sufficient category and there are no students who are in the poor category. from the analysis of each question item on the indicator of time management competence good which consists of 3 questions. the lowest mean score was 2.98, which is in the item question number 21 with the question: "i fill my spare time at home by doing math assignments". this statement has the lowest average score among the statements in the questionnaire regarding the application of the project-based learning model. this can happen because of the duration of the class meeting the students feel that they have had bad, because in one face-to-face duration the duration lasts 10 very bad for hours. this means that from morning class hours to completion, students are faced with one subject. this is what makes students sometimes feel bored and bored. therefore, the teachers applies a project-based learning model to overcome this problem. given this learning model, students are given the freedom to think and learn while adhering to the learning objectives. data obtained from questionnaires given to 63 respondents at the time of management competency indicators demonstrated that the tendency of the average score (mean) of 9.49 (79.10%) lies in the class interval 7.5 – 9.75 in both categories. from the findings that have been explained, it shows that students agree with the application of the project-based learning model in mathematics for the competency aspects of time management good. the data show that students only agree and do not really agree, this is because the duration of studying at school is too long and students tend to feel bored. from this indicator, it can be measured that students work on mathematics only during class meetings. so, in this aspect needs more attention when considering that the project-based learning model has the goal of making students more independent in doing tasks including managing study time students with good (scarbrough, bresnen, et al., 2004). 3.6. students’ perception of the term learning outcomes the results of data analysis on student perceptions about project-based learning models on indicators of student learning outcomes (see table 8). table 8. students’ perception in the term of learning outcomes ideal score interval frequency % category > 9.75 39 61.90 very good 7.5 to 9.75 20 31.75 good 5.25 to 7.5 4 6.35 bad < 5.25 0 0 very bad table 8 show that there are 39 students (61.90%) who are in the very good category, 20 students (31.75%) are in the good category, 4 students (6.35%) are in the sufficient category and there are no students who are in the poor category. from the analysis of each question item of the indicators of student learning outcomes which consist of 3 questions. obtained the lowest average score (mean) of 3.22, which is in question item 23 with the question: "i am satisfied with my score results". from this statement, there were 4 students who disagreed with the results of their learning scores. however, from the results of the evaluation conducted by the teachers, the overall student learning competency achievement has met the complete limit, namely with a minimum score of 75. volume 10, no 1, february 2021, pp. 109-120 117 data obtained from questionnaires given to 63 respondents on indicators of learning outcomes of students who demonstrated that the tendency of the average score (mean) of 9.92 (82.67%) lies in the class interval > 9.75 in the excellent category. from the findings that have been explained, that students strongly agree with the application of project-based learning models in mathematics as seen from the aspect of good student learning outcomes. this is also corroborated by the results of the teacher competency evaluation. that all students reach the minimum completeness limit of 75. so that in its application the project-based learning model has been said to be successful and has achieved the learning objectives. 3.7. students’ perception of the term of suitability of learning model application with subject characteristics the results of data analysis on student perceptions about project-based learning models on indicators of suitability of the application of learning models with subject characteristics (see table 9). table 9. student perceptions in terms of suitability of learning model application with subject characteristics ideal score interval frequency % category > 16.25 33 52.38 very high 12.5 to 16.25 30 47.62% high 8.75 to 12.5 0 0 moderate < 8.75 0 0 low table 9 shows that there are 33 students (52.38%) who are in the very high category, 30 students (47.62%) are in the high category and there are no students who are in the medium and low categories. from the analysis of each question item on the indicator of the suitability of the application of the learning model with the characteristics of the subject which consists of 5 questions. the lowest mean score was 3.29, which is in question item number 27 with the question: "the application of project-based learning models makes mathematics more interesting". and item number 28 with the question: "the picture i am working on making my math assignment more real". from these two statements, it can be seen that students think that using a project-based learning model has not been able to make mathematics more interesting and make it real. however, that statement is on a small scale. so that it does not really affect the application of project-based learning models in mathematics subjects. data obtained from questionnaires given to 63 respondents in conformity indicator learning model application with the characteristics of the subjects showed that the tendency of the average score (mean) amounted to 16.81 (84.05%) lies in the class interval > 16.25 in very high category. from the findings of the data that have been explained, that students strongly agree with the application of the project-based learning model in mathematics on the aspects of the suitability of the characteristics of the learning model with the subjects (gary, 2015). so that the project-based learning model on the subject has achieved success. the learning model is successful if it includes 3 stages, namely, planning, implementation and evaluation. the third phase of the project-based learning model in the eyes of subjects of mathematics has gone good and get a positive response from students (scarbrough, swan, et al., 2004). nasution, ahmad, & mohamed, pre service teachers’ perception on the implementation … 118 4. conclusion the results of this study indicate that: (1) the students' perceptions of the interaction aspects of students and lecturers are in the very good category with a mean score of 85.32%. (2) students' perceptions on the aspect of motivation / increasing student interest in learning are in the very high category with an average score of 85.53%. (3) students' perceptions on the competency aspect of understanding subject matter are in the very good category with an average score of 85.48%. (4) students' perceptions of the competency aspects of critical, effective and efficient thinking are in the category of strongly agree with a mean score of 82.62%. (5) students' perceptions of the aspects of good time management competence are in the good category with an average score of 79.10%. (6) students' perceptions on aspects of good student learning outcomes are in the very good category with a mean score of 82.67%. (7) students' perceptions on the conformity aspect of the learning model with subject characteristics are in the very high category with a mean score of 84.05%. acknowledgments the authors would like to express my special thanks to university of muhammadiyah north sumatra, university of muhammadiyah purwokerto and university of sultan idris for supporting the facilities and finances to accomplish this paper. references alacapınar, f. (2008). effectiveness of project-based learning. eurasian journal of educational research (ejer), 33, 17-34. amamou, s., & cheniti-belcadhi, l. (2018). tutoring in project-based learning. procedia computer science, 126, 176-185. https://doi.org/10.1016/j.procs.2018.07.221 anazifa, r. d., & djukri, d. 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(2020). process of algebra problem-solving in formal student. journal of physics: conference series, 1657(1), 012092. https://doi.org/10.1088/1742-6596/1657/1/012092 https://doi.org/10.1109/mc.2015.268 https://doi.org/10.22460/infinity.v9i1.p59-68 https://doi.org/10.28945/967 https://doi.org/10.18848/1447-9494/cgp/v14i10/45493 https://doi.org/10.18848/1447-9494/cgp/v14i10/45493 https://doi.org/10.1088/1742-6596/1657/1/012003 https://doi.org/10.1016/j.sbspro.2014.09.169 https://doi.org/10.1177/1350507604048275 https://doi.org/10.1177/0170840604048001 https://doi.org/10.7771/1541-5015.1323 https://doi.org/10.1016/j.compedu.2008.07.012 https://doi.org/10.1088/1742-6596/1657/1/012092 nasution, ahmad, & mohamed, pre service teachers’ perception on the implementation … 120 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 8, no. 2, september 2019 e–issn 2460-9285 https://doi.org/10.22460/infinity.v8i2.p143-156 143 designing camtasia software assisted learning media toward students’ mathematical comprehension in numeral setiyani *1 , dian permana putri 2 , derin prakarsa 3 1,2,3 universtas swadaya gunung djati article info abstract article history: received dec 31, 2018 revised mar 27, 2019 accepted august 29, 2019 mathematics is one very important lesson. if students have difficulty in solving mathematics, this supports the ability to communicate a mathematical idea. students must understand mathematics well. this study aims to determine the feasibility of learning media in the form of videos used camtasia software on numeral material based on mathematical understanding using the r and d methodology with addie models. the research instrument used is a practicality questionnaire, an interview questionnaire and validation sheet. from the results of interview questionnaires found that students prefer learning with the presence of learning media and the results of teacher interviews found that lack of facilities for using media in the learning process. the instrument of validation questionnaire produce an average score of 85% so that it can be said that the learning media in the form of videos are very valid and can be used. the instrument of practicality questionnaire filled by nine students with three high-ability, moderatecapable, and low-ability students produced an average score of 86.77%. it can be said that the practice was very high. based on the results of each instrument, it can be stated that the learning media in the form of cd-shaped videos is practical and can be used. keywords: addie, camtasia software, learning media, mathematical comprehension, numeral material copyright © 2019 ikip siliwangi. all rights reserved. corresponding author: setiyani, departement of mathematics education, universitas swadaya gunung jati, jl. perjuangan no. 02 cirebon, west java, indonesia email: setiyani_0401509081@yahoo.com how to cite: setiyani, s., putri, d. p., & prakarsa, d. (2019). designing camtasia software assisted learning media toward students’ mathematical comprehension in numeral. infinity, 8(2), 143-156. 1. introduction mathematical comprehension is one ability that need to have to learn mathematic. that ability is an important foundation for thinking in solving mathematical and real-life problems. besides that mathematical understanding ability is very supportive for the development of other mathematical abilities such as communication skills, problem solving, reasoning, connection and other mathematical abilities. the problems that require understanding of mathematical concepts have not been optimally mastered by students, such as the weak understanding of one concept with other concepts needed to solve of mathematical problems (kariadinata, yaniawati, sugilar, & riyandani, 2019). students mailto:setiyani_0401509081@yahoo.com setiyani, putri, & prakarsa, designing camtasia software assisted learning media … 144 must have ability mathematical comprehension as mathematical understanding is a musthave ability and should be developed in each students self. the ability of students' mathematical understanding can be measured based on the indicators. while its level can be seen based on completeness on indicators of mathematical understanding. but based on the results of observations conducted by researchers there are still indications that students do not have a level of understanding in accordance with the current level of thinking, as experienced by students in mtsn 2 cirebon in the subject matter numbers. the source states that students are still not maximal in understanding the concept of addition to fractions as shown in tab 1. figure 1. student exercise result from the operation steps to add the fraction number is correct, that is to look for the smallest guild multiplication (sgm) to equate the denominator, but when determining the numerator 34% of students are still confused and caused the students’ answer to be incorrect. students still do not master the concept of multiplication in fractions in operating the multiplication of fractions by simply multiplying the numerator with the numerator and denominator with the denominator. but from 25% of students’ answer above use the steps of the operation of addition or subtraction is by looking for the sgm and equating the denominator. that is what caused student answers less precise as shown in figure 2. figure 2. students who have not mastered the concept of multiplication in fractions. students' lack of understanding of the daily problems given related to the subject matter number with the question "andi is an amateur diver, first practiced diving at a depth of 3 meters uder sea level. after feeling swift diving at a depth of 3 meters, then andi decided to dive again 7 meters under the sea level. what is the difference in depth in the two conditions, present using a number line! ". student answers as shown in figure 3. volume 8, no 2, september 2019, pp. 143-156 145 figure 3. student who do not understand the mathematical concepts related to indicators change the form of representation to other form. figure 3 shows students trying to answer using a number line. but what can be seen in the answers of 47% of students shows that they lack understanding in using number lines and on the operation, hence students' answers are less precise. students also have not been able to identify the properties of a concept related to material numbers with the question "are commutative and associative properties also valid for integer reduction operations. if yes, show it. if not, explain with an example of a denominator? " student answers are shown in figure 4. figure 4. students who have not been able to identify the properties of a concept figure 4 shows the answers of students in proving the properties of a concept in material numbers. in proving the nature of a concept, it must be understood first what communicative properties are and how to prove them. the communicative nature is where a + b = b + a, but what is requested is in the reduction, then the fixed answer "communicative nature does not apply to subtraction, because the result is definitely not the same" so that the answers of 22% of students above prove a lack of communicative right. based on the answers above, it shows that there is still minimal of students’ mathematical comprehension ability in mtsn 2 cirebon. if this fact is ignored, as time goes by this issue can decrease students’ interest in learning if, because they feel that mathematics is difficult. mathematical comprehension ability is the initial ability that must be given as early as possible to students. based on the results of interviews with several students in vii grade at mts 2 cirebon, the researcher found some difficulties that students faced when studying material numbers. 20% of students stated that they found it difficult when they encountered questions about proving the properties of numbers, as well as the operation of negative summation. in the learning process students express that they are more interest of learning with media and some exercises. based on the results of the interview above, the learning process requires learning media as teaching aids in delivering material. learning materials is very important for teachers and students. it have a major contribution to the success of the learning process is implemented (noto, pramuditya, & fiqri, 2018). criticos state that media is one component of communication, namely as a messenger from the communicator to the communicant (daryanto, 2013). if communication does not go well, the message conveyed by the teacher is difficult for students to understand. conversely, if communication is setiyani, putri, & prakarsa, designing camtasia software assisted learning media … 146 effective and efficient, more and more learning objectives are achieved. the use of learning media in the teaching process can make students better understand and learn according to their interests and abilities (kintoko & sujadi, 2015). the word media comes from latin is the plural form of the word medium boundary about the notion of media is very broad, but we limit it to the world of education only, namely the media used as tools and materials for learning activities. learning media is very important to be used by teachers in the teaching and learning process. learning media provide motivation to students in mathematics. with learning media students are more enthusiastic in learning in the classroom. of course the learning media needs to be created interestingly and designed practically, these aims to provide students with interest and interest in following the teaching and learning process in the classroom. media learning cd can be used as an alternative to convey messages by the message giver (teacher) to the recipient (student). the use of the learning cd media allows students not only to study at school, but also to learn by themselves at home. learning cds have characteristics such as attractive shapes and colours that can increase the activity of students to learn and clarify a concept. so with the use of this media, the learning process will feel more interesting and not boring and will stimulate students to learn mathematics. by using the learning cd, the contents of the subject matter can be modified using various applications such as camtasia studio and microsoft power point which can be combined into a more interesting unified learning media. so that it can help teachers in delivering subject matter and can help students understand mathematical concepts. the development of interactive learning cd assisted by camtasia studio software on integer material has been studied before. the feasibility test results are very good and the results of student trials using interactive learning cd using the problem based learning model assisted by camtasia studio software on integer material are better than conventional learning in class vii of the 2nd middle school in the 2015/2016 (prasetyawan, 2017). based on the description of the background above, the author wants to find out how camtasia software design helps learning media in students' mathematical understanding ability in numeral material? is the design of learning media assisted by camtasia software on the ability of students' mathematical understanding of material numbers that have been developed practice? 2. method this study uses the r & d (reserch and development) method with the addie model. to compile various systems, both formal and non-formal systems of instructional systems that are often used, namely addie. the addie model is one of the most commonly used models in the field of instructional design to produce effective designs (aldoobie, 2015). the addie model consists of five stages, namely: analysis, design, development, implementation, and evaluation. the complete stages are shown in figure 5 (branch, 2009). volume 8, no 2, september 2019, pp. 143-156 147 figure 5. model addie the explanation of the addie model which consists of five stages is as follows: the analysis stage consists of two stages, namely needs analysis and identification of needs. at this stage, analysis is carried out to determine the learning needs of students, by conducting a needs analysis, identifying problems, and performing task analysis. analysis must include learning characteristics, motivation, technological abilities, and learning objectives (wang & hsu, 2009). the design stage is the stage after learning needs are identified then selecting media and then designing learning media. this stage teaching and learning activities are designed. the activities carried out are formulating competencies determining learning materials, strategies, evaluations, sources and media makers. the development stage is in the form of making or producing or realizing a product specification learning that has been determined by the design resistance. in this phase the researcher builds and develops with the help of media software and supporting documentation (muruganantham, 2015). besides that at this phase also began to make examples of real products and good designs (aldoobie, 2015). after the product is produced the next step is validating the product by experts. the implementation stage is the stage of utilizing or using learning products in learning activities. activities that need to be prepared include preparing classrooms, schedules, tools and media, preparing students physically and mentally. the purpose of this phase is to convey or promote product results to students on the material and learning objectives (muruganantham, 2015). the evaluation stage is a process to see whether the learning system that is being built is successful, in accordance with initial expectations or not. to find out this, an evaluation of the product has been made with the aim to find out whether students can immediately understand the material or competencies taught in class. the results of this evaluation are used to provide responsiveness or opinion to the product maker. this addie model provides an opportunity to evaluate activities at each stage. the modified research flow that the author did can be seen in figure 6. analiysis impementation development design evaluation revision revision revision revision setiyani, putri, & prakarsa, designing camtasia software assisted learning media … 148 figure 6. addie research flow 3. results and discussion learning media design carried out by researchers has some stages, namely analysis, design, development, implementation and evaluation which will be presented by the researcher as follows. 3.1. analysis phase analysis is the initial stage carried out by researchers in the process of making learning cds. this stage is used to find out the learning needs and difficulties experienced by students during the learning process in material numbers. this stage consists of two activities namely needs analysis and identification of needs. the two activities will be presented as follows: 3.1.1. needs analysis needs analysis is a way of knowing student learning difficulties and what are needed by students in the teaching and learning process. at this stage the researcher analyzes the needs of students by conducting interviews and giving questions about the test of mathematical abilities in the material numbers. interviews were conducted to the mathematics teachers and some seventh grade students at mts negeri 2 cirebon to find out the opinions of teachers about the difficulties experienced by students and how teachers overcome learning difficulties and know the opinions of students regarding the teaching and learning process in popular classes and difficulties experienced by students. student test results on number material show that students are still not maximal in understanding the concept of addition of fractions, the concept of multiplying fractions, solving problems in daily life, and not being able to identify the properties of a concept in numbers material. from the students’ interview found some difficulties that students faced analysis phase needs analysis give questions about testing to students conduct interviews with students and teachers identification of needs design phase media selection learning media design development phase learning media development learning media validation valid ? instructional media implementation of learning media implementation phase evaluation phase evaluation of learning media information : : flow of activities : cycle line revision volume 8, no 2, september 2019, pp. 143-156 149 when learning material numbers. 20% of students stated that they found it difficult when they encountered questions about proving the properties of numbers, as well as the operation of negative additions. in the learning process students reveal that students are more interest to learn learning media and lots of practice questions. while the results of the interview with teachers found some difficulties experienced by students when studying material numbers. mathematics teachers at mts negeri 2 cirebon stated that students were still having difficulty in learning number material, it can be seen from the learning evaluation carried out by the teacher there was still many students who got scores under minimum completion criteria. the way to overcome this is by giving practice questions that contain comprehension skills, where comprehension ability is the initial ability that must be possessed by students. the learning process still uses lectures and does not use media in learning related to material numbers. 3.1.2. identification of needs at this stage, it is identifying the needs that have been obtained from the results of the trial questions and the results of interviews with students and mathematics teachers. from the needs analysis, several important points are obtained: students are still not maximal in understanding material numbers, the level of students' mathematical understanding ability is still not maximal related to material numbers, learning media have not use in the learning process, and students are more excited about learning with media and lots of practice questions. the results of identification of these needs are used by researchers as a reference in designing learning media for the learning process of students in the classroom. 3.2. design phase design is the second stage carried out by researchers. based on the identification of needs researchers will design or create learning media that appropriate to the needs and overcome the difficulties experienced by students. at this stage includes activities: collect material references in this activity the researcher makes material by reference to various sources or reference books. beside compeling material, the researcher also determines the sub-chapter of the material that will be discussed in the learning media created. based on the results of the analysis phase, the researcher took the sub chapter of integer operating material and the operation of fraction numbers. the material included in the learning media has been adjusted in terms of language and structure to make it easier for students in the learning process. the language used in the preparation of the material is to use polite language according to eyd (enhanced spelling), but still easy to understand by students. as explained in the analysis phase, that in the learning process at mtsn 2 cirebon class vii related to material numbers has not used learning media and only with lectures. this makes students bored in learning, so researchers are interested in creating learning media that aim to attract interest and provide learning enthusiasm for students in the form of learning videos assisted by camtasia software and produce products in the form of learning cd. in this activity the researcher designed learning media with the help of camtasia software. the integer material is designed in this stage assisted by camtasia software makes it easier for students to understand each step of the problem solving. besides that this application can be installed via an android phone, so students can study anywhere and anytime. next is a presentation on the design of learning media design. making a camtasia video in the initial stages starts with entering the title of the video. select the menu to enter the text as shown in figure 7. setiyani, putri, & prakarsa, designing camtasia software assisted learning media … 150 figure 7. to write text from this step, the researcher will start assembling and designing operating material with a round and fraction operation. the following page is for entering material text in the camtasia video setup (figure 8). figure 8. includes material text in compiling the flow of activities in the camtasia video researchers also pay attention to the material, examples of questions and practice questions must be in accordance with the initial objectives of making learning media assisted by camtasia software towards mathematical understanding skills. the following are the design results that the researchers made, namely the video camtasia with integer operating material and fractional number operations on mathematical comprehension abilities for class vii junior / mts students. the following is the display made by the researcher: 3.2.1. making slides in making the initial slide, the researchers made several slides. the slide is the opening, an explanation of ki (core competence) and kd (basic competence), an explanation of mathematical indicators, indicators of mathematical understanding and learning objectives. the purpose of the slides is to make the teacher or students loyal to the media know the goals that must be achieved by the students and the contents of the video. 3.2.2. making material slides in making the material slide the researcher is include integer operating material and fractional number operations in the camtasia video. the content of the material is in the form of an explanation of each sub chapter of the material number. the material that will be volume 8, no 2, september 2019, pp. 143-156 151 presented are integer addition operations, integer reduction operations, integer multiplication operations, integer division operations, fraction operations with fractions, fractional reduction operations, fractional multiplication operations, and fraction division operations. 3.2.3. making sample slides of questions along with discussion and understanding ability test exercises in making examples of questions, the researcher encloses discussion and problem training. it is intended that students understand from each example of the problem given. the placement of each sample slide is given directly after an explanation of each material. 3.2.4. making the final slide this slide contains the closing of the camtasia video by providing motivation for students, and the biodata of the maker 3.3. development phase this stage is the third stage carried out by researchers. at this stage the researcher embodies the design into a product in the form of a cd learning. to create the product there is a development where the results of the video learning design in the camtasia software are converted into mp4 by clicking produce and share then select hd so that the quality is good then next as shown in figure 9. figure 9. changing to mp4 after mp4 learning videos are created, the next step is burning the mp4 video into a cd / dvd that has been prepared to become a learning cd. when it has turned into a learning cd, it is then continued to the learning cd validation stage that has been made. the goal is to find out whether the product is valid or not. in the validation stage this learning cd was validated by three mathematics lecturers and one mathematics teacher. the last step in making a valid learning cd is to test the validity level of the learning cd. this stage aim to find out whether the learning cd is worthy of use or not. validation used is an assessment in the form of a questionnaire. the validator consists of three mathematics lecturers at swadaya gunung jati university and one mathematics teacher at mtsn 2 cirebon. setiyani, putri, & prakarsa, designing camtasia software assisted learning media … 152 this validation is done to find out whether the product created by the researcher is valid or not. based on the results of validation that each validator provides a good assessment of the learning cd produced. this is the result of the overall assessment which is quite high with the acquisition of results about 62 to 72 from a maximum score of 80. the next step that must be done is to analyze the data. data analysis will be divided into two stages, namely the analysis of validation data for each validator and overall data analysis. recapitulation of analysis calculations from each validator as shown in table 1. table 1. recapitulation of each validator validator score achieved expected maximum score overall validation criteria (%) v-1 68 80 85 v-2 62 77.5 v-3 72 90 v-4 70 87.5 average 85 based on the calculation of the analysis results from each validator, it has been obtained for v-1 = 85% (very valid), v-2 = 77.5% (quite valid), v-3 = 90% (very valid), and v-4 = 87.5% (very valid). this shows that there is one validator who gives an evaluation with sufficiently valid criteria and there are three more validators who provide very valid criteria. so based on these assessments the resulting learning cd can be used. overall validation then the overall analysis calculation is done to find out that this learning cd is valid or not. the following formula will be used. based on the results of these calculations, obtained for v_combined = 85%. furthermore, the calculation results are interpreted with the following criteria (table 2). table 2. validation criteria validation criteria level of validation 85% ≤ v ≤ 100% very valid or can be used without revisions 70% ≤ v < 85% it is quite valid or can be used but needs to be small revisions 50% ≤ v < 70% less valid, it is recommended not to be used because it needs major revisions v < 50% invalid or may not be used based on the validation criteria, the assessment of the validator is v_combined = 85% included in very valid criteria. 3.4. implementation phase the implementation phase is the fourth stage. at this stage the researcher carried out the implementation of the product created in the form of a mathematics learning cd at volume 8, no 2, september 2019, pp. 143-156 153 mts 2 cirebon. the implementation of a mathematics learning cd is using the talking stick model with a scientific approach. in the core learning process, the researcher explained the material about summing operations and reduction by round using learning media in the form of videos. after explaining the researcher also gave an example of a question along with explaining how to solve the sample problem and the student observing then giving the question what the students did not understand. when the question and answer process between researchers and students is completed and students understand what is conveyed by the researcher, then the researcher gives questions to students and prepares music and sticks. students do exercises on the questions given by the researcher individually. the researcher does a talking stick game to test students' mathematical abilities. for students who get a section to discuss the questions the researcher cooperates with the answers that have been obtained. after the game is finished the students record all the answers that have been answered with the talking stick game. at the end of the implementation the researcher gave a brief explanation and gave conclusions and offered to students if they wanted to have a learning video, they could copy paste or share it to pc / handphone. before implementation, the researcher gave a practical questionnaire to students which aimed to find out the practicality of the learning cd. 3.5. evaluation phase the evaluation phase is the fifth stage. at this stage the researcher asks for input from the teacher and the students that aimd to find out whether the learning media in the form of video learning cd, can overcome student learning difficulties in material numbers and realize the desired needs of students in the learning process. judging from the students' answers and the input of teachers and students that with the use of learning cds in the learning process in the classroom can overcome students' learning difficulties in material numbers and give enthusiasm to students in the learning process. this shows that by making learning media in the form of learning vide in cds can overcome the difficulties of students in understanding material numbers and realizing the needs of students in the learning process. after five stages, the researcher then processes the practical data that is filled in by the students at the implementation stage. the data is in the form of quantitative data. practicality is used to find out the products produced, namely learning media in the form of mathematical learning cds in the form of videos that are practical or not used in the learning process in mathematics subjects with sub chapter numbers in addition, subtraction, multiplication, integer division and fraction numbers. based on table 3, it appears that each assessor gives a good assessment of the learning cd produced. this is the result of a high overall assessment with yields around 26 to 31 from a maximum score of 32. the next step that must be done is to analyze practical data. it aims to find out the scores obtained from each assessor so that they can formulate practical criteria or not. recapitulation of analytical calculations from each assessor as shown in table 3. table 3. recapitulation of analysis calculations from each assessor assesor (p) score achieved overall assessment criteria (%) p-1 29 90 p-2 31 96 p-3 30 93 p-4 28 87 setiyani, putri, & prakarsa, designing camtasia software assisted learning media … 154 assesor (p) score achieved overall assessment criteria (%) p-5 28 87 p-6 29 90 p-7 27 84 p-8 26 81 p-9 27 84 average 97.66 expected maximum score = 32 tabel 3 shows that the assessment of all students with criteria is very practical. as the result based on the assessment the learning cd produced is practical. mathematics learning is done very much. one of the learning media development approaches with rectangle-based geographic post problems. after learning is done using this media, this media can facilitate students in asking about the characteristics of getting a quadrilateral, facilitating students to learn the relationship between the types of building rectangles that have the same nature, and provide opportunities for teachers to conduct discussions about mathematical communication students when asking and writing (saputro, 2016). the results of the research carried out have the advantages of the research conducted by latif, darmawijoyo, & putri (2013) which produced a product from the camtasia software in the form of videos that were learned through edmodo and the learning process needed the internet, different from what the researchers produced. learning process does not require an internet connection.the disadvantage of learning media that uses camtasia software is not the availability menu equation. thus it was developed on mathematical subjects that use formulas difficult to use. 4. conclusion making learning media with software aided by camtasia on the ability of students' mathematical understanding of material numbers that have been completed, this is proved by each example and practice about the problem of the ability to access understanding. and in the learning process using learning media consisting of learning cds that make students more enthusiastic in learning and more practical for students because the created learning cd contains videos that can be used anywhere both on pc / hanphone, so students can learn everytime students want. assessments of products produced by researchers by experts indicate that learning is made very valid, with a presentation of 85%. it can be deny that learning cds can be used by students. practicality of learning cd media conducted by nine students consisting of three high abilities, three moderate abilities, and three low abilities. based on the results of nine seventh grade students at mts negeri 2 cirebon who are capable of high, medium and low shows that the learning cd produced is very practical, with presentations of 97.66%. it is important to state that the learning cd is very practical for learning class vii students in material numbers. suggestions that researchers can convey based on the results of research in the framework of making mathematics learning cds are firstly in the process of implementing media learning cds in the form of videos do not use a projector (infocus), so each student must have the video. secondly, in evaluating the questions there needs to be a more diverse question additionhe conclusion should contain the confirmation of the problem that has volume 8, no 2, september 2019, pp. 143-156 155 been analyzed in result and discussion section. the conclusion should contain the confirmation of the problem that has been analyzed in result and discussion section. references aldoobie, n. (2015). addie model. american international journal of contemporary research, 5(6), 68-72. branch, r. m. (2009). instructional design: the addie approach (vol. 722). springer science & business media. daryanto, d. (2013). media pembelajaran: perannya sangat penting dalam mencapai tujuan pembelajaran. yogyakarta: penerbit gava media. kariadinata, r., yaniawati, r. p., sugilar, h., & riyandani, d. (2019). learning motivation and mathematical understanding of students of islamic junior high school through active knowledge sharing strategy. infinity journal, 8(1), 31-42. kintoko, k., & sujadi, i. (2015). pengembangan media pembelajaran matematika berbantuan komputer dengan lectora authoring tools pada materi bangun ruang sisi datar kelas viii smp/mts. jurnal pembelajaran matematika, 3(2). latif, y., darmawijoyo, d., & putri, r. i. i. (2013). pengembangan bahan ajar berbantuan camtasia pada pokok bahasan lingkaran melalui edmodo untuk siswa mts. kreano, jurnal matematika kreatif-inovatif, 4(2), 105-114. muruganantham, g. (2015). developing of e-content package by using addie model. international journal of applied research, 1(3), 52-54. noto, m. s., pramuditya, s. a., & fiqri, y. m. (2018). design of learning materials on limit function based mathematical understanding. infinity journal, 7(1), 61-68. prasetyawan, a. (2017). pengembangan cd pembelajaran interaktif dengan menggunakan model problem based learning berbantuan software camtasia studio pada materi bilangan bulat. aksioma: jurnal matematika dan pendidikan matematika, 7(1), 26-35. saputro, b. a. (2016). learning media development approach with a rectangle problem posing based geogebra. infinity journal, 5(2), 121-130. wang, s. k., & hsu, h. y. 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(2021). identification of junior high school students’ error types in understanding concept about relation and function. infinity, 10(2), 175-190. 1. introduction indonesian 2013 curriculum says that relation and functions is a compulsory topic for junior high school students. in the attachment of education and culture ministry regulation no. 24 of 2016 states that the basic competencies that must be achieved in the material of relations and functions in the aspect of knowledge are to describe and to state relations and functions using various representations (words, tables, graphs, diagrams, and equations), and in the aspects of skills, the material covers solving problems related to relations and functions by using various representations (mecri, 2016b). relations are defined as relationships, and a function is defined as a process that connects each element from one set (domain) to exactly one element from another set (codomain) (as’ari et al., 2017; blanco et al., 2014). functions are not simple concepts, at least three systems of representation are used to represent the concept of functions in high school. they are tables (including ordered pairs), graphs, and formulas or equations. the characteristics of the https://doi.org/10.22460/infinity.v10i2.p175-190 fitrianna & rosjanuardi, identification of junior high school students’ error types … 176 concept of function make it able to be studied from two perspectives, as a part of mathematics and as an object in learning mathematics (blanco et al., 2014). based on studies regarding the analysis of students' abilities in relation and function material, the following results are obtained: 1) students experience epistemological obstacles related to the concept of relations and functions, 2) students experience misconceptions, 3) students have great difficulty in stating the definition of functions, solving problems in different contexts, and solving problems related to function (irawati et al., 2014; istiqomah, 2015). the results of interviews conducted by researchers with mathematics teachers at one of the tsanawiyah madrasah in kabupaten bandung barat, showed that the results of students' daily tests on relation and function material obtained an average value of 70.2, which is below the specified minimum completeness criteria, 72. hence, in this study, the types of errors made by students and students' conceptions of relations and functions will be identified. education and culture ministry regulation no. 21 of 2016 concerning content standards in primary and secondary education, states that one of the objectives of mathematics is to understand mathematical concepts, explain the relationship between concepts, and apply concepts or algorithms in a flexible, accurate, efficient, and precise manner in problem solving (mecri, 2016a). concepts are ideas that can be used or allow someone to classify an object (bell, 1981). abstract concepts are understood as two different forms, structurally as an object and operationally as a process. one is said to have an object of the concept if he/she is able to show the properties of the concept, while someone is said to have had a conceptual process if that he/she can discuss the concept using a mathematical object (sfard, 1991). a concept can be learned through definition (simon, 2017). when a student understands the definition of a concept presented in textbooks and classroom learning, the student will form an image of the concept in his mind (viholainen, 2008). concept images consist of all cognitive structures in an individual's mind that are associated with a particular concept, while concept definitions are the words used for a concept. initially a person has a mental picture of a given concept, all visual representations such as graphics, symbols of the concept, as well as a collection of properties related to the concept. the combination of these characteristics with mental images is called concept image (tall & vinner, 1981). furthermore, the concept image can be used as a guide which has been estimated to be the starting point for the emergence of students’ learning difficulties in certain materials and students' conceptions related to a concept. zetterberg (1966) provides an explaination that there are three components that make up a concept, they are symbols, objects and conceptions. conception is a model of explaining learners about a certain concept (simon, 2017). another explanation of conception is a form of internal representation of the concept, which is owned by students and becomes an element of a student's knowledge (sfard, 1991). bell (1993) states that several reasons for the importance of identifying students’ conceptions are: 1) students' conceptions are often not in accordance with scientific conceptions or the conceptions of experts, 2) students’ conceptions can help or hinder understanding of other concepts causing students’ difficulties in learning. students' difficulties in solving math problems can be seen from the mistakes made by students. this error can be seen from the identification of the student's work in doing the test (kariadinata et al., 2019). johari and shahrill (2020) show that it is very important to know the causes of common mistakes made by students. therefore, the teacher is able to facilitate students in reducing their errors in terms of analyzing the problem and reasoning about every step taken to solve it. analysis of students 'difficulties in this study was to reveal in depth the types of errors occurred, the factors that caused these errors, and students' conceptions regarding the material of relations and functions. volume 10, no 2, september 2021, pp. 175-190 177 the objectives of this study are to: 1) identify the types of errors made by students in relation and function material, and 2) identify students' conceptions regarding the concepts of relations and functions. 2. method this research is a descriptive study with a qualitative approach. this research involved 26 eighth grade students at one of the tsanawiyah madrasah, in kabupaten bandung barat. the research instrument used is in the form of a 6-question-diagnostic test of the relations and functions material (see table 1). before being given the test instrument, students had received online learning through the whatsapp group by the mathematics teacher, but in this study it would be limited to analyzing student errors seen from the results of student work and interviews. eight students were selected as interview subjects based on consideration of the types of errors made and the need to confirm students' answers. the interview questions are open-ended, and the questions are arranged based on basic competencies and indicators in the relationship and function material. table 1. distribution of indicators and question numbers basic competences indicators number 3.3. describing and expressing relations and functions using various representations (words, tables, graphs, diagrams, and equations) presenting relations with arrows, cartesian diagrams, and ordered pairs 1a 1b 1c showing examples of functions and not functions 2a 2b 2c 2d specifying the domain, codomain and result area of the function 3a 3b 3c expressing a function in an equation formula 6a 6b 6c 4.3. solving problems related to relations and functions by using various representations solving problems related to relations and functions 4 solve problems related to relations and functions in the form of equation formulas 5 the data that has been collected, then analyzed of students’ answer who made mistakes based on the types of errors and indicators as follows. the types of errors and indicators made by students are as follows (kiat, 2005): 1) errors in understanding questions (m) are the errors that occur in translating questions are indicated by errors in interpreting the language of the questions, 2) conceptual error type 1 (k1) is an error that occurs because students do not understand the concepts involved in the problem, 3) conceptual error type 2 (k2) is an error arising from the inability of students to determine the relationships involved in the problem, 4) procedural errors (p) are errors due to students' inability to manipulate or fitrianna & rosjanuardi, identification of junior high school students’ error types … 178 algorithms even though students already understand the concept behind the problem, 5) technical errors (t) are the errors due to carelessness. 3. results and discussion after checking the students' answers, the results obtained in the form of recapitulation of students' answers to each question (see table 2). the recapitulation of student’s answer is used to see the percentage of students who answered correctly, wrongly or not. table 2. recapitulation of student’s answer number true false no answer 1a 54% 23% 23% 1b 4% 62% 35% 1c 15% 42% 42% 2a 46% 46% 8% 2b 8% 85% 8% 2c 58% 35% 8% 2d 27% 35% 38% 3a 50% 31% 19% 3b 31% 50% 19% 3c 19% 62% 19% 4 77% 15% 8% 5 8% 92% 0% 6a 23% 46% 31% 6b 38% 31% 31% 6c 15% 42% 42% based on table 2, the students made mistakes in almost all the question numbers. the types of errors made by students were classified according to the types of errors that were made. volume 10, no 2, september 2021, pp. 175-190 179 figure 1. students’ types of errors recapitulation the types of errors made by students shown in figure 1 are quite diverse. to see the percentage of students who made each type of error (see table 3). table 3 is used to compare the number of students who make one type of error with another through the percentage. table 3. percentage of students’ error types error types understanding question conceptual procedural technical type 1 type 2 percentage 13% 62% 21% 2% 2% based on table 3, it can be seen that type one conceptual error (k1) and type two conceptual error (k2) were mostly committed by students. this is in accordance with research of hidayat and sariningsih (2018) that the mistakes often made by students in solving math problems, one of which is a conceptual error. the eight subjects selected for analysis on the results of their work, not all of them commit these types of errors. each question related to the causes of errors made by students and students’ conceptions related to indicators on the questions will be analyzed. 3.1. error analysis on question number 1 the first indicator for question number one is to present a relation with an arrow diagram, a cartesian diagram, and a set of consecutive pairs. the question can be seen in figure 2. figure 2. question number 1 for the first indicator 0 5 10 15 20 25 30 types of error m k1 k2 p t fitrianna & rosjanuardi, identification of junior high school students’ error types … 180 based on figure 1, it is found that the types of errors made by students on indicators presenting relations with arrow diagrams, cartesian diagrams, and consecutive sets of pairs are conceptual errors (k1 & k2). look at the answer given by s-3 (see figure 3), this student already had an idea of the concept of the arrow diagram but had not paired between set a and set b, after the interview it was known that she already understood the questions, but she did not understand the concept of relations and arrow diagram. this error includes the type of conceptual error (k1). thus, the conceptual error (k1), in this case, the student already had an image in the presentation of the relationship in various forms but she answered in another form that was not in accordance with the requested question, another form that was close to the arrow diagram. the reason was that she did not understand the arrow diagram and she answered by looking at the context of the sentences in the questions. s-19’s understanding was confused with another representation, the cartesian diagram. figure 3. the answer of s-3 on question number 1a based on the results of the interview, student’s assumptions about arrow diagrams were diagrams with arrows (see figure 4). thus, the conceptual error (k2) made by students was that students' understanding was confused with the concept of presenting one relationship with another. based on the results of the interview, student’s assumptions about arrow diagrams were diagrams with arrows on them, so that the students' conception of representations with arrow diagrams, consecutive sets of pairs and cartesian diagrams was still wrong. figure 4. the answer of s-19 on question number 1a volume 10, no 2, september 2021, pp. 175-190 181 3.2. error analysis on question number 2 the indicator for question number 2 showed examples of functions and not functions. the question can be seen in figure 5. figure 5. question number 2 for the second indicator based on figure 1, it was found that the types of errors made by students on indicators showing examples of functions and not functions are conceptual errors (k1 and k2) and technical errors. error types k1 and k2 will be analyzed. figure 6 show that s-3 didn’t answer accordingly to the concept of function. so, the conceptual error (k1) made was that the students had understood the problem, identifying a function and not a function but the student answered with another concept. s-3 gave the same answer pattern in picture 1-4. when the interview was conducted, the students already understood the problem, but the students' conception was a function is when there is a parallel straight line. figure 6. the answer of s-3 on question number 2 fitrianna & rosjanuardi, identification of junior high school students’ error types … 182 s-22's answer in figure 7 was correct, but for the reasons given it was still incorrect, because there was an empty domain. thus, the conceptual error (k2) was incorrect reasons although students had correctly answered. based on the results of the interview, the students' conception was that it is called a function if the domain and codomain were paired (nothing is empty). it is called not function because there were empty domains and codomains. the domain that the student meant was the one in b area. figure 7. the answer of s-22 on question number 2 3.3. error analysis on question number 3 indicator of question number 3 is determining the domain, domain and result area of the function. the question can be seen in figure 8. figure 8. question number 3 for the third indicator based on figure 1, it is found that the type of error made by students is conceptual error (k1 and k2). based on figure 9, the s-2’s answer shows that the students already understood the context of the question, but had not shown the conceptual image of the domain, codomain and result area. based on the results of the interview, the reason was that the students had not yet understood the concept of the domain, codomain and result area. so that the conceptual error (k1) made by students is that the students already understood the problem, determining the domain, codomain and result area, but did not understand the concept of domain, codomain, and result area. volume 10, no 2, september 2021, pp. 175-190 183 figure 9. the answer of s-2 on question number 3 the s-14’s answer in figure 10 shows an error in determining the result area. students already had an idea of the concept that the codomain is the set that will be paired with the domain, but in determining the result area, the students added up all members of the codomain that had pairs, 1 + 4 + 9 + 16 = 30. s-23 assumed that the result area was the final count or the final result so that all the numbers were added up. the conceptual error (k2) made by students was the answers in the results area were still incorrect although they had correct answers in the domain and codomains. students have a conception that the results area is summing up the elements in the paired domains. figure 10. the answer of s-14 on question number 3 3.4. error analysis on question number 4 the question indicator of number 4 is solving problems related to relations and functions. the question can be seen in figure 11. figure 11. question number 4 for the fourth indicator based on figure 1, it is found that the types of errors made by students are conceptual errors (k1) and technical errors. based on figure 12, s-21 had not answered correctly. the results of the interview stated that the students already understood the context of the questions, but this student did not understand what concepts were used and how to solve the fitrianna & rosjanuardi, identification of junior high school students’ error types … 184 questions. so that the conceptual error (k1) made was that he already understood what was known and asked, but did not understand the concepts used. figure 12. the answer of s-21 on question number 4 meanwhile, the s-26 made technical errors, this student already understood what was known and asked and carried out the calculation procedure, but were not careful in reading the questions (see figure 13). figure 13. the answer of s-26 on question number 4 3.5. error analysis on question number 5 indicator of question number 5 is solving problems related to relations and functions in the form of an equation. the question can be seen in figure 14. figure 14. question number 5 for the fifth indicator based on figure 1, the type of error made by students is a mistake in understanding the question (m). errors in understanding the questions made by s-22 was s/he did not volume 10, no 2, september 2021, pp. 175-190 185 understand the questions and concepts used, s/he only continued to compute from the table that has been given (see figure 15). figure 15. the answer of s-22 on question number 5 3.6. error analysis on question number 6 the indicator of question number 6 is to express the function in the equation formula and the graph of the function. the question can be seen in figure 16. figure 16. question number 6 for the sixth indicator based on figure 1, it is found that the types of errors made by students are conceptual errors (k1 and k2) and procedural errors (p). figure 17 show that s-14 already has a conceptual image of finding the value of the function by substituting the x value into the function, but the x variable remains in the final result and multiplying the value of the known variable by the second term. based on the interview, this student forgot to determine the procedure for determining the value of the function, as she remembered that the value in the brackets was multiplied, but the she forgot to multiply it by one (syllable) or both. so that at point a, the student made procedural errors, the students already understood the questions and concepts used but were wrong in carrying out the calculation procedure. in point b, the student made a conceptual error (k1), that is, the students already understood the questions but she was not correct enough to relate to the correct concept. in point c, students made conceptual errors (k2). in this case, students already understood the questions and concepts that must be used but had wrong understanding of the concept of the domain and result area. fitrianna & rosjanuardi, identification of junior high school students’ error types … 186 figure 17. the answer of s-14 on question number 6 the students s-25 can perform operations to determine the value of the function, but in point b students still cannot distinguish between codomains and result areas, and in point c in drawing function graphs there are still errors in writing the correct domain on the x-axis and the result area should be on the y-axis (see figure 18). based on the results of the interview, this student called the domain as the group that was on the right and the codomain as the group was on the left, the result area is the final result. as for the graph, s/he assumed that there were no certain conditions to place the domain and the result area. figure 18. the answer of s-25 on question number 6 based on the results of the answer analysis, students who made conceptual errors (k1), students had understood the questions well, but in answering it was not in accordance volume 10, no 2, september 2021, pp. 175-190 187 with the concept used. the following is the conceptual error type one (k1) on each question indicator: (a) in presenting the relationship with an arrow diagram, students presented it in another form that was close to the arrow diagram; (b) in identifying functions and not functions, students saw from the picture presented in the question, there were several parallel and crossed lines, so that students made mistakes in understanding the concept of function seen from parallel or cross arrows; (c) students did not understand the concept of domain, codomain and result area; and (d) in solving problems related to the concept of relations and functions, students did not understand what concepts used in solving problems. the following is the conceptual error type two (k2), students already understood the questions well and even they answered the questions correctly but they gave wrong reasons and were associated with concepts other than relations and functions: (a) in presenting relations with arrow diagrams, students' understanding was confused on the concept of presenting the form of relations and functions, one with another. the reason was that students had a different conception of the arrow diagram; (b) in identifying a function and not a function, students had a conception that it was called a function if the domain and codomain were paired (there was no one that was not paired). it was called not a function because there were domains and codomains that did not have a partner; (c) students had correctly answered for the domain and codomain, but the answer in the result area, the students had a conception for the result area that summing up the elements in the paired codomain; and (d) in solving problems related to the concept of relations and functions, they had used the requested concept, but in graphical presentation students did not pay attention to the location of the domain and result area. types of conceptual errors (k1) and (k2) are closely related to students' knowledge of the concept of relations, functions, domains, codomains, result areas and their presentation using arrow diagrams, sequential pairs and cartesian diagrams. for students who made conceptual errors (k1), they had a conceptual image that was asked for in the questions, but did not have the proper knowledge of the concepts, so they answered by paying attention to sentences in questions and other concepts outside the concept of relations and functions. this showed that the understanding of other concepts that were already owned by students affected students' understanding of concepts in the next material. these concepts were understood by students through visible characteristics. this is in accordance with (slavit, 1997), that a person understands the concept through various examples of functions and seeing its properties, students can understand the function as an object that has these properties. for students who made type two conceptual errors (k2), the reason was that they had a different conception of the correct concept. the wrong conception of students was the cause of mistakes made by students in relation to material and functions. the results of research by hatısaru and erbaş (2010) indicate that vocational secondary students have very weak perceptions of the concept of function. kamariah and marlissa (2016) also give similar results that students with the average ability had misconceptions, determining relations which are functions and determining certain values that fulfill a function. other error made by students was procedural errors, which are related to finding the value of the function of an equation. students had not been able to solve problems systematically which involved a thinking process. the cause of this error was students forgot how to perform the procedure for substituting variable values into equation functions. research results by hakim et al. (2020) show that the percentage of procedural errors committed by grade eight students at a junior high school in yogyakarta in the 2019/2020 school year in solving relationship and function problems is 93.7.%. in addition, the technical errors made were in the indicators of solving relationship and function problems. students were not careful in reading what questions were asked, even though the concepts fitrianna & rosjanuardi, identification of junior high school students’ error types … 188 and procedures were correct but the expected answers were still wrong. the students already had the concept description but there was inaccuracy from the students, resulting in errors. errors in understanding questions also occurred in indicators of solving problems of relations and functions, students did not understand what was known and asked about the questions and the use of concepts. students did not understand what was being asked so they did not have a conceptual description that will be used in solving the questions. the three types of errors were closely related to cognitive factors and students' conceptual images. this explanation is in line with tall and vinner (1981) that concept images consist of all cognitive structures in an individual's mind that are different from the formal concept definition and contain several factors that cause cognitive conflict. tall (1988) states that empirical research has emphasized that a person constructs a mental image of a concept in a way that may be inconsistent, and previous student experiences can influence the meaning of the phenomenon when students meet in a new context. 4. conclusion based on the results of the study, 62% of students did the first type conceptual and 21% of the students did the second type conceptual error. for students who make type one conceptual errors (k1), they have a conceptual image that is asked for in the question, but do not understand the correct concept, so that students solve the problem by paying attention to the sentence on the question and answer with other concepts that have nothing to do with the concept of relations and functions. for students who make type two conceptual errors (k2), students have a different conception of the correct concept. in procedural errors, students have not been able to solve problems systematically which involve a thinking process. in the misunderstanding of the questions, students do not know what is being asked so they do not have a conceptual description that will be used in solving the questions. then in technical errors, the concept description is already owned by students but there is inaccuracy from students, resulting in errors. incorrect students' conception regarding relation and function material are: (a) the arrow diagram is shown by a cartesian diagram and arrows are given on both axes; (b) it is called a function if the domain and codomain are paired (none of which is empty), it is called not function because there are empty domains and codomains; (c) the result area is summing up the elements in the paired codomain; (d) domain is the group that is on the right and the codomain is the group that is on the left, the result area is the final result; and (e) there are no rules for placing domains and codomain in drawing graphs of functions. references as’ari, a. r., tohir, m., valentino, e., imron, z., & taufiq, i. 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(2017). explicating mathematical concept and mathematical conception as theoretical constructs for mathematics education research. educational studies in mathematics, 94(2), 117-137. https://doi.org/10.1007/s10649-016-9728-1 https://doi.org/10.30738/union.v8i1.7611 https://doi.org/10.1016/j.sbspro.2010.03.617 https://doi.org/10.22460/infinity.v9i2.p263-274 https://doi.org/10.22460/infinity.v8i1.p31-42 https://doi.org/10.1007/bf00302715 https://doi.org/10.1007/s10649-016-9728-1 fitrianna & rosjanuardi, identification of junior high school students’ error types … 190 slavit, d. (1997). an alternate route to the reification of function. educational studies in mathematics, 33(3), 259-281. https://doi.org/10.1023/a:1002937032215 tall, d. (1988). concept image and concept definition. senior secondary mathematics education, 1983, 37–41. tall, d., & vinner, s. 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(1966). on theory and verification in sociology. science and society, 30(1), 114-117. https://doi.org/10.1023/a:1002937032215 https://doi.org/10.1007/bf00305619 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 9, no. 2, september 2020 e–issn 2460-9285 https://doi.org/10.22460/infinity.v9i2.p183-196 183 relationship between statistical literacy and mathematical representation of students through collaborative problem solving model johannis takaria1*, wahyudin2, jozua sabandar3, jarnawi afgani dahlan2 1universitas pattimura, indonesia 2universitas pendidikan indonesia, indonesia 3institut keguruan dan ilmu pendidikan siliwangi, indonesia article info abstract article history: received mar 14, 2020 revised sep 5, 2020 accepted sep 6, 2020 the purpose of this study was to find out the relationship between statistical literacy and mathematical representation of students as pre-service elementary school teachers through the collaborative problem solving (cps) model. the relationship between statistical literacy and mathematical representation was analyzed by using a product-moment correlation with a sample of 35 students of elementary school teacher education study program at one of the state universities in ambon city. the results showed that there was a positive and strong relationship between statistical literacy and mathematical representation with a correlation value of 0.66. this relationship means that if students have good mathematical representation abilities, statistical literacy abilities are also getting better. exploration of statistical literacy and mathematical representation abilities can be facilitated by using the cps learning model. the cps learning model can facilitate student learning as a structure in mathematical thinking so that statistical literacy and mathematical representation abilities of students can be explored through the transformation of ideas among students. the cps learning model aspects were implemented in high and very high categories while the indicators were at rating-2 and rating-3. keywords: statistical literacy, mathematical representation, cps learning model copyright © 2020 ikip siliwangi. all rights reserved. corresponding author: johannis takaria, department of mathematics education, universitas pattimura jl. ir. m. putuhena, poka, tlk. ambon, maluku 97233, indonesia email: johannistakaria007@gmail.com how to cite: takaria, j., wahyudin, w., sabandar, j., & dahlan, j. a. (2020). relationship between statistical literacy and mathematical representation of students through collaborative problem solving model. infinity, 9(2), 183-196. 1. introduction thinking skills are important to be developed in statistical and mathematical learning. hendriana et al. (2019) stated that mathematical thinking skills are the focus of mathematical learning in schools. takaria and talakua (2018a) stated that the abilities of students in statistical learning must be supported by good mathematical abilities so that https://doi.org/10.22460/infinity.v9i2.p183-196 takaria, wahyudin, sabandar, & dahlan, relationship between statistical literacy … 184 students can be actively involved in facing and solving various challenging statistical problems. statistics in the school curriculum is an integrated material in mathematics. best and khan (1995) stated that statistics are part of mathematical techniques, related to the collection, organization, analysis, and interpretation of numerical data. mastery of statistical concepts requires students to have good mathematical abilities. in higher education, statistics are taught separately and not integrated into mathematics, but mathematics is crucial in understanding statistics. takaria (2015) showed a gap between the importance of statistics and the abilities of students. it was found that the statistical abilities of students as pre-service elementary school teachers at one of the state universities in ambon city had not yet achieved the expected results. this is caused by the lack of basic skills in statistics and mathematics. there is a lack of basic statistical knowledge possessed by students, so that showed a phobia of mathematics and statistical anxiety that had an impact on learning interest (garfield, 1995; garfield & ahlgren, 1988; tishkovskaya & lancaster, 2010; verhoeven, 2006). garfield (1995) stated that in statistical learning, students are not empowered to apply aspects of statistical knowledge in solving general problems from certain contexts. based on the researcher's experience as a teaching lecturer in educational statistics courses and basic concepts of mathematics, it was found that problems with basic statistics and mathematics knowledge is also a problem for students who are pre-service elementary school teachers in the study location. in the basic ability of mathematical compute operations, students made a frequency distribution table to determine classes by using the sturgess rule k = 1 + 3.3 log n. students showed wrong basic calculation skills, where students added 1 + 3.3 first then the results were multiplied by log n. this showed that students did not understand the level in mathematical operations, 3.3 log n was completed first, then the result was added with 1. other findings showed that students calculated the average by not using the procedure correctly. students are directly calculated without writing the equations and statistical symbols first. the basic ability of analysis and interpretation is important to be improved, especially the ability to understand statistical information, read and write (graphs and tables), and interpret correctly. the main thing that is often overlooked by students is not writing the title of tables and graphs. statistical and mathematical learning requires literacy. fatmanissa and sagara (2017) stated that literacy is the ability to read and write that is used when reading and understanding a problem to be written in a mathematical model. literacy has been developed in various fields, one of which is statistical literacy, although there are still many problems with statistical knowledge. lack of statistical knowledge due to low statistical literacy abilities. the lack of statistical literacy abilities is due to the inability to apply it in everyday life (gal, 2002; tishkovskaya & lancaster, 2010; verhoeven, 2006). schield (1999) stated that statistical literacy is more than just the use of numbers, but individuals must be able to understand what is affirmed, think critically about statistical arguments, and have inductive reasons for those arguments. research conducted by watson (2003) found that statistical literacy is important and becomes part of the curriculum. according to him, several factors that contribute to the development of statistical literacy in schools are due to: 1) the expectation to participate as citizens in accessing information related to data; 2) the importance of abilities and skills in every possible decision making on data. basic skill and is important to use in understanding statistical information or research results. these skills aim to organize data, compile and display tables, and work with different volume 9, no 2, september 2020, pp. 183-196 185 data representations. statistical literacy also includes an understanding of concepts, vocabulary, symbols, and includes an understanding of probability as a measure of uncertainty (ben-zvi & garfield, 2004; callingham & watson, 2017). this problem is inversely proportional to the importance of statistical literacy. the reading and interpreting statistical reports requires statistical literacy abilities which include sufficient knowledge and understanding of calculations, statistics, understanding of literacy in general, utilize quantitative data for data presentation and make summary reports on personal or professional assignments (chick & pierce, 2013; gal, 2002; ben-zvi & garfield, 2004; watson, 2006). the study on statistical learning stated that statistical learning through problem-solving can improve student skills, especially when they interact directly with data (garfield, 1995; garfield & ben-zvi, 2007; marriott et al., 2009). statistical literacy is the ability to critically interpret and evaluate statistical information in argument-based data on various media channels and their ability to discuss it (gal, 2002). aoyama and stephen (2003) stated that statistical literacy is the ability to extract qualitative information from quantitative and make new information from qualitative and quantitative data. bidgood et al. (2010) stated that statistical literacy requires skills in problem-solving namely, abilities in reading, writing, listening, and speaking. statistical literacy is defined as the ability to read, write, understand, interpret, analyze at a basic level, and interpret data through the abilities possessed and can understand and present information in the form of tables, graphs and statistical symbols in various media. statistical literacy also plays a role in minimizing errors that occur in activities with data, so that data users can overcome the problems encountered. various media are used to improve the statistical literacy of students, namely electronic media, print media, internet, journals, and various other statistical literacy media. media literacy can be used as information in statistical learning, so as to increase the abilities of students in reading and writing statistically. statistical literacy abilities need to be supported by good mathematical abilities. one of them is mathematical representation. the representation can be used as a tool through diagrams, graphs, tables, and symbols in expressing mathematical abilities for problemsolving, communication (learning by oral, written, drawing, graphic, and concrete concepts), and see the relationship to a mathematical problem (bal, 2014, nctm, 2000; takaria & talakua, 2018a). ainsworth (2006) stated that representation is a way to interpret what is captured and interpreted through an image, on the screen or in words where someone can say whatever they want to say. mathematical representation in statistical learning is the ability to convey ideas or mathematical ideas in various forms (tables, graphs, symbols, the meaning of words, and mathematical equations) of what is seen or observed through statistical information obtained and can interpret information. mathematical representation in statistical literacy learning for students is important, because students can convey mathematical ideas in various forms (tables, graphs, symbols, meaning of words, and mathematical equations) from something seen/observed through statistical information obtained on various media and the student's ability to give meaning to this information (takaria & talakua, 2018b). statistical literacy and mathematical representation are two capabilities that synergize with each other and contribute to the learning process. the relationship between statistical literacy and mathematical representation can be facilitated with the collaborative problem solving (cps) learning model. collaborative learning involves intellectual efforts to seek understanding, solutions, meanings, and produce a product based on mutual agreement (van den bossche et al., 2006). takaria, wahyudin, sabandar, & dahlan, relationship between statistical literacy … 186 the selection of the cps learning model is based on the idea that this model is a form of group learning to form students into individuals who are strong in problem-solving. the cps learning model requires skills in problem-solving and managing differences, which are implemented through a collaborative process. the cps learning model consists of five stages namely, engagement, exploration, transformation, presentation, and reflection (ngeow, 1998). the cps learning model is used to analyze the relationship between statistical literacy and mathematical representation of students as pre-service elementary school teachers. 2. method 2.1. method and sample this study used a correlational analysis method. the purpose of this study was to analyze the relationship between statistical literacy and mathematical representation of the abilities of students with the cps learning model. the sample of this study was 35 students of the elementary school teacher education study program enrolled in statistical education at one of the state universities in ambon city, maluku province, indonesia. this study used a purposive sampling technique. this technique was used by researchers based on several considerations: (1) researchers expected the study to be carried out well and effectively; 2) researchers analyzed the problem according to the objectives to be achieved; and 3) students passed mathematical education i and ii as prerequisite courses before enrolling statistical education. 2.2. instrument an instrument is a tool used to measure the variables to be studied. therefore, research instruments need to be prepared appropriately, so that the data collected comprehensively can answer the problem and research objectives. the instruments used were statistical literacy and mathematical representation tests, and non-test instruments were in the form of observation and interview guidelines. 2.3. data analysis data analysis used a product-moment correlation. the pearson product-moment correlation coefficient is widely used in social science research as a correlational technique between two variables (x and y) and also in accordance with various univariate and multivariate methods (smithson, 2000; walker, 2017). to analyze the feasibility of the cps learning model, the feasibility rating model was used. table 1 presents the feasibility rating of the cps learning model that refers to the new teacher project (takaria, 2015; takaria & talakua, 2018b). table 1. the feasibility rating of the cps learning model rating indicator 3 all indicators are implemented 2 half or most indicators are implemented 1 more than half of the indicators are not implemented 0 all indicators are not implemented the ratings in table 1 were analyzed using the percentage qualifications in table 2 adapted from (linnusky & wijaya, 2017) volume 9, no 2, september 2020, pp. 183-196 187 table 2. percentage qualifications of learning model feasibility qualification category k ≥ 90% very high 80% ≤ k < 90% high 70% ≤ k < 80% fair 60% ≤ k < 70 low k < 60% very low 3. results and discussion 3.1. results 3.1.1. correlational analysis the correlational analysis is a technique for looking at linear relationships between two or more variables. based on that definition, the analysis statistically tests the relationship between statistical literacy and mathematical representation abilities with the cps learning model. the analysis was used to see the relationship between statistical literacy and mathematical representation. the hypothesis was “there is no relationship between statistical literacy and mathematical representation” (h0) and the working hypothesis was (h1) “there is a relationship between statistical literacy and mathematical representation”. based on the classical assumption test, it was obtained that the data were not normally distributed so that the transformation of the data with square root transformation was carried out. after the data of statistical literacy and mathematical representation were transformed, the data were normally distributed (see table 3). the homogeneity test showed that both data were homogeneous (see table 4). table 3. normality tests of statistical literacy and mathematical representation ability significance normality test kolmogorovsmirnov decision statistical literacy (sig.) 0.054 normal mathematical representation 0.136 table 4. homogeneity tests of statistical literacy and mathematical representation ability significance homogeneity test levene test decision statistical literacy (sig.) 0.230 homogenous mathematical representation 0.164 after the assumptions are fulfilled, a correlational test is carried out using the pearson correlation test with the test criteria, if sig. greater than 0.05 then h0 is accepted and h1 is rejected. table 5 show the results of correlation testing. takaria, wahyudin, sabandar, & dahlan, relationship between statistical literacy … 188 table 5. correlational test of statistical literacy and mathematical representation pearson correlation sig. decision 0.661 0.000 h0 is rejected table 5 showed that the value of sig (0,000) was smaller than 0.05 so that h0 was rejected. these results conclude that there was a significant relationship between statistical literacy and mathematical representation. the pearson correlation value obtained was 0.661, if confirmed by the test criteria, the relationship between statistical literacy and mathematical representation was in a positive and strong relationship. this relationship showed that if students have good mathematical representation abilities, statistical literacy abilities are getting better. strengthening statistical literacy and mathematical representation of students was facilitated through the use of the cps learning model and supported by a good mathematical disposition so that there would be solutions for statistical problems. figure 1 showed the relationship between statistical literacy and mathematical representation with the cps learning model in mathematical problem solving. figure 1. relationship between statistical literacy and mathematical representation with the cps learning model 3.1.2. collaborative assessment the collaborative assessment of students was conducted by using the rubric of feasibility assessment, both in groups and individually. for group assessment, the aspects assessed were: 1) group formation (gf) with several indicators namely, independence in group formation, group division according to ideal group division criteria, and division of roles of each individual in the group; 2) idea construction and transformation (ict) with several indicators namely; mutually building ideas, interactions, and the ability to express opinions or ideas; 3) presentation of results (pr) with several indicators namely, effective use of time, represent the results of collaboration well, and be able to answer questions from other groups; 4) group reflection (gr) with several indicators namely, group reflection on weaknesses when exploring and transforming ideas, reflection on the results of presentations, and reflection when arguing. based on the observation results through an observation sheet on the collaboration process to observe and record various processes in accordance with the observation statistical literacy conceptual knowledge ▪ mathematical abilities ▪ statistial abilities ▪ communication skills ▪ reasoning ability (bidgood et al., 2010; gal, 2002) disposition ▪ motivation ▪ criticism mathematical representation statistical information collaborative problem solving model statistical learning media as learning resource problem solving solution volume 9, no 2, september 2020, pp. 183-196 189 guidelines provided, the aspects of collaboration were in very good and good qualifications, with a rating that all indicators were implemented (rating-3) and half or most indicators were implemented (rating-2). table 6 presents the rating and qualification ratings for each cps aspect. table 6. rating and qualification of cps aspects aspect cps group cps group percentage of average qualification 1 2 3 4 5 6 7 1 2 3 4 5 6 7 rating (rg) qualification (%) gf 3 3 3 3 3 3 3 100 100 100 100 100 100 100 100 ict 2 3 2 2 3 3 3 75 86.7 71 75 76.7 83.3 86.7 79.2 pr 2 3 2 3 3 3 3 66.7 83.3 79.3 83.3 83.3 86.7 90 81.8 gr 3 2 3 3 3 3 3 83.3 90 86.7 86.7 90 90 90 83.3 through the observation sheet it can be observed that the lecturer: 1) developed cognitive conflict through several inducement questions during the collaboration to explore insights from students more deeply; 2) commented and examined the results of group work for each meeting after collaborating; and 3) used assessment rubrics in the form of percentages and records of the feasibility of collaboration to assess student activities both individually and in groups. the results of observations through the feasibility observation sheet, assessment rubric, and important notes during the collaboration process were obtained: (1) overall, the use of the cps learning model was carried out properly and in accordance with the learning steps; (2) at the beginning of the meeting (1st), students were less flexible in collaborating; (3) only a few students were aggressive in expressing opinions (1st & 2nd meetings), other students were not having the courage in conveying ideas; (4) constructed ideas were not in accordance with the expectations of the concept of collaboration; (5) in arguing, only a few students that were proactive in defending the ideas conveyed; (6) individuals in the group had difficulty in reaching an agreement, due to various opinions that must be united (1st meeting); (7) some students tended to emphasize personal ego in the argument (1st meeting). based on these problems, the lecturer as a facilitator, motivated and directed students in accordance with the principles and objectives of collaboration, so that the implementation of the collaboration can run well at the next meeting, students who had the low ability and were being aggressive in conveying their ideas. students were more flexible in collaboration, which was demonstrated through the exploration and transformation of ideas. decision making on collaboration results was no longer a group problem, where each individual appreciated the ideas conveyed by peers. radical obtrusiveness was also diminishing. reflection on collaboration was very useful for students, where students individually or in groups reflected the weaknesses they had at the time of collaboration. reflection is a process that is needed by students when collaborating, this makes students know their weaknesses and strengths. reflection can be in the form of attitudes when collaborating and also towards collaborated concepts. at the end of the meeting, there were several students sharing with the lecturer to discuss issues that were still being considered. figure 2 presents the ladder of reflection between students and lecturers. takaria, wahyudin, sabandar, & dahlan, relationship between statistical literacy … 190 figure 2. ladder of reflection in students based on the findings, it can be explained that students who have good statistical literacy and mathematical representation abilities will drive them to become strong individuals in the field of statistics so that they have better goals and expectations in statistical problems oof society. figure 3 shows the goals and expectations of statistical literacy and mathematical representation abilities. the confrontation results of collaboration in the minds of students students hypothesize collaborated results sharing with lecturers convey information from the results of collaboration and interpretation obtain an explanation from the lecturer & are advised to look for related references obtain the solution volume 9, no 2, september 2020, pp. 183-196 191 figure 3. goals and expectations of statistical literacy and mathematical representation abilities 3.2. discussion statistical literacy is the ability students must have in critically interpreting and evaluating statistical information contained in various media. students with good statistical literacy abilities can be actively involved in addressing statistical problems in society. to complete statistical literacy abilities, mathematical representation is needed, related to the ability to represent statistical problems in various forms through the representation of tables, graphs, mathematical equations, symbols, interpretation of words, and other mathematical representations. the relationship between statistical literacy and mathematical representation explicitly through testing obtained a product-moment correlation index of 0.66, which was in strong and positive category. the results showed that students with good mathematical representation abilities will have an impact on good statistical literacy abilities. mathematical representation abilities owned by students in statistical learning has a purpose to help students in presenting creative ideas on challenging statistical problems, views on the importance of statistical literacy skills, mathematical representations, and attitudes of students as preservice elementary school teachers ability that is exposed ▪ mathematical abilities ▪ statistical abilities ▪ think logically, critically, and creatively ▪ analysis & interpretation statistical media literacy: ▪ internet ▪ television and print media ▪ journals ▪ textbook ▪ billboards and other media. supported by mathematical representation abilities: ▪ visual representation ▪ representation of mathematical equations ▪ symbol representation ▪ interpretation of wordskata statistical literacy ability are required: ▪ speak and write ▪ communicate ▪ arguing ▪ proficient the importance of statistics ▪ statistics plays an important role in various activities ▪ important for the final project & research supported by attitude: ▪ communicating ideas ▪ self confidence ▪ appreciate opinion ▪ cooperate ▪ self reflection. ▪ tough in mathematics & statistics ▪ can compete in the global era ▪ become a professional elementary school teacher ▪ further study ▪ answering problems in the community ▪ strong self concept statistics goals and expectations takaria, wahyudin, sabandar, & dahlan, relationship between statistical literacy … 192 namely: 1) can present information from tables into the graphical form or vice versa represent graphs in tabular form; 2) can write symbols and interpret terms; 3) use mathematical procedures correctly in solving statistical problems; 4) make arguments mathematically in contextual situations related to statistics; 5) can use variables, make equations and calculations; and 6) can use mathematical representation in other forms to solve statistical problems. based on figure 1, students need to be given a reinforcement of statistical literacy abilities on the basis of strengthening mathematical knowledge, statistics, communication skills, and reasoning. statistical literacy abilities need to be supported by mathematical representation abilities and dispositions, in this case, motivation and critical attitude. through statistical literacy skills, students can find a variety of statistical information that can be used as learning resources and facilitated through the cps learning model to find solutions to statistical problem-solving. bidgood et al. (2010) stated that the two major components needed in statistical literacy are: 1) the knowledge components namely; literacy skills, mathematical knowledge, statistical knowledge, communication skills, and reasoning; 2) disposition components namely; attitude in evaluating, constructing, recognizing, challenging and communicating ideas. both components should be owned by students in responding to statistical information in various media ladder of reflection in figure 2 shows the existence of student ideas that are not channeled and become problems for students, but in the process of reflection, the problem can be overcome. reflection is a process that is needed by students for what they do when collaborating, this makes students know their weaknesses and strengths. according to jonassen and rohrer-murphy (1999), learning activities are important activities but are not enough to interpret the learning, but must reflect the learning experience so that learning is more meaningful. the results of identification through a series of questions to several students who performed sharing showed that students were hesitant to convey their ideas during the process of transformation and interpretation of work in front of the class. this is due to the lack of confidence in conveying the ideas. the problems experienced by students can be sought for solutions through reinforcement and direction given by the lecturer. the steps taken are directing thought processes in constructing creative ideas through structured experiences during collaboration and students are encouraged to be more confident in conveying ideas. according to figure 3, it can be seen that students who have statistical literacy and mathematical representation abilities have an impact on their future prospects, where they are tough in the field of statistics, can compete, become professional teachers, further study, able to answer statistical problems in society, and has a strong statistical self-concept. statistical information is the main source to improve literacy and representation skills. to understand, analyze, and interpret the information, several literacy skills are required namely; speaking and writing skills, communication, argumentation, and representation skills. attitudes in communicating ideas and self-confidence, are the main indicators and are important for students to have. attitudes need to be supported by abilities of mathematics, statistics, logical thinking, critical, creative, analysis and interpretation. attitudes and abilities possessed will make students a formidable individual in finding solutions to challenging statistical problems in society. the results of observations on the strengthening of statistical literacy and mathematical representation through the use of the cps learning model showed that all aspects of collaboration were carried out in good and very good qualifications. the volume 9, no 2, september 2020, pp. 183-196 193 feasibility indicator of the model was at rating-2, with criteria for half or most of the indicators that were implemented and rating-3 of all indicators were implemented. the cps learning model was feasible because the lecturer was able to apply the model according to stages of collaborative learning. the results of interviews with several students obtained information that, the cps learning model was effectively used in the learning process. the problem was that collaboration time needed to be added. another response showed that collaborating can facilitate students to understand statistical material with the help of statistical literacy learning media. by collaborating, students are trained to construct ideas individually in understanding statistical information (determining main ideas, seeing relationships and differences), and can present information in tables or graphs. related to anxiety, students had diverse opinions. students stated that lectures by collaborating can minimize anxiety. lectures on statistics with statistical literacy media for students can help them in writing a bachelor thesis, especially the ability to read graphs, tables, statistical symbols, and be able to describe them. the results of this study expect a reformation of the statistics learning paradigm for students which is oriented towards increasing the ability to analyze and interpret data from a statistical problem through the use of statistical literacy media in learning. statistical literacy and mathematical representations also need to be maximally developed for elementary school students through the use of information literacy-based media that contains contextual statistical problems. 4. conclusion based on the results, it can be concluded that there was a strong relationship between statistical literacy and mathematical representation of students as pre-service elementary school teachers facilitated through the cps learning model. overall, the qualification aspects of the cps learning model had an increase in high and very high qualifications, while the feasibility of the model indicators was at rating-2 (half or most of the indicators were implemented and rating-3 (all indicators were implemented). references ainsworth, s. 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(2006). issues for statistical literacy in the middle school. icots-7 conference proceedings. iase, salvador (cd-rom). 1-6. https://doi.org/10.21831/jk.v2i2.18768 https://doi.org/10.30870/jpsd.v4i2.3852 http://iase-web.org/documents/papers/icots8/icots8_c193_tishkovskay.pdf http://iase-web.org/documents/papers/icots8/icots8_c193_tishkovskay.pdf http://iase-web.org/documents/papers/icots8/icots8_c193_tishkovskay.pdf https://doi.org/10.1177%2f1046496406292938 https://www.stat.auckland.ac.nz/~iase/publications/17/3a4_verh.pdf https://www.stat.auckland.ac.nz/~iase/publications/17/3a4_verh.pdf https://www.stat.auckland.ac.nz/~iase/publications/17/3a4_verh.pdf https://doi.org/10.22237/jmasm/1509496140 http://iase-web.org/documents/papers/isi54/3516.pdf http://iase-web.org/documents/papers/isi54/3516.pdf http://iase-web.org/documents/papers/icots7/6c1_wats.pdf http://iase-web.org/documents/papers/icots7/6c1_wats.pdf takaria, wahyudin, sabandar, & dahlan, relationship between statistical literacy … 196 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 8, no. 2, september 2019 e–issn 2460-9285 https://doi.org/10.22460/infinity.v8i2.p167-178 167 implementation of realistic mathematics education based on adobe flash professional cs6 to improve mathematical literacy uba umbara *1 , zuli nuraeni 2 1,2 stkip muhammadiyah kuningan article info abstract article history: received nov 13, 2018 revised june 17, 2019 accepted sept 2, 2019 students' mathematical literacy abilities are important to master, especially to formulate mathematical concepts that can be used in everyday life. mathematical literacy has become an important issue lately to be developed in the study of mathematics learning. however, mathematical literacy has not become the main goal in the implementation of the learning carried out. the purpose of this study was to examine the comparison of students 'mathematical literacy skills with adobe flash professional cs6-based rme learning with conventional learning and to examine the comparison of improvement in students' mathematical literacy skills with adobe flash professional cs6-based rme learning with conventional learning. the research method used in this study was quasi-experimental with the design of a non-equivalent control group design. the results of the two research hypotheses were accepted. it is possible that the increase in students' mathematical literacy skills is triggered by the adobe flash professional cs6-based rme learning which in the implementation of learning always focuses on self regulated learning. keywords: adobe flash profesional cs 6, mathematical literacy, rme copyright © 2019 ikip siliwangi. all rights reserved. corresponding author: uba umbara, departement of mathematics education, stkip muhammadiyah kuningan, jl. r.a. moertasiah soepomo no. 28 b, kuningan, jawa barat 45511, indonesia email: uba.bara@upmk.ac.id how to cite: umbara, u., & nuraeni, z. (2019). implementation of realistic mathematics education based on adobe flash professional cs6 to improve mathematical literacy. infinity, 8(2), 167-178. 1. introduction one of the goals that students need to achieve in order to obtain deep and meaningful literacy in mathematics learning is to understand the mathematics they learn through constructing students' abilities regarding various mathematical concepts. constructing these capabilities, can be done if students have the ability to read and write mathematical symbols known as mathematical literacy abilities. mathematical literacy skills help individuals to recognize that mathematics plays a role in every aspect of life. mathematical literacy is an individual’s capacity to formulate, employ and interpret mathematics in a variety of contexts. it includes reasoning mathematically and using mathematical concepts, procedures, facts and tools to describe, explain and predict phenomena. it assists individuals to recognise the role that mathematics plays in the world mailto:uba.bara@upmk.ac.id umbara & nuraeni, implementation of realistic mathematics education … 168 and to make the well-founded judgements and decisions needed by constructive, engaged and reflective citizens (oecd, 2017). by looking at this, literacy can be placed as a very important ability, not only in mathematical learning but also mathematical literacy further in life. mathematical literacy helps one to understand the role or usefulness of mathematics in everyday life. in a discussion, mathematical literacy is not limited to the ability to apply quantitative aspects of mathematics but involves mathematical knowledge in a broad sense (de lange, 2003). this action has mandated the teacher to think differently about what learning means and understanding mathematical concepts for students to align more closely with mathematical literacy (nctm, 2000). meanwhile, gallimore and tharp (draper, 2002) stated in the most general sense that the ability to read, write, speak, calculate, reason, and manipulate symbols, concepts of verbal and visual as a form of literacy must be taught in school . in daily life, the equalization of students and teachers' perceptions of the importance of mathematical literacy is so important to do (venkat, 2010). thus, we consider someone to be mathematicsally illiterate, if he is unable to read and write. this mathematical literacy is the impact of demands that encourage people to survive under the culture and civilization they have in an area. mathematical literacy refers to the ability and knowledge of students to take and apply the knowledge and abilities acquired from the classroom into their reallife understanding and experience in situations involving mathematical concepts (sumirattana, makanong, & thipkong, 2017). in particular, mathematical literacy can be interpreted as the ability of an individual to understand and use mathematics in daily life activities. the subject that is specifically driven by the application of mathematics in life is at the core of a discussion of mathematical literacy that must be owned by someone (julie, 2006). in this connection, someone who studies mathematics is required to have and develop the ability to solve mathematical problems, especially those related to daily activities. some activities that can encourage mathematical literacy are (1) mathematical and mathematical concepts of reasoning, (2) recognizing the roles played by mathematicians in the world, (3) making reasonable decisions and decisions, (4) solving problems set in pupils of the world life context (sandström, nilsson, & lilja, 2013). in mathematics, students are expected to build knowledge by reading, analyzing, and writing mathematical texts (for example, numbers, symbols, graphics) to be considered mathematical literacy (siebert & draper, 2012). mathematical literacy has become a serious oecd study through pisa which began in 2000. nevertheless, rico (sáenz, 2009) explained that pisa is often not directly related to the mathematics curriculum taught in schools, but revolves around the functional model of mathematics learning by developing competencies that are directly related to real world. this concept is then seen to be highly related to realistic mathematical concepts that are focused on the application of contextual mathematics (gravemeijer, 1994). furthermore, larochelle & bednarz (colwell & enderson, 2016) integrates literacy into mathematics, and promotes the vision of constructivist learning. this ability can help students formulate mathematical concepts in solving problems in their daily lives in a structured and systematic way. however, even though it has been stated that mathematical literacy skills are very much needed by students, in reality this field of ability is still not fully controlled by students. one effort that can be implemented in improving students 'mathematical literacy skills is learning realistic mathematics education (rme) which is supposed to be able to generate students' enthusiasm in learning so that in the end it is expected to be able to improve their literacy skills. the main idea of rme learning is that students must be given the opportunity to rediscover mathematical concepts. volume 8, no 2, september 2019, pp. 167-178 169 therefore, rme is a potential model that integrates open problem-based learning, collaborative learning, error analysis and problem solving in the real world (hidayat & iksan, 2015). rme can be understood as an approach that emphasizes social processes, because learning is based on the principle of mutual respect for students' ideas in completing mathematical problems (umbara, 2015). furthermore, as a form of development of rme learning, in this study computer-assisted rme learning will be used using adobe flash professional cs6 software. there are many benefits to using flash animation in learning especially in helping students understand mathematics more meaningfully, connecting mathematics with the real world, visualizing, and understanding the importance of mathematics (salim & tiawa, 2015). the use of animated courseware is seen as very useful to see concrete examples of abstract concepts that require a deep understanding of mathematics learning (pesonen, 2003). learning material compiled using adobe flash software is expected to facilitate students in understanding contextual problems presented in learning. previous research was conducted the mathematical thinking process based on the rme approach assisted by vba excel helps students bridge the horizontal mathematization process towards vertical mathematization mathematical formations (fitriani, suryadi, & darhim, 2018). furthermore, salomon states that integrating ict in education has the motivation to support students' ability to explore constructive thinking that enables them to have the ability to transcend cognitive limitations that they might not be able to do before (lim et al., 2003). integrating ict in learning is seen as being able to develop a culture of thinking by involving students with problems that are challenging but meaningful personally through the use of the world conceptually and the learning culture of the students themselves. however, one challenge is to find methods that can increase the effectiveness of learning in learning and teaching through ict (cañas, novak, gonzález, & hammond, 2004). learning with rme based on adobe flash professional cs6 is expected to be able to improve mathematical literacy skills significantly because it is based on the process of providing learning experiences to students and is not limited to the process of transferring knowledge and knowledge with display of contextual problems that are not only imagined by students but real for students. based on the background above, research aims to review whether mathematical literacy of students with rme based on adobe flash professional cs6 is better than students who obtain learning with conventional learning and assessing the increasing of mathematical literacy of students who apply the rme based on adobe flash professional cs6 learning better than students who obtain learning with conventional learning. 2. method the research method chosen was quasi-experimental research, because the subjects were not randomly grouped but the researchers accepted the condition of the subject as a minimum. the design used in this study is the design of non-equivalent control groups. in this experimental design there were two sample classes, the pretest, the different treatment and the posttest. the sample in the first class is an experimental class that uses rme learning based on adobe flash professional cs6. meanwhile the second class as a control class that gets learning using ordinary learning. the existence of this control class is a comparison, to what extent changes occur due to the treatment of the experimental class. the design diagram of this study is as follows (ruseffendi, 2005). umbara & nuraeni, implementation of realistic mathematics education … 170 o x o o o information : o : pretest and posttest in the form of tests of mathematical literacy skills x : the treatment uses the rme learning based on adobe flash professional cs6. --: subjects are not randomly selected the population in this study were all eighth grade students of smp negeri 3 kuningan totaling 284 students. the sampling technique is done by using purposive sampling technique. the reason for choosing the sample was purposive sampling because the two groups were not actually randomized, only based on the existing class. the sample chosen from the class viii-a students was used as the experimental class and class viii-c which was used as the control class with the number of students in both classes amounting to 65 students. the instrument that will be used in the research is a mathematical literacy test. to provide an objective assessment, the criteria for scoring the test questions for mathematical literacy skills researchers adopted from quasar general rubric (maryanti, 2012), as shown in table 1. table 1. scoring guidelines mathematical literacy score student response mathematical knowledge strategy communication 0 does not show literacy concepts and mathematical principles of the problem. using irrelevant information, it fails to identify an approach that can be used to answer questions, copy some problems without any solution being given. ineffective communication, words do not describe the problem, not completely illustrate the problem. 1 very little shows the literacy of mathematical concepts and principles, one fails in mathematical terms and the majority of calculations are wrong. using irrelevant information, failing to identify an important part, the strategy used is incorrect, the facts provided are incomplete, difficult to identify or not systematic. some parts are explained but not complete and do not pay attention to the important parts of the problem, explanations are less and difficult to understand, the concepts given do not represent problems or are not clear (difficult to interpret) 2 understanding some mathematical concepts and principles, there are still many mistakes in calculations. identify the important parts of the problem, but only show a little literacy about the relationship between the two parts, showing the facts of the calculation process but not complete and not systematic. some of the sections explained have led to problems, but some explanations are still ambiguous or unclear, the mathematical concepts presented are not precise or unclear, the arguments provided are incomplete and the explanation does not enter the basic logic of the problem. volume 8, no 2, september 2019, pp. 167-178 171 score student response mathematical knowledge strategy communication 3 most literacy concepts and mathematical principles, the use of terms and mathematical notation are close to true, outline calculations are correct but there are some calculations that are still wrong. using relevant information, identifying a number of parts and showing in general the relationship between these parts, giving clear facts in the calculation and systematic process, the answers are close to true. the responses given are close to complete, with clear explanations and descriptions, mathematical concepts are presented in full, answers are generally communicated effectively so that they are easily understood by others, provide supporting arguments and the arguments given are reasonable but there are some small parts that are omitted and not explained 4 showing correct literacy concepts and mathematical principles, the use of terms and mathematical notation is correct, calculation and use of complete and correct algorithms. using relevant information, identifying all the important parts and showing the general relationship between these parts, describing the systematic approach and strategy, presenting facts clearly in the calculation process, correct and systematic answers. providing complete and clear responses, unambiguous explanations and descriptions, mathematical concepts are presented in full, effectively communicated so that they are easily understood by others. give a strong argument where the argument is reasonable and complete. furthermore, at the stage of processing research data, the procedure is carried out as follows: (1) give a score on student answers according to alternative answers and scoring system used; (2) make a table of the pretest and posttest students scores of the experimental class and the control class; (3) calculate the average test score for each class; (4) calculate the standard deviation to find out the distribution of groups and show the level of variance in the data group; (5) conduct normality tests to determine the normality of the pretest, posttest and n-gain scores as a whole using the saphiro-wilk test; (6) if the data is not normally distributed, then the mann-whitney nonparametric test can be directly carried out; (7) if the data meets normal assumptions, then the variance homogeneity test can be carried out using the lavene statistics test. if the variance of the two classes is not homogeneous, a t test can be done directly; (8) after a normal and homogeneous assumption is fulfilled, then it can then test the two average differences (t-test) using compare mean independent samples test; (9) next to test the difference between two data gain averages, in this case between the data gain of the experimental class and the data gain of the control class. if the data is normally distributed and homogeneous, then to see whether there are differences in the increase in mathematical literacy skills viewed from kam, a two-way anova test can be carried out. if the data is not normally distributed, umbara & nuraeni, implementation of realistic mathematics education … 172 it can be continued with the kruskal-wallis test. meanwhile, the statistical test used to determine the interaction between the factors of the learning model provided with the category factors of increasing students' mathematical literacy skills can be carried out by two-way anova test using the general linear model univariate analysis. 3. results and discussion 3.1. results after processing the pretest and posttest score data on the aspects of mathematical comprehension ability in the experimental and control groups, descriptive statistics were obtained as shown in the following table 2. table 2. descriptive statistics mathematical literacy capability score test experiment class control class n xmin xmax s n xmin xmax s pretest 31 44 72 52.26 4.12 34 32 76 54.97 10.74 postest 31 60 92 75.10 7.48 34 35 92 66.24 12.89 table 2 presents students' mathematical literacy descriptive statistics. the statistical data states that students' abilities are obtained through pretest and posttest consisting of: number of subjects (n), lowest score (xmin), highest score (xmax), average ( ̅) and standard deviation (sd). based on table 5.4 the average value of the experimental class pretest is 52.26 and the control class average value is 54.97. the control class has an average greater than the experimental class. meanwhile, the experimental class posttest score was 75.10 and the control class was 66.24. the experimental class has a higher average value than the control class. the initial analysis carried out in this study was to conduct a pretest score analysis. analysis of the pretest score was done to see the students' initial abilities or find out whether the difference in the average score of the pretest students in the experimental group and the control group was done using the mann-whitney non parametric test, because based on the normality and homogeneity tests that had been done previously, it was known that one the data are distributed abnormally but are homogeneously distributed, so that the similarity test of the average pretest score is done. testing the hypothesis with a one-way test with α = 0.05 with the testing criteria is accept h0, if asymp.sig (1-tailed)> α, besides h0 is rejected. the test results of the difference in post-test average mathematical literacy ability are shown in table 3. table 3. test results differences in average post-score mathematical literacy ability test statistics a post mathematical literacy mann-whitney u 287.000 wilcoxon w 882.000 z -3.175 asymp. sig. (2-tailed) .001 a. grouping variable: research class volume 8, no 2, september 2019, pp. 167-178 173 table 3 show the asymp. sig (2-tailed) value for the posttest data of students' mathematical literacy ability is 0.001. if taken α = 0.05 then asymp.sig (1-tailed) <α so that h0 is rejected. in conclusion, one research hypothesis was accepted, that: students' mathematical literacy skills using rme based on adobe flash professional cs6 were better than students who used conventional learning. to determine the significance of the difference in the average of the two data classes, a two-way analysis of variance (anova) was conducted. this analysis was conducted to see the direct effect of two different treatments given to students 'mathematical literacy abilities, as well as the interaction between the learning approaches used to the students' ability categories. the results of the calculation of variance analysis test using the general linear model (glm) univariate carried out at a significance level of 5% (α = 0.05). the results of the analysis are shown in the following table 4. table 4. analysis of gain variance in mathematical literacy source type iii sum of squares df mean square f sig. corrected model 1.576 a 5 .315 10.876 .000 intercept 3.695 1 3.695 127.480 .000 kam .690 2 .345 11.898 .000 model .479 1 .479 16.516 .000 kam * model .018 2 .009 .309 .735 error 1.710 59 .029 total 11.588 65 corrected total 3.286 64 a. r squared = .480 (adjusted r squared = .436) table 4 show the value of fcount = 16.516 with a significance level (sig.) is 0.000 smaller than α = 0.05. therefore, the null hypothesis is rejected, meaning that the increase in mathematical literacy skills of students who get learning using the rme based on adobe flash professional cs6 is better than students who get learning using conventional approaches. in other words, it can be concluded that the second hypothesis is accepted. 3.2. discussion the results showed that students with rme learning based on adobe flash professional cs6 had higher average mathematical literacy abilities than students who used conventional learning. this result is possible because through this learning students are able to learn independently, the teacher as a facilitator who provides clues and suggestions in group discussions conducted by students when students feel difficulty in understanding and resolving contextual problems so that students get an understanding of the mathematical concepts better. rme seems to be a promising teaching approach that meets indonesia's needs to improve mathematics teaching (lestari & surya, 2017). on the other hand, the rapid development of ict supports the development of multimedia learning, one of which can be done using adobe flash. the effort aims to improve the quality of learning better. in this ever-changing era, schools must maximize the contribution of new technologies that can be implemented in teaching and learning (psycharis & kallia, 2017). computer technology devices as learning tools have great potential if they can be utilized in the learning process (suartama, 2010). umbara & nuraeni, implementation of realistic mathematics education … 174 rme learning based on adobe flash professional cs6 makes students active in mathematical learning and can rediscover mathematical concepts in their own way. rme was a movement to reform mathematical education, so it was not only a mathematical learning method, but also an attempt to carry out social transformation (sembiring, 2010). mathematical learning with adobe flash professional cs6-based rme is learning that takes advantage of contextual problems that are easily understood by students and students are given the widest opportunity to solve problems given independently according to their initial knowledge. this activity means that students are given the opportunity to describe, interpret and look for appropriate strategies. meanwhile, these activities did not occur in mathematical learning using conventional learning. in general, the learning process that occurs in the experimental class is in accordance with the guidelines and criteria and characteristics of rme learning. this is reflected in the active process of students in discussions, asking questions, answering problems in more than one way, explaining and displaying the results of their work in front of the class. student activities during the learning process seem to run smoothly, even though at first the students have not been able to adapt optimally. this is understandable because the learning process carried out is somewhat different from the learning they have been used to. rme which is carried out based on the principle of constructivism provides space for students to provide their abilities in carrying out mathematical activities. the final benefit of this adaptation is an active and fun math class based on constructivist understanding by accommodating student needs and involving communication between students and teachers (draper, 2002). the enthusiasm of students in learning is seen when they begin to understand the contextual problems related to daily activities, they really feel the aspects of the usefulness of mathematics. this corresponds to the mathematical literacy aspects that are trying to be developed. in mathematics, to improve mathematical literacy, change is needed to focus on communicative and language-centric activities to hone students' mathematical literacy skills (colwell & enderson, 2016). in this study, rme learning based on adobe flash professional cs6 was seen to be able to influence the way students learn so that they can improve their learning achievement. the use of rme increases students 'mathematical achievements and encourages students to actively participate in mathematics teaching and learning, but students' attitudes towards mathematics are still the same as conventional learning (zakaria & syamaun, 2017). collaboration between rme as an approach and the use of adobe flash in bringing ict-based learning into its own advantages that complement each other. this is consistent with a similar study which provides the conclusion that animated content developed using macromedia flash students is far better than conventional approaches to high school students' mathematical connection skills (rohendi, 2012), and make mathematics learning more active and fun (chotimah, bernard, & wulandari, 2018). the influence of the learning method in question is primarily on the independence of learning by context-based learning in learning. furthermore, if you look at the results of the research that has been stated, it shows that rme learning based on adobe flash professional cs6 is significantly better in improving students' mathematical understanding skills compared to learning using conventional learning. rme learning based on adobe flash professional cs6 provides an interesting learning experience for students, because the problems presented in learning are relevant to their daily activities, technology support allows students to easily explore the concepts being studied. from this perspective, the use of technology in learning has a central role (mills, 2003). specifically, that new knowledge can be possessed by students through a systematic and ongoing process with the help of animation media used in learning (taylor, pountney, & baskett, 2008). volume 8, no 2, september 2019, pp. 167-178 175 rme learning based on adobe flash professional cs6 designed by displaying animation applications seems to provide significant changes in learning. in other words, this technology-based learning has great potential in learning especially helping in the development of mathematical concepts and improving student achievement (kurz, middleton, & bahadir yanik, 2004). in addition, ict has a role in helping visualize abstract mathematical concepts (oktavianingtyas, salama, fatahillah, monalisa, & setiawan, 2018). this concept is in line with the theory of cognitive development, where children at the formal-operational stage have the capacity to use abstract hypotheses and principles both simultaneously and sequentially (umbara, 2017). on the other hand, the basic reason that can be stated is that in the implementation of learning in the control class that uses conventional learning, the teacher only provides informative learning. so that the learning carried out tends to be passive and the ability of students to develop mathematical concepts cannot be explored to the maximum. duranti & goodwin (mkhwanazi & bansilal, 2014) states that when context problems are raised, it is usually debated that focus events cannot be properly understood, interpreted correctly, or explained in a relevant way, unless someone looks beyond the event itself to another phenomenon (eg cultural settings, speech situations, share the background assumptions) where the event is pinned, or alternatively that the features of the lecture itself use certain background assumptions that are relevant to the organization of the next interaction. overall, based on the implementation of rme learning based on adobe flash professional cs6, students' mathematical literacy abilities appear simultaneously because students are trained to reason and solve problems. two factors suggested as the development of literacy skills centers are mathematical reasoning and problem solving (venkat, graven, lampen, nalube, & chitera, 2009). 4. conclusion based on the results of the study, obtained several research conclusions, including mathematical literacy of students with rme based on adobe flash professional cs6 are better than students who obtain learning with conventional learning and increasing of mathematical literacy of students who apply the rme based on adobe flash professional cs6 learning better than students who obtain learning with conventional learning. acknowledgements we are very grateful to the drpm ministry of research, 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(2017). the effect of realistic mathematics education approach on students’ achievement and attitudes towards mathematics. mathematics education trends and research, 1(1), 32-40. https://www.tandfonline.com/doi/abs/10.1080/14794800903569865 https://www.tandfonline.com/doi/abs/10.1080/14794800903569865 https://www.tandfonline.com/doi/abs/10.1080/14794800903569865 https://journals.co.za/content/amesal/2009/7/ejc20795 https://journals.co.za/content/amesal/2009/7/ejc20795 https://journals.co.za/content/amesal/2009/7/ejc20795 https://www.researchgate.net/profile/effandi_zakaria/publication/314298463_the_effect_of_realistic_mathematics_education_approach_on_students'_achievement_and_attitudes_towards_mathematics/links/59a244ef0f7e9b0fb89e553e/the-effect-of-realistic-mathematics-education-approach-on-students-achievement-and-attitudes-towards-mathematics.pdf https://www.researchgate.net/profile/effandi_zakaria/publication/314298463_the_effect_of_realistic_mathematics_education_approach_on_students'_achievement_and_attitudes_towards_mathematics/links/59a244ef0f7e9b0fb89e553e/the-effect-of-realistic-mathematics-education-approach-on-students-achievement-and-attitudes-towards-mathematics.pdf https://www.researchgate.net/profile/effandi_zakaria/publication/314298463_the_effect_of_realistic_mathematics_education_approach_on_students'_achievement_and_attitudes_towards_mathematics/links/59a244ef0f7e9b0fb89e553e/the-effect-of-realistic-mathematics-education-approach-on-students-achievement-and-attitudes-towards-mathematics.pdf sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 9, no. 2, september 2020 e–issn 2460-9285 https://doi.org/10.22460/infinity.v9i2.p247-262 247 infinity the role of scaffolding in the deconstructing of thinking structure: a case study of pseudo-thinking process imam kusmaryono*, nila ubaidah, mochamad abdul basir universitas islam sultan agung, indonesia article info abstract article history: received jun 17, 2020 revised sep 21, 2020 accepted sep 22, 2020 this study aimed to (1) analyze the role of scaffolding in deconstructing pseudo-thinking structure, and (2) analyze the development of students' thinking structures after receiving scaffolding. the study was framed with a qualitative methodology by involving case study design. this research was conducted at state junior high school 31 in semarang city, indonesia. data was collected through tests, observation, and interview methods. result of the study indicated that (1) scaffolding has changed the pseudo thinking process into a real thought process, and (2) scaffolding could develop students’ thinking structure into a more complex (abstract) level. their thinking structure was initially on the stage of comparative thinking structure before receiving scaffolding assistance and after receiving scaffolding, to developed into the stage of logical reasoning thinking structure. in other words, scaffolding could become a useful strategy to help students go through different zone of proximal development (zpd). keywords: pseudo thinking, scaffolding, thinking structure, zone of proximal development copyright © 2020 ikip siliwangi. all rights reserved. corresponding author: imam kusmaryono, departement of mathematics education, universitas islam sultan agung, jl. kaligawe raya km. 4, semarang, center java 50112, indonesia. email: kusmaryono@unissula.ac.id how to cite: kusmaryono, i., ubaidah, n., & basir, m. a. (2020). the role of scaffolding in the deconstruction of thinking structure: a case study of pseudo-thinking process. infinity, 9(2), 247-262. 1. introduction develop students’ ability in problem-solving is one of the teacher’s roles (keiler, 2018; simamora, saragih, & hasratuddin, 2018). in problem-solving, the procedure of mathematics problem solving is a cognitive process based on what had been known (ekawati, kohar, imah, amin, & fiangga, 2019; samsonovich, kitsantas, o’brien, & de jong, 2015). in this case, students should use cognitive strategy to determine how they learn, reprocess information, to use what had been learned. they must think to obtain a suitable problem-solving strategy, so they could achieve the cognitive purpose, that is, to solve problems (evans & swan, 2014; novita, widada, & haji, 2018; susanti, 2018). students in the activity of thinking to solve mathematical problems can occur the possibility of answers obtained is true or false. incorrect answers are not necessarily caused https://doi.org/10.22460/infinity.v9i2.p247-262 mailto:kusmaryono@unissula.ac.id kusmaryono, ubaidah, & basir, the role of scaffolding in the deconstruction of thinking … 248 by thinking processes that are also wrong (herna, nusantara, subanji, & mulyati, 2016; subanji & nusantara, 2016). this wrong answer does not mean that the subject (student) cannot solve it. when students solve problems, they often give "false" answers relatively quickly, spontaneously, and do not check or reflect the results of their work. this happens because of the low ability to think reflective in solving problems, so their thought processes tend to produce wrong answers (choy, yim, & tan, 2017; deringöl, 2019). this process of thinking is still "raw" rather than the actual thought process so that the process of pseudo thinking occurs (herna et al., 2016). the pseudo-thinking process is a thinking process in which students thought as if they had solved a problem, but they just imitated what the teacher or someone else did (subanji & nusantara, 2016; vinner, 1997). the students did not understand what they just did. they often provide answers spontaneously without any check or control on the thinking process (thanheiser, 2010; vinner,1997). pseudo-thinking process has become interesting as students experienced it "unreal", just a pseudo-thinking. the pseudo-thinking process could be discovered in two forms i.e., (1) the answer is correct, but the student could not justify it. this is called as "true" pseudo (caglayan & olive, 2010; herna et al., 2016; thanheiser, 2010) and (2) the answer is incorrect, but the student actually could solve it well. this is called as "false" pseudo (subanji, 2013; vinner, 1997). both pseudo-thinking processes could be fixed after being reflected with or without scaffolding (wibawa, nusantara, subanji, & parta, 2018). this pseudo-thinking process could still be fixed as it is not the real thinking process as incapability. furthermore, through the reflection process, the teacher should believe that the students actually have the potentials to develop with assistance from teachers and or more capable peers. according to vygotsky, each student had the zone of proximal development (zpd), usually mentioned as a distance between actual development level and higher potential development level. vygotsky suggested that students could achieve maximal area if they received enough assistance. if students learned without assistance, they would still be in the actual area and could not develop to higher potential development level (chairani, 2015). given that the pseudo thinking process is not a real thought process, it can still be improved through the process of reflection. at the time of reflection, the teacher provides scaffolding with the aim of improving students' thinking structures. the improvement of this thinking structure is based on the belief that when students are in the zone of proximal development (zpd), they have the potential to develop optimally. cognitive structure is a basic mental process used by an individual to understand information (garner, 2007). then it was also called a mental structure, or thinking pattern (kusumadewi, kusmaryono, jamallullail, & saputro, 2019). a students thinking pattern would develop based on the cognitive development stage (mascolo, 2015). however, some students met obstacles in cognitive development, so that it is the time for the student to get assistance to face learning barriers. after the scaffolding was given, the student’s cognitive structure became more developed and more complex. scaffolding was learning assistance provided by teachers to students who had barriers to learning. the learning would be more effective if teachers helped students to develop cognitive structures that would equip them for individual learning (kusumadewi et al., 2019). this research focuses on two objectives. the first objective is to analyze the role of scaffolding in deconstructing pseudo-thinking structures. the second objective is to analyze the development of students' thinking structures after receiving scaffolding. volume 9, no 2, september 2020, pp. 247-262 249 infinity 2. method 2.1 research design this research was conducted in qualitative methodology by involving case study design. this research was conducted at state junior high school 31 in semarang city, indonesia. setting of the study involved kind of naturalistic investigation because the scaffolding was studied on natural situation without manipulating any variables (kalu & bwalya, 2017). 2.2 participants this study involved 36 students in grade 8, a teacher, and a supervisor. the students had attended mathematics learnings with a group investigation approach and attended problem-solving test. based on the test results, students whose scores did not reach the specified criteria and had the most error answers, it is reasonable to suspect that these students experienced a pseudo thinking process, then considered as data sources. researchers act as supervisors of learning in the classroom. where as the instructor is a senior teacher who has more than 10 years of teaching experience in school. 2.3 instruments the data collection method included tests, observation, and interviews. the instruments used in this study were written test questions and a list of interview questions. the interaction in scaffolding between students and teachers is observed by supervisors during the mathematics learning process. the deep interview was conducted on students by purposive snowball technique in order to collect complete information. an instrument of the written test was a test of problem-solving as follows. problem: a water storage tank had 10 meters length, 5 meters in width, and 4 meters in height. the tank is full of water and will be distributed to 40 houses. each house receives 500 liters of water every day. if the tank is empty, the company will refill it again until it is full. question: how many times does the company should refill the water storage tank in one month to fulfill the need of water for 40 houses? 2.4 procedure the subject of the study was focused on students who were in the lower group, namely students who received low test scores or did not reach the minimum completeness criteria of 70.0. the study was conducted by tracking the response of students' answers in solving problems. then so that students can correct their mistakes students are given the opportunity to reflect with the help of scaffolding. the author conducted this research by exploring the response of student answers in solving problems. then, in order to correct the mistakes, the students are given a chance to do reflection with scaffolding assistance. scaffolding is carried out through the steps: (1) giving questions; (2) problems to solve for students; (3) asking students to express what they knew; (4) giving a chance for students to review their work; (5) asking students to describe the plan of problem-solving; (6) asking students to combine their ideas; (7) asking students to share with others; (8) giving question and keywords to students; (9) if the students need further information, teachers guide them to go back to step 4, dan restart until it is finished kusmaryono, ubaidah, & basir, the role of scaffolding in the deconstruction of thinking … 250 (buli, basizew, & abdisa, 2017; san martín, 2018; van de pol, volman, & beishuizen, 2010). 2.5 data analysis, and validation this research is natural, researchers as data collection tools (human instruments). the data is analyzed inductively and is a descriptive one. data analysis was described as an interactive cycle through stages of data collection, data reduction, data display, and drawing conclusions (miles & huberman, 2016; moleong, 2007). to ensure data validity, the authors used the triangulation of theory and data source (moleong, 2007). 3 results and discussion 3.1 results after students complete formative tests at the end of learning, all student answers are analyzed and presented in table 1. table 1. description of the test score statistics for each group group students test score range mean std. deviation top 10 95 100 98.5 2.415 middle 17 70 90 74.4 11.023 bottom 9 40 65 45.6 5.270 total 36 based on the data in table 1, there were 9 students in the lower group whose test scores did not reach the minimal completeness criteria of 70.0. so that the students' answers were analyzed for errors, and the following results were obtained (see table 2). table 2. error analysis of student answers no. subject analysis of student answers 1 (s.01) incorrect concept 2 (s.05) incorrect concept 3 (s.17) incorrect concept 4 (s.18) incorrect concept 5 (s.20) incorrect concept 6 (s.22) incorrect concept 7 (s.06) incorrect analysis 8 (s.29) incorrect analysis 9 (s.31) incorrect analysis the following is the result of students' answer response to represent 2 cases happened i.e., the case of incorrect concept (s.01) and incorrect analysis (s.06). student (s.01) was volume 9, no 2, september 2020, pp. 247-262 251 infinity supposed to experience a "false" pseudo-thinking process, and the student (s.06) was supposed to experience a "true" pseudo-thinking process. student’s answer response to mathematics problem that was tested in this research was taken as a sample to discuss in figure 1. figure 1. student answer (s.01) before reflection considering the student answer (s.01) in figure 1, finally, it was found that the company should refill the tank 10 times a month. the answers given by students are not right. to find out the student's thought process when solving a problem, the researcher conducted the interview as follows. ………………………. researcher : why did you write down 1 liter = 1 dm3, and 1 m3 = 1000 liter? subject (s.01) : i have been thinking that i would convert the volume of the cube in liter measurement. researcher : did you understand how to solve question number 1? subject (s.01) : i do, and i have some ideas to do. researcher : was your answer saying that the company should refill the tank 10 times a month, correct? subject (s.01) : i can not explain, but i hope it is correct. researcher : the calculation you made had not finished yet. it still had to be continued to the next step. subject (s.01) : oh, i see. (the subject looked disappointed). researcher : did you conduct a recheck? subject (s.01) : i did not recheck it. ………………………. kusmaryono, ubaidah, & basir, the role of scaffolding in the deconstruction of thinking … 252 based on students' answers in the interview passage indicated that students experience pseudo thinking processes. this pseudo thinking process occurs because the answers are spontaneous, and students do not check their work in the form of reflection. the structure of student thinking (s.01) in solving problems before reflection (see figure 2). thinking scheme code information a. problems should be defined: amount of tank refill in a month. b. providing information of the known data c. questioning : volume of water storage tank d. converting cubic measurement into liter e. calculating the need of water for 1 day f. water adequacy in the water stage tank g. prediction of time the water will be used up in 10 days h. the work is done: the subject was unsure of what had been done. rf. recheck of reflection should be conducted figure 2. the structure of student thinking (s.01) before reflection based on the student (s.01) thinking structure as displayed in figure 2, it could be said that the student was on a comparative thinking structure. it is basic to learn and as a requirement for other more complex cognitive structures (garner, 2007). student mathematical ability on this level was processing information by identifying how the data were similar or different, including recognition, memorization, constant conservation, classification, spatial orientation, temporal orientation, and metaphoric thinking. thinking structure on this stage could still be developed with scaffolding assistance from the teacher. the scaffolding was given to the students to reflect on what had been done and direct their initial knowledge to solve the problems they faced (maharani & subanji, 2018). the role of the teacher in learning as resource persons and facilitators who provide assistance as needed (scaffolding) in order to facilitate the construction process of knowledge that is built by students. at a certain level of cognition, teachers provide scaffolding assistance by guiding them or providing key instructions, cues, questions, and justifications so that students will be easier to move or develop into higher thought processes. to correct the mistakes, the students were given a chance to do a reflection. they rechecked the steps of problem-solving. while students were having difficulties, the teacher gave the scaffolding. the work of students after reflection with the help of scaffolding is shown in figure 3. h rf ? g f e c d b a volume 9, no 2, september 2020, pp. 247-262 253 infinity figure 3. student answer (s.01) after reflection to understand the student (s.01) thinking structure, consider the following interview between the researcher and the student. ………………………. researcher : please check whether the result you obtained had answered the question? subject (s.01) : i had rechecked and i found that my answer did not solve to the problem questioned. researcher : was there any mistake you did while working on it? subject (s.01) : i did a mistake. researcher : in which part did you find the mistake? subject (s.01) : the answer should not be 10. i would recheck it. ………………………. to help the student, the scaffolding was implemented through words to track or keywords. by the keywords, the student could find the solution. ………………………. researcher : please calculate the need for water in a month. subject (s.01) : the need for water in a month is 500 liters x 40 x 30 = 600.000 liters. researcher : then, make an equation (relation) with the volume of the water tank. subject (s.01) : the volume of the water tank as 200,000 liters will be used up in 10 days (1-time refill). so, in a month should be 600.000 liters divided by 200.000 liters equals to 3 or (3 times refill). researcher : have you found your answer? kusmaryono, ubaidah, & basir, the role of scaffolding in the deconstruction of thinking … 254 subject (s.01) : the answer is 3 times a refill in a month. researcher : what conclusion did you obtain? subject (s.01) : the need for water for 40 houses in a month equals to 3 times of water tank volume. researcher : are you sure? how do you prove it? subject (s.01) : i’m sure it’s correct. subject (s..01) : (volume of water tank) x (amount of water refill) = need of water in a month. it was (10 m x 5 m x 4 m) x 3 = 40 x 500 liters x 30. obtained 600 m3 = 6.000 liter. ………………………. based on the result of the student’s work and the interview, the following is the thinking structure after reflection (see figure 4). thinking scheme code information rf. rechecking or reflection. a. problems should be found: number of time to refill water in a month b. displaying information of the data known c. questioning : volume water storage tank d. calculate volume of water tank e. converting cubic measurement into liters f. calculating the need of water in one day g. calculating the need of water in one month h. forming an equation, the need of water in a month equals to numbers of water refill in the tank j. result of number of water refill in a month end done. no doubt. figure 4. the structure of student thinking (s.01) after reflection the response of student answer (s.06) on mathematics questions tested in this research was chosen as sample to discuss and present in figure 5. j end h d c b a f g rf. e volume 9, no 2, september 2020, pp. 247-262 255 infinity student: (s.06) figure 5. student answer (s.06) before reflection based on the result of the analysis on the student (s.06) response answer, it indicated that the final result was correct. however, there were some solving steps missing that were not written by the student (s.06). furthermore, an interview was conducted to determine how student's (s.06) thinking process was, as presented below. ………………………. researcher : what is the conclusion (answer) of this problem? subject (s.06) : the company should fill the water tank 3 times a month. researcher : are you sure about your answer? subject (s.06) : probably. researcher : did you re-check it? subject (s.06) : i did not. researcher : could you prove that your answer is correct? subject (s.06) : sorry, i have no idea. i could not explain it. ………………………. the student's thinking structure (s.06) could be described in the following scheme (see figure 6). kusmaryono, ubaidah, & basir, the role of scaffolding in the deconstruction of thinking … 256 thinking scheme code information a. problems should be defined: amount of tank refill in a month. b. providing information of the known data c. question: lots of water needed for a month. d. calculate the volume of a water tank e. converting cubic measurement into liter f. calculating the need of water for 1 day g. adequacy of water in the tank h. prediction of time the water will be used up in 10 days j. the work is complete, but the subject cannot prove the argument rf. re-examination or reflection is required figure 6. the structure of student thinking (s.06) before reflection after that, the student (s.06) got a chance to do reflection in order to correct the answer with scaffolding assistance from teacher, through the following steps. ………………………. researcher : calculate the need for water in a month! subject (s.06) : need of water = 40 x 500 liters x 30 = 600.000 liters researcher : what is the volume of the water tank? subject (s.06) : volume of water tank = 10 m x 5 m x 4 m = 200 m3 = 200.000 liters. researcher : explain the correlation between the need for water and the volume of the water tank! subject (s.06) : the need for water in a month should be equal to the volume of water in the tank. researcher : create the equation for the correlation of both variables! subject (s.06) : (volume of the tank) x (number of water refill) = need of water in a month. (10 m x 5 m x 4 m) x k = 40 x 500x 30. 200.000 liters x k = 600.000 liters. k = 600.000 : 200.000 k = 3 a rf. ? b d f e g h j c volume 9, no 2, september 2020, pp. 247-262 257 infinity researcher : what is your conclusion? subject (s.06) : the number of water refill into the tank is 3 times a month. researcher : please re-check your answer! subject (s.06) : (volume of the tank) x (number of water refill) = need of water in a month. (10 m x 5 m x 4 m) x 3 = 40 x 500 liters x 30 600 m3 = 600.000 liters. yes, the result is similar. researcher : are you sure? subject (s.06) : pretty sure. ………………………. the following is a student's (s.06) answer response after the reflection process with scaffolding assistance as presented in figure 7. figure 7. student answer (s.06) after reflection after reflection with scaffolding, the student could find the solution and provide an explanation for the answer obtained correctly. through scaffolding, the student (s.06) could fix the thinking structure as presented in figure 8. kusmaryono, ubaidah, & basir, the role of scaffolding in the deconstruction of thinking … 258 thinking scheme code information rf. reflection a. problems should be defined: amount of tank refill in a month. b. displaying information of the data known c. question: lots of water needed for a month. d. calculate volume of water tank e. converting cubic measurement into liters k. calculating the need of water in one month m. forming an equation, the need of water in a month equals to numbers of water refill in the tank n.. resolve the equation end. work completed: subject confident of the results of the solution figure 8. the structure of student thinking (s.06) after reflection 3.2 discussion 3.2.1. before scaffolding considering the result of analysis on students' answer responses (s.01 and s.06) and interview toward the students on how they solved mathematics problems, it could be said that the students experienced a pseudo-thinking process before the reflection process. the student (s.01) experienced a "false" pseudo-thinking process, while the student (s.06) experienced a "true" pseudo-thinking process. based on the interview, the student (s.01) was detected to have a "false" pseudothinking process. the student did not understand what he has done. the concept of problemsolving was not complete yet. the solution obtained did not receive treatment of re-checking, but it had been considered as a conclusion, so the answer was incorrect. specifically, the student (s.01) was said to experience the so-called “pseudo-conceptual” thinking process, as the main process focused on the inappropriate concept, reasoning, correlation between concepts, and implementation (vinner, 1997). the student's answer (s.06) in the interview was a manifestation of "true" pseudothinking process behavior (caglayan & olive, 2010; herna et al., 2016; thanheiser, 2010). although the answer was correct, the student (s.06) was unsure and could not provide explanation (proof) for the answer. in addition, the student did not conduct reflection. according to experts, a "true" pseudo-thinking process happens when the answer provided by a student is correct, but the student (s.06) could not provide justification (caglayan & olive, 2010; herna et al., 2016; a j b d e n c k rf m end volume 9, no 2, september 2020, pp. 247-262 259 infinity thanheiser, 2010). specifically, the student (s.06) was said to experience the so-called “pseudo-analytical” thinking process, as the main process is a problem-solving process (vinner, 1997). considering the student's thinking structure (s.01) before reflection (figure 2), it could be said that both of the students were on a comparative thinking structure. it is basic to learn and as a requirement for other more complex cognitive structures. student's mathematical ability on this level is to process information by identifying how data is similar or different. it includes recognition, memorization, constant conservation, classification, spatial orientation, temporal orientation, and metaphorical thinking. on the other hand, a student's thinking structure (s.06) before reflection (figure 6) was on a symbolic representation thinking structure. the symbolic representation structure changes information into a coding system that could be accepted in general (culture) including verbal and nonverbal language; mathematics; graphics (2-dimension figures, painting, logo); construction; simulation and multimedia (garner, 2007). both comparative and symbolic representation thinking structures could still be developed to construct more complex mathematics knowledge structures with scaffolding assistance from the teacher. the role of the teacher is to provide assistance (scaffolding) as needed in order to ease the process of knowledge construction that is built by students themselves (hmelo-silver, 2004; darling-hammond et al., 2019). 3.2.2. after scaffolding scaffolding describes processes to support students for (puntambekar & hubscher, 2005; van de pol et al., 2010). scaffolding is given to students in order to reflect the learning outcome and direct the initial knowledge in solving problems (maharani & subanji, 2018). learning would be more effective if the teacher helps students (to provide scaffolding) to develop a cognitive structure for them to study independently (kusumadewi et al., 2019). after reflection with scaffolding assistance, the pseudo-thinking process never happened anymore. students' answers after reflection indicated that they succeeded to correct mistakes and turn them into correct answers. it was in line with the interview result in which the students could provide explanations or proof for the answer with proper reason. the answers had been re-checked it’s solving steps, the students became sure with no doubt, and the thinking process became true. on certain cognition levels, teachers provide scaffolding assistance by providing students guidance, key instruction, signs, questions, and corrections, so the students could move or develop more easily into higher thinking processes (van de pol et al., 2010). after having scaffolding, the students succeeded to do reflection and correct the previous mistakes. moreover, scaffolding had developed students' thinking structure (s.01 and s.06). before reflection, their thinking structure was on comparative and symbolic representation structure. after the reflection, the thinking structure developed into a logical reasoning structure (figure 4 and figure 8). on the logical reasoning structure, the students (s.01 and s.06) had used an abstract thinking strategy to systematically process and produce information. they could conduct analysis on problems, causal relation, and evaluation in problem-solving (garner, 2007). the provision of scaffolding to students is based on vygotsky's theory (the zone of proximal development) has proven to be effective. that it can reach the level of potential development that students can actually do like problem-solving abilities under adult guidance or through collaboration with other more capable students. according to van de pol et al. (2010), scaffolding could become a useful strategy to help students move through different zpd. the scaffolding involved support from teachers kusmaryono, ubaidah, & basir, the role of scaffolding in the deconstruction of thinking … 260 to students while working on a task that can’t be done alone (van de pol et al, 2010). however, it was a different mental process, constructing a new mental structure to adjust and model the model they have learned with an emphasis on the relationships among thinking objects (navaneedhan & kamalanabhan, 2017). the success of scaffolding in this research was because the teacher and students were in the correct place. the teacher as a facilitator had applied steps of scaffolding correctly and effectively. the teacher showed an attitude of appreciating student ideas and then directed them to a decision or choice that they needed to develop based on the basic rule. the final decision was brought back to the students to decide how they used the teachers’ suggestions in redesigning their work. it leads to boost their confidence and activities to encourage them to use reasoning, communicating, and connecting ability between knowledge and experience they had before. scaffolding concept could be used as an analytical tool to help students obtaining much more understanding in learning. 4 conclusion in the scaffolding process, effective learning interactions have occurred between the teacher and students, so the conclusions of this study are (1) scaffolding changes the pseudo thinking process into a real thought process, and (2) scaffolding could help develop students' thinking structures from simple ones to more complex (abstract) level. the development of students' thinking structures is at the stage of comparative thought structures before scaffolding is given, and then developed into logical reasoning thinking structures after receiving scaffolding. in other words, scaffolding can be a useful strategy to help students move through different zona of proximal development (zpd). acknowledgements special thanks to students and teachers at state junior school 31 semarang, indonesia. the head of sultan agung islamic university, which provides funding to conduct research. references garner, b. k. 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(2021). supporting solving word problems involving ratio through the bar model. infinity, 10(1), 149-160. 1. introduction students’ poor academic achievement in mathematics has always been a concern and a worrying issue in brunei every year. these poor results are reflected in all examinations at both national and school levels, and one such example is the national examination for year 6 pupils, penilaian sekolah rendah (psr) before students enter the secondary level. in 2014, it was reported that only 62.29% of pupils managed to get grades a to c in mathematics for that year’s psr (jalil, 2015), whereas in 2015, the percentage increased to only 64.81% (hajar, 2015). although there was an improvement, the percentage was still considered low when compared to the other four subjects that the pupils sat for. there are several possible explanations for this low mathematics performance and one of them is the inability of the pupils to solve mathematics word problems, which is an integral component of such public examinations, and mathematics content specifically (saman, 2000; raimah, 2001; pungut & shahrill, 2014). https://doi.org/10.22460/infinity.v10i1.p149-160 said, & tengah, supporting solving word problems involving ratio through the bar model 150 brunei changed its old education system to a new one in 2009 to keep up with the fast changing world. the new system has identified problem solving skills as one of the essential skills for the 21st century in mathematics at both primary and secondary levels. some of the aims and focus under the new mathematics curriculum are the ability to interpret and communicate mathematics processes, mathematics reasoning and visualisation. the new national education system for the 21st century, spn21, suggests six modes of mathematics representations, namely, real life, verbal, concrete, symbolic representations, technology and diagram. a mathematics word problem is defined as a written description of some situation (greer, 1997). whereas, charles (2011) defined it as a real life situation in which both related known and unknown quantities given and described, a question is asked to determine value of unknown through one or a combination of operations to solve the problem. students who can form mathematical algorithms may not necessarily be able to solve word problems if they do not have the ability to apply mathematical concepts that they already learned in different situations given. according to saman (2000), a large number of year 6 pupils in the country find mathematics word problems to be difficult especially when multiplication and division are involved. while there are several factors that contribute to students’ poor performance in solving word problems, some of the common problems that are observed are such that they do not know when to apply certain mathematical concepts, students tend to misinterpret mathematical concepts (chin & clements, 2001; vaiyatvutjamai & clements, 2004) and they lack the ability to visualise the mathematical problem and subsequently cannot form the appropriate arithmetical algorithm to solve the problem. khalid and tengah (2007) stated that most students are unable to understand what is being asked when attempting word problem tasks. there are a considerable number of problem solving strategies developed by mathematicians to help students solve word problems. one effective strategy that can be taught to students is the famous polya’s four-step problem solving strategy: understand the problem, devise a plan, carry out the plan and look back at the solution (polya, 2004). liu and soo (2014) suggested several ways that students can devise a plan to solve a problem, such as work backwards, guess and check, look for a pattern, choose an operation, act it out, make a list, simplify the problem, draw a picture. the common strategy used by teachers in brunei is the use of keyword or phrases in attempting such word problem. examples of keyword include ‘altogether’, ‘more than’ and ‘total’ for addition, and ‘less’ and ‘reduced’ for subtraction. these at times might cause errors as students that uses keywords or keyphrases approached tend to ignore the whole context of the question being asked and just focuses on the keyword. for example: i have three marbles more than ali, and we have 9 marbles altogether. how many marbles do ali have? for such example, several students will look at ‘altoghter’ or ‘more than’ as addition process and add 9+3 marbles, where in context the question should be focusing on subtraction. in visual representation approach in mathematics, model(s) that reflect information is created to understand the problem as a whole (van garderen & montague, 2003). the use of visual representation to model a mathematical problem has been known to be useful and powerful to aid students in the problem solving process (pungut & shahrill, 2014; denis, 1991; piaget & inhelder, 1966), particularly in word problem. creation, interpretation, utilisation and reflection on pictorial representation enable students to develop greater understanding of the topic when they are able to form strong link between representations and abstract concepts (arcavi, 2003) and take into account the whole context of the problem. the ability to visualise mathematics concepts is what distinguishes competency between high and low achieving mathematics students (van garderen, 2006). volume 10, no 1, february 2021, pp. 149-160 151 an example of a tool for visual representation is the application of bar model. the bar model uses a series of bars or rectangles to model a word problem, and take into account of the whole context of the problem and actual question being asked, where the bars represent the quantities in the problem and the relationship between given and unknown quantities is made clear through diagrams created by the students. the bar model method was developed in 1983 in singapore by its ministry of education to address a national problem in the 1980s with the goal to raise mathematical competencies and improve problem solving abilities (kho, yeo & lim, 2009). therefore, it would be worth to determine if applying bar model should be considered as an alternative approach by brunei teachers when teaching their students. there are two main types of the bar model and they are the part-whole model and the comparison model (liu & soo, 2014). a variation of these two main types has resulted in other types of bar models. the use depends on the quantities and situation given in the word problem. the bar model can be used across many topics and some of them include whole numbers, fractions, ratio and percentage. figure 1. a part-whole (a) and a comparison (b) bar model, as illustrated by madani et al. (2018) as explained by liu and soo (2014), the comparison model can be used to relate or compare two quantities in the problem. the model shows the difference between the quantities and this helps to reduce students’ reliance on equating the terms ‘more than’ to addition and ‘fewer than’ to subtraction because depending solely on key words may not be helpful after all as ‘more than’ does not necessarily mean to add. figure 1 shows both partwhole and comparison bar model. for ratio problems, the comparison model is suitable to represent the quantities in the problem, hence the focus of this research intervention lessons. ratio is about comparing two or more quantities. word problems involving ratio require students to understand the relationship between the quantities contained in the problem and apply the correct arithmetic operations. however, students often fail to see the relationship and subsequently unable to form the correct arithmetical algorithm. with a bar model, the relationship between the quantities can be visually shown and this enables students to decide on the mathematical procedure to use (liu & soo, 2014). whilst bar diagram is useful in solving word problems, care must be taken when drawing the bars. ng and lee (2009) cautioned that every detail of the information in the text must be clearly, precisely and correctly translated to ensure correct solution of the word problem. the purpose of this research study was to examine the impact of using the bar model method on the academic achievement of students in solving word problems involving ratio through the use of bar model. the research question used to guide this study was: how does the bar model affect students’ performance in word problems involving ratio? said, & tengah, supporting solving word problems involving ratio through the bar model 152 2. method convenient sampling of thirty-three participants from two year 8 classes enrolled in an all-girls secondary school in the brunei-muara district were involved in this experimental research study. the participants have mixed mathematical abilities ranging from high to low. english language is their second language and their age ranged from 12 to 13, and all had already learned the topic ratio previously. the pre-test and post-test in this study contained the same questions. the ten questions were in the form of simple word problems on ratio and were designed to include different levels of difficulty from easy to challenging (see figure 2). the questions, adapted from past spe papers and spn21 mathematics year 8 textbook, include asking students to form ratio of two quantities, finding missing quantities given the ratio, finding the total quantities as well as finding difference in quantities. 1. there are 10 boys and 14 girls in a field trip. what is the ratio of boys to girls? 2. the total number of fruits in a basket is 30. there are 12 apples and the rest are oranges. what is the ratio of the number of apples to the number of oranges? 3. the ratio of green m&m’s to yellow is 2:5. if there are 20 yellow m&m’s, how many green m&m’s are there? 4. the ratio of the weight of wani’s cat to the weight of azam’s cat is 5:7. wani’s cat weighs 20 kg. how much does azam’s cat weigh? 5. the ratio of the number of students who wear glasses to the number of students who do not wear glasses is 2:3. if there are 25 students in the class, how many students do not wear glasses? 6. the ratio of red to green crayons in a box is 3:5. if there are 9 red crayons, what is the total number of crayons in the box? 7. the ratio of the number of dina's comics to the number of alif's comics is 5:2. if dina has 15 comics, how many comics do they have altogether? 8. farhan and azim get paid $49 for washing cars in a day. they split the money in the ratio 4:3. how much more does farhan receive? 9. the ratio of boys to girls at the football game is 5:3. there are 33 girls. how many more boys are there than girls? 10. a rope that is 18 metres long is cut into three strips in a ratio of 2:3:4. how long is the longest piece? figure 2. the 10 items in pre-test and post-tests prior to collecting data at the school of study, the validity and reliability of the test had been previously checked. a test-retest reliability method was administered to a group of twelve students not involved in the main study, produced correlation coefficient of 0.783. this positive correlation between the test and the retest shows that the test questions are reliable in producing stable and consistent results. both descriptive (mean, median, standard deviation) and inferential statistics were used in the analysis of the collected data to answer the above research question, namely through students’ overall scores and item-analysis of correct versus incorrect responses. for the pre-test and post-test, the sample paired t-test was used to analyse the results quantitatively to measure if there is a significant difference in students’ achievement before and after introducing the bar model method. volume 10, no 1, february 2021, pp. 149-160 153 the intervention lessons were delivered over the course of three lessons within a week and each lesson took one hour. the introduction lesson focused on introducing concept underlying bar model in this topic. it included testing whether students know how to evaluate the unknown quantities of given two bars, and constructing and partitioning bars of required quantities (see figure 3). here, the unitary method was the students’ preferred method to find the unknown quantities, where they calculated the value of 1 unit first by dividing appropriately and then once known, they multiplied it by the number of parts of the unknown quantities. similar approach was used in the deconstruction of the bar, where information were extracted from drawn bars. without the mention of the topic ratio, students received proper scaffolding when they transit from drawing bars to word problem. once the students were confident, this skill was transferred to represent different ratios using bars, which was covered in the end of the first and throughout the second lesson. figure 3. questions in lesson 1, focusing on understanding the concept and drawing of bar model in the second lesson, the students continue to represent ratio using bars as well as to solve word problems involving ratio using the bar model method. in this lesson, the importance of having accurate and correct size bars following the information in the word problem was emphasised. students learned to label the model correctly to represent the known and unknown quantities and finally utilised the model appropriately to solve the problem. the practice problems were varied, ranging from simple to slightly more challenging problems (see figure 4). said, & tengah, supporting solving word problems involving ratio through the bar model 154 1. hayati made 20 white chocolate cookies and 16 milk chocolate cookies. what is the ratio of milk chocolate cookies to white chocolate cookies? 2. at a summer camp the ratio of boys to girls was 5:4. if there were 45 boys, how many girls were there? 3. a classroom had 24 glue sticks. if the ratio of glue sticks to glue bottles was 4:3, how many glue bottles did the classroom have? 4. there were 220 girls who watched tennis. some of these girls wore caps. the ratio of the number of girls wearing caps to the number of girls not wearing caps was 4:7. how many girls did not wear caps? 5. bella gave a pocket money of $100 to her daughters, hani and emma, in the ratio 2:3. how much did emma receive? 6. kerrie ordered helmets and basketballs in the ratio 3:8. she ordered 64 basketballs. how many sports items did she order altogether? 7. the ratio of karen's cds to mary's cds is 5:6. if mary has 66 cds, how many cds do they have altogether? 8. azimah bought chicken and beef for a barbecue in the ratio 5:3. if she bought 6 kg of beef, how much chicken did she buy? 9. the ratio of the weight of meg’s cat to the weight of anne’s cat is 5:7. meg’s cat weighs 20 kg. how much more does anne’s cat weigh? 10. nina has a bag of 30 candies. the ratio of strawberry to orange to grape candies in the bag is 3:2:1. how many orange candies are there? figure 4. word problems in lesson 2 with and without prepared bar model in the final lesson, students worked on the provided worksheet to practise solving word problems using the bar model (see figure 5). they were encouraged to work in pairs and then by themselves to solve the given ratio problems. selected students were invited to explain their solutions to the whole class and this was used for class discussions. it was during this lesson as well that any errors demonstrated by the students were identified and corrected on the spot so that students could learn from their mistakes. volume 10, no 1, february 2021, pp. 149-160 155 1. a box of candy has 14 pieces total. if two of the pieces are cherry flavoured, what is the ratio of other flavours to cherry flavored pieces? 2. the ratio of girls to boys in a chess club was 5:4. there were 32 boys. how many girls were there in the club? 3. in a bag of red and green candies, the ratio of red candies to green candies is 3:4. if the bag contains 120 green candies, how many red candies are there? 4. the ratio of girls to boys in a swimming club was 1:3. there were 11 girls. how many total members were there in the club? 5. a teacher had 18 red pens. if the ratio of red pens to blue pens she owned was 3:5, how many pens did she have total? 6. a necklace is made using gold and silver beads in the ratio 3:2. if there are 100 beads in the necklace, how many are gold and silver beads? 7. jack and nina share a reward of $140 in a ratio of 2:5. how much of the total reward does jack get? 8. at an ice cream shop the ratio of chocolate ice cream sold to vanilla ice cream sold is 3:4. if there are 12 chocolate ice cream sold, how many more vanilla ice cream would be sold? 9. in one day a movie store rented out 9 comedies. if the ratio of comedies rented to action movies rented was 1:5, how many more action movies were rented? 10. a truck is carrying pear juice, cherry juice, and apple juice bottles in a ratio of 3:1:3. if there are 16 cherry juice bottles, then how many juice bottles in total are there? figure 5. word problems used in lesson 3 at different complexity 3. results and discussion as seen in figure 6, in the pre-test, only two students managed to achieve the maximum mark of 10 while there were eleven students scored zero. more than half of the students did not score past mark of 5, with only fifteen students obtaining marks 5 and above. these low scores indicated students’ poor performance and ability in solving word problems involving ratio to begin with. figure 6. bar chart of students' overall marks in the pre-test vs. post-test in the post-test, overall improvement can be seen in the number of students obtaining higher marks, with considerable reduction in the lower end. only two students obtained the lowest mark of 2 whereas twelve scored the maximum mark of 10. the bar chart also shows that a majority of the students successfully scored 5 marks and above, with just three getting 11 2 1 3 1 2 4 2 2 3 2 0 0 2 1 0 1 3 1 8 5 12 0 2 4 6 8 10 12 0 1 2 3 4 5 6 7 8 9 10 n o o f s tu d e n ts overall marks pre-test post-test said, & tengah, supporting solving word problems involving ratio through the bar model 156 mark 0-4. a total of twenty-five students obtained high marks of 8 and above, making up 76% of the sample. table 1. descriptive statistics of pre-test and post-test of the two classes test n minimum maximum mean std. dev class x pre-test 18 0 10 6.17 2.995 post-test 18 7 10 9.17 1.043 class y pre-test 15 0 6 1.13 1.995 post-test 15 2 10 6.73 2.738 overall pre-test 33 0 10 3.88 3.603 post-test 33 2 10 8.06 2.318 table 1 summarises the performance of each class as well as the whole group’s pretest and post-test. students in the study school were grouped into classes according to their abilities or more specifically, their primary year 6 psr results. class x was supposedly made up of students of high to average abilities, whereas, class y had students of low academic levels. the mean marks of the pre-test is reflective of the classes’ ability. the mean mark of pre-test of class x was 6.17, just slightly over the marginal mark of 5. the marks in this class ranged from 0 to max 10. as expected, the low mean mark of class y (m = 1.13) reflected the low ability students’ struggles in solving word problems involving ratio. the highest mark from this class y is just 6. both classes showed improvement in their class post-test result. the mean score increase in class x to 9.17 implied great achievement overall. the small range of marks between 7 and 10 marks being the minimum and the maximum respectively indicated all the students in class x scored in the high range. likewise, class y also showed great improvement, with post-test mean mark of 6.73. a majority of the students obtained good mark with only three students who did not manage to score past 5 marks. as a whole, the sample group produced mean mark of 3.88 for the pre-test, and increased to 8.06 in the post-test. before the paired sample t-test for the students’ marks was conducted, the four assumptions for the test were first inspected. firstly, the dependent variable, which is the students’ marks, was continuous as it measured from 0 to 10. due to the students’ scores spread almost evenly within this range, there was no outliers. thirdly, the same group of students was used for the pre-test and the post-test. lastly, through visual inspection on the bar graph of the differences between the paired marks, the data was approximately normally distributed. with these conditions fulfilled, a paired-sample t-test was carried out to determine significance of the mean difference. the paired sample t-test was used to test the following hypotheses: h0 = there is no significant difference between the pre-test and post-test results. h1 = there is a significant difference between the pre-test and post-test results. table 2. paired sample t-test of pre-test and post-test for overall sample (n=33) paired differences t df sig (2tailed) mean std. dev std. error mean 95% ci of difference lower upper prevs post test -4.182 2.973 0.518 -5.236 -3.128 -8.079 32 0.000 the t-test result revealed that there was a significant difference in the students’ mean marks (t = -8.079) at 𝑝 < 0.05 level (see table 2). hence, the null hypothesis, h0, was volume 10, no 1, february 2021, pp. 149-160 157 rejected indicating that there is a significant difference between the pre-test and post-test results. this implied that the lesson intervention of the bar model method had successfully enhanced the students’ performance in solving word problems involving ratio. this result is consistent with studies by gani et al. (2019), madani et al. (2018), mahoney (2012), and timah (2006), where the use of the bar model successfully improved the students’ problem solving performance in their respective topics. while the paired sample t-test of the overall sample has proven that the bar model method enhanced the sample students’ performance in the problem solving involving ratio, the analysis of post-test results particularly shows that students with lower academic abilities in class y could have benefited greatly from the bar model strategy, given the bigger increase in mean from pre-test to post-test of class y from 1.13 to 6.73, compared to class x with just mean increase of 3. however, due to the limitation of small number of students in each class (15 in class x and 18 in class y), t-test could not be used for significant difference test. from only 2 of them scoring 5 marks or more in the pre-test, this figure rose to 12 students in the post-test. a student from that class only obtained 1 mark in the pre-test but went on to obtain a full 10 marks in the post-test. the impact of the bar model method on the lower ability groups in solving word problems involving ratio is immense, as similarly found in goh (2009), where the bar model method especially helped the weaker students in her study. likewise, the bar model strategy helped all the mixed ability students in class x to do well in the ratio test with a mean mark of almost 10. furthermore, students performed significantly better in the post-test with thirty students scored 5 or more. this shows that the bar model is a problem solving heuristic that can cater to varying abilities of students but most significantly for the low abilities. a comparison of the number of correct responses against the number of incorrect responses in the pre-test and post-test is shown in figure 7. in the pre-test, there were clearly more incorrect responses than correct responses committed in almost all of the questions. except for q4 and q5, more than half of the students could not solve the problems posed. q2 and q8 have the highest number of incorrect responses (n = 27). q4 has the lowest number of students giving incorrect responses (n = 15), yet still considered high as almost half of the students failed to solve the problem. (a) (b) figure 7. comparison between the number of correct responses and incorrect responses in the pre-test (a) and post-test (b) looking at the post-test bars in figure 7(b), there is clearly a great improvement in the number of correct responses in each question after the students learned the bar model 14 6 15 18 17 15 15 6 11 11 19 27 18 15 16 18 18 27 22 22 q 1 q 2 q 3 q 4 q 5 q 6 q 7 q 8 q 9 q 1 0 n o o f s t u d e n t s item number correct incorrect responses 30 17 27 30 28 31 31 22 26 24 3 16 6 3 5 2 2 11 7 9 q 1 q 2 q 3 q 4 q 5 q 6 q 7 q 8 q 9 q 1 0 n o o f s t u d e n t s item number correct incorrect responses said, & tengah, supporting solving word problems involving ratio through the bar model 158 method. more than half of the students could solve all the problems correctly in the post-test as opposed to in the pre-test. questions 1, 6, 7 and 8 have the highest increase in correct responses by sixteen students. meanwhile, questions 2 and 5 have the smallest increase (eleven students) in the number of correct responses but this is still regarded as high. q2 which started with lowest correct responses in the pre-test ended up also being the lowest correct responses in post-test. overall, there is a positive indication of development in the students' problem-solving skills on ratio. the majority of the correct responses applied correct use of bar model in their answers in post-test, compared to keyword and unattempted questions in a pre-test. it suggests that teachers can consider different strategies for different topics such as: applying visual approach by using the graphic organizer in tackling word problem (sian et al., 2016); implementing thinking aloud pair and pólya in word problem approach (simpol et al., 2017); strengthening pattern discovery skills in the problem-solving task (tengah, 2011). the use of the bar model is also one of the strategies adopted in singapore classrooms taught as early as possible in elementary schools, thus making singaporean students one of the best math problem solvers as reported in timms and pisa. besides, previous empirical studies have shown the bar model's effectiveness in improving students' performance in word problems in singapore and brunei (gani et al., 2019; madani et al., 2018; mahoney, 2012; timah, 2006). all of this is a good justification for introducing the bar model to students in the country to solve word problems. this study particularly adds information to the existing body of knowledge regarding using the bar model in brunei. the positive results are evidence that the bar model strategy can be implemented into the local classrooms. it is also hoped that this study can encourage and convince more teachers to start using this type of diagram representation as part of their instructional approach as recommended by the new curriculum (cdd, 2006a; 2006b). furthermore, this bar model is very flexible and can be used across many topics such as whole numbers, fractions, and percentages. the bar model's simple nature, which does not consume time and money to teach, makes it a problem-solving heuristic that every mathematics teacher should practice as early as in primary levels across the country. early exposure would help provide a strong solid foundation in mathematics for young children, according to one of the intended learning outcomes of the new mathematics curriculum (cdd, 2006a; 2006b). moreover, the bar model's visual nature enables teachers to identify some of the difficulty’s students have with word problems. that information would be useful for the teaching of word problems (ng & lee, 2005). 4. conclusion this study was to examine the effects of using the bar model method on secondary students’ performance in solving word problems involving ratio. the results of the paired sample t-test revealed that there was a significant difference in the students’ mean marks between the pre-test and post-test results. furthermore, the results showed that students performed significantly better after they learned the bar model method as indicated by higher marks and more correct responses. weaker students particularly benefited from the introduction of the bar model as evident in the number of students scoring 5 marks or more in the post-test. hence for this study, the bar model successfully enhanced the lower secondary students’ performance in solving word problems involving ratio. it is evident from this empirical study that the bar model method is capable of helping students of different learning abilities and it can be an effective alternative strategy to solving word problems involving ratio. volume 10, no 1, february 2021, pp. 149-160 159 references arcavi, a. (2003). the role of visual representations in the learning of mathematics. educational studies in mathematics, 52(3), 215-241. https://doi.org/10.1023/a:1024312321077 cdd. (2006a). mathematics syllabus for lower primary school. gadong: curriculum department, ministry of education, brunei darussalam. cdd. (2006b). mathematics syllabus for upper primary school. gadong: curriculum department, ministry of education, brunei darussalam. charles, r. (2011). solving word problems: developing quantitative reasoning. retrieved from http://assets.pearsonschoolapps.com/playbook_assets/matmon110890charles_sw p_revise_ebook1.pdf chin, k. s., & clements, m. a. k. (2001). o-level students’ understanding of lower secondary school geometry. in energising science, mathematics, and technical education for all: proceedings of the sixth annual conference of the department of science and mathematics education, 213-222. denis, m. 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(2006). primary 5 pupils' performance on mathematical word problems using model-drawing/box-diagram strategy. dissertation. universiti brunei darussalam. vaiyatvutjamai, p., & clements, m. a. (2004). analysing errors made by middle-school students on six linear inequations tasks. globalisation trends in science, mathematics and technical education 2004, 173-182. van garderen, d. (2006). spatial visualization, visual imagery, and mathematical problem solving of students with varying abilities. journal of learning disabilities, 39(6), 496506. https://doi.org/10.1177/00222194060390060201 van garderen, d., & montague, m. (2003). visual‐spatial representation, mathematical problem solving, and students of varying abilities. learning disabilities research & practice, 18(4), 246-254. https://doi.org/10.1111/1540-5826.00079 https://doi.org/10.22342/jme.7.2.3546.83-90 https://doi.org/10.1088/1742-6596/943/1/012013 https://doi.org/10.1088/1742-6596/943/1/012013 https://doi.org/10.7916/jmetc.v2i1.710 https://doi.org/10.1177/00222194060390060201 https://doi.org/10.1111/1540-5826.00079 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 10, no. 2, september 2021 e–issn 2460-9285 https://doi.org/10.22460/infinity.v10i2.p259-270 259 mathematical literacy ability and metacognitive characteristics of mathematics pre-service teacher christina m. laamena*, theresia laurens universitas pattimura, indonesia article info abstract article history: received oct 1, 2020 revised feb 14, 2021 accepted july 4, 2021 this study aims to determine the characteristics of students' metacognition in solving mathematical literacy problems. the metacognitive traits explored are related to awareness in planning, monitoring, and evaluating the design of the thinking process used. the research method used is a mixed-method (sequential explanatory), which uses quantitative research results to conduct qualitative research. the research subjects were 80 early semester students who took the literacy test and chose six respondents representing the upper, middle, and lower groups, with two people in each group to be interviewed. the results showed that the mathematical literacy skills of pre-service teachers were at a low level. metacognitive characteristics that appear in the low group are (1) realizing that the solution of strategy is not right but not improved; (2) planning to develop a settlement strategy, but are not sure, (3) do not carry out the re-check process, and (4) do not believe what is being thought and do not understand the concept. metacognitive traits in the middle group are (1) aware of what they are thinking, (2) consciously plan various strategies to improve thinking accuracy, but do not always use these strategies, (3) tend to monitor the thinking process, and (4) show tendency to master the basic mathematical concepts of the problems at hand. the characteristics of metacognition in the high group during problem-solving are (1) using various strategies to demonstrate or improve the accuracy of thinking (sketching, drawing), (2) analyzing the problem before solving it, and (3) understanding and mastering the mathematical concepts that underlie the problem which is given. keywords: mathematical literacy, metacognition copyright © 2021 ikip siliwangi. all rights reserved. corresponding author: christina m. laamena, department of mathematics education, universitas pattimura jl. ir. m. putuhena, poka, tlk. ambon, maluku 97233, indonesia email: christinmath18@gmail.com how to cite: laamena, c. m., & laurens, t. (2021). mathematical literacy ability and metacognitive characteristics of mathematics pre-service teacher. infinity, 10(2), 259-270. 1. introduction mathematics has an important role in life, but in practice some students still consider mathematics to be a difficult subject (angateeah, 2017; khiat, 2010; laurens, 2010; sholihah & afriansyah, 2017). this is because mathematics is always introduced as an abstract discipline without relating it to everyday realities (fitriani et al., 2018; kadarisma et al., 2020; kariadinata, 2021; novriani & surya, 2017). in addition, students are also less https://doi.org/10.22460/infinity.v10i2.p259-270 laamena & laurens, mathematical literacy ability and metacognitive characteristics … 260 taught with mathematical skills, as a result they are not skilled at solving problems even according to tambychik and meerah (2010) and heong (2005) there are phases in problem solving that are not implemented properly. problems in mathematics are interpreted differently by the individuals who face them. according to schoenfeld (1987), mathematics problems for students are tasks that: (1) attract students' attention and challenge them to solve them, (2) it is not easy to find solutions. the problem as a situation that requires resolution and for which the individual sees no apparent or obvious means or path to obtaining the solution. there are problems that challenge a person but not others (laurens, 2010). in learning mathematics students need to be introduced to the problem and how to solve it. problems presented to students need to be studied for their relationship with the reality they are facing, meaning that these problems must be contextual problems that have been experienced by students. mathematical problems that are far from the reach of students will give the impression that mathematics only fills the curriculum without being useful in everyday life. therefore, the mathematical concept introduced must be related to its use in everyday life (basibas, 2020; reyes et al., 2019; root et al., 2020; yee & bostic, 2014). the ability to apply mathematical concepts in everyday reality is known as mathematical literacy. stacey (2011) state that the concept of literacy is closely related to several other concepts discussed in mathematics education, but the most important is modeling (mathematical modeling) which is called the process of mathematics. according to de lange (2003), the mathematical process begins with problems in real life, then the problem solver tries to identify relevant mathematical information, and reorganizes the problem according to the identified mathematical concepts, followed by gradually reducing real situations, the third step takes from real world problems to mathematical problems, and the fourth step is interpreting mathematical solutions in the real world. mathematical literacy is the application of mathematical knowledge, methods and processes in a variety of contexts. mathematical literacy contains more than the use of basic knowledge and procedures that enable individuals to have it. de lange (2003) explains that mathematical literacy is related to (1) numerical literacy which consists of material related to quantity (quantity), (2) quantitative literacy which consists of the form of relationships and changes (change and relationship) and uncertainty (uncertainty) and (3) spatial literacy which consists of form and space (space and shape). numerical literacy is concerned with the ability to use numerical data to evaluate statements relating to problems and situations that require mental processing and estimation of real-world context. quantitative literacy developing numbers includes the use of mathematics as it relates to change, quantitative relationships and uncertainty. spatial literacy emphasizes the ability of individuals in the context of three dimensions that are encountered in their daily lives. this requires an understanding of the properties of objects, the relative positions of objects and a visual perception of the object's dimensions. there is a level of mathematical literacy suggested by bybee (2008). this level is based on reading literacy skills, namely: (1) the lowest level called illiteracy which means the inability to deal with information that is considered relevant, namely ignorance of the basic concepts and methods of mathematics, (2) the second level is nominal literacy, namely literacy that is limited to understanding term or name. in this case the individual understands mathematical terms, questions or topics as part of mathematics, but is minimal in comparing these understandings, (3) the third level is functional literacy, which is the level where a person can use the knowledge gained in the activities required. in this case the standard method of mathematics can be applied to solve simple problems, (4) the fourth level is the conceptual and procedural literacy level. this dimension consists of developing an understanding of interrelated concepts. procedural knowledge leads to a mathematical volume 10, no 2, september 2021, pp. 259-270 261 discovery process, in which individuals understand and use mathematical concepts in the context of mathematical investigations. conceptual and procedural literacy contains some understanding of the structure and central function of mathematical ideas such as optimization and recognition patterns, (5) the highest level is the multidimensional literacy level. this level includes the conceptual understanding of mathematics and the social dimensions of mathematics. individuals may develop some understanding and connections in mathematics, and other knowledge content. its main focus is to apply mathematics functionally in order to solve problems and modeling as well as the transition process from the real world to mathematics and vice versa. based on the understanding of literacy, in the teaching and learning process, students need to be given an understanding of the benefits of studying mathematics, so that they feel that mathematics is not a scary subject but a subject that forms a mindset in analyzing problems faced in everyday life and finding solutions. students need to be faced with context problems that force them to find solutions by utilizing mathematical concepts and procedures that are learned. the use of mathematical concepts and procedures requires simple to complex levels of thought. according to charles and lester (1984) there are 3 aspects that influence solving mathematical problems, namely (1) cognitive aspects, including conceptual knowledge, understanding and strategies for applying this knowledge; (2) affective aspects, which are aspects that affect the tendency of students to solve problems; and (3) metacognition aspects, including the ability to organize one's own thoughts. metacognition aspects are important because they relate to one's awareness of the processes and results of thinking. metacognition is defined variously by experts, but in general the notion of metacognition is related to the awareness, knowledge and control that a person exerts over his own thinking processes and results. according to yong and kiong (2005), “metacognition refers to one's knowledge concerning one's own cognitive processes and products or anything related to them. metacognition refers, among other things, to the active monitoring and consequent regulation and orchestration of these processes in relation to the cognitive objects or data on which they bear, usually in the service of some concrete goal". flavell (2004) defines the first aspect of metacognition as one's knowledge of cognitive processes and results or everything related to it, then the second aspect of metacognition is defined as monitoring and self-regulation of one's own cognitive activities. the same understanding was put forward by garofalo and lester (1985) that to describe a person's knowledge and control over his mental processes, including knowledge about himself, his tasks, and the strategies used. for example, a student can find out his ability to solve problems well if he takes the time to check the results of his work, especially if he uses diagrams as one of his strategies. schoenfeld (2016) defines metacognition as follows: “metacognition is thinking about our thinking and it comprises of the following three important aspects: knowledge about our own thought processes, control or self-regulation, and belief and intuition (that is, metacognition is thinking about our own thinking which consists of three important aspects, namely: knowledge of our own thought processes, selfcontrol or self-regulation, and belief and intuition). metacognition is the knowledge, awareness, and control of our cognitive processes. metacognition is very important because our knowledge of cognitive processes can help to organize and choose strategies for solving problems that are being experienced (akben, 2020; desoete & de craene, 2019; lingel, lenhart, & schneider, 2019; yong, gates, & chan, 2019). in relation to literacy, israel et al. (2006) state that metacognitive skills should be taught within the context of authentic literacy engagement, and students should be given sufficient practice in their application that they know, when, why, and how to use them relatively effortlessly. in this study, the metacognition activities that were considered were laamena & laurens, mathematical literacy ability and metacognitive characteristics … 262 (1) how students recognized and identified problems and defined the elements of the situation presented; (2) how do students represent the problem and make connections between the information found; (3) how to plan and decide steps for completion and determine how to achieve these goals; (4) how to check / monitor the results it has obtained; (5) how to evaluate the results and solutions made. the low ability of mathematical literacy is due to the fact that indonesian students are not used to solving problems with the types of pisa and timss questions (ekawati, susanti, & chen, 2020; sulistiyarini, 2021) and metacognition that do not run smoothly. therefore, prospective teachers are the first to have their metacognition improved so that they can help their students in the future. in addition, the characteristics of metacognition based on the level of mathematical literacy have not been carried out, so this study will help educators to encourage the emergence of students' metacognition according to their literacy level. thus, the purpose of this study is to describe the mathematical literacy skills of mathematics pre-service teachers and to analyze the metacognitive characteristics used in mathematical literacy. metacognition characteristic analysis was based on the grouping of students (upper group, middle group and lower group). 2. method the research method used is a mixed method, which uses the results of quantitative research to conduct qualitative research. data from the test results were used as the basis for conducting interviews and document analysis to determine metacognition activities from data sources consisting of 80 students and 6 students were selected to be interviewed and become research subjects. quantitative data in the form of test scores were analyzed using descriptive statistics by calculating the mean value of literacy skills and the percentage of level grouping at each literacy ability level. the research instrument used was a literacy ability test which consisted of 5 questions, namely 1 social mathematics question, 2 work questions, 2 geometric questions as well as interview guidelines and an assessment rubric. interviewed subjects consisted of 6 people representing each group. the analysis of metacognition characteristics that appears is based on the analysis of the test results document and the analysis of the results of the interviews with the data analysis technique used, namely reducing data, presenting data and concluding the results. 3. results and discussion 3.1. results there are 2 types of research data that will be discussed, namely literacy ability test results which are quantitative data and work analysis data and interview transcripts which are qualitative data. the test result data for 3 classes shows that the mean value obtained is class a = 30.8, class b = 27.6 and class c = 22.2. this shows that there are differences in the results of literacy skills tests between subjects in the three groups. based on the results of the test, grouping was carried out in the upper, middle and lower groups in order to obtain the percentage of the upper group (high category) as much as 19%, the middle group (medium category) 60% and the lower group (low category) 21%. furthermore, based on the results of this work and based on the indicator of literacy levels put forward by bybee (2008), then the literacy level is analyzed with the results can be seen in table 1. volume 10, no 2, september 2021, pp. 259-270 263 table 1. data of literacy level (bybee, 2008) no level of literacy number 1 2 3 4 5 1. illiteracy 21.30% 12.50% 13.80% 17.50% 10.00% 2. nominal literacy 37.50% 12.50% 13.80% 23.50% 20.00% 3. functional literacy 12.50% 16.25% 28.60% 28.80% 13.80% 4. conseptual & procedural literacy 20.00% 7.50% 11.30% 11.30% 8.80% 5. multidimensional literacy 0.00% 0.00% 0.00% 0.00% 0.00% based on the analysis of the document results, it is known that not all subjects worked on the questions given. subjects who did not do question number 1 were 10%, question number 2 was 10%, question number 3 was 11.3%, question number 4 was 25% and question number 5 was 48.5%. table 1 shows that the level of literacy of mathematics pre-service teachers on all question numbers does not reach 50%, even if no one is at the multidimensional literacy level. persetance illteracy which only reaches 20% indicates that 80% of mathematics preservice teachers are able to identify information that is considered relevant or already know the basic concepts and mathematical methods that must be used to solve problems. the level of conceptual literacy and procedural literacy only reaches 20% and none of the mathematics pre-service teachers have the ability at the multidimensional literacy level. based on the analysis of worksheets documents (see figure 1), it can be seen that there are indications of the use of metacognition, for example the results of work that are crossed out, deleted then replaced, represent problems visually indicating the use of metacognitive knowledge, especially on the strategy variable. figure 1. example of students’ work based on the work done by the students (see figure 1), six people were selected as respondents to be interviewed. each of a number of two people representing the high, low and medium groups. interviews were conducted to reveal metacognitive characteristics in mathematical literacy. the following is an excerpt of an interview from one of the subjects. r : pay attention to the first problem. after reading this issue what do you think s1 : how to get the answer r : apart from that, is there anything else? s : remember fractions laamena & laurens, mathematical literacy ability and metacognitive characteristics … 264 r : why fractions? s : because what is written (pointing to the results of his work) is one-half, one-third r : what does this matter tell s1 : distribution of money r : did your reading time know what to want in this matter s1 : how much money did dony collect r : the answer? s1 : pointing at the answer with a smile to answer 437, (slowly said "it seems wrong") r : so why was it crossed out? s1 : first, the number must be equal to 1500, but i'm confused, i think it's not like this, then i crossed it out the results of the interview indicated that the metacognitive characteristics that emerged were (1) recalling the mathematical symbols contained in the problem which were metacognitive knowledge specifically referred to as metamemory; (2) know the meaning of the question but do not believe the answer is correct. this indicator is included in the metacognitive experience component, especially with regard to cognitive monitoring and evaluation. consider the following interview excerpt (subject at the conceptual and procedural literacy level) r : why do you draw like this s2 : this only helps me to understand the position of the blocks r : what is the position of the blocks s2 : there is an incoming beam, you need to know its position r : but the solution looks like this (pointing to the block image) s2 : because the block is put into the tub, r : are you sure the answer is correct? s2 : well, because i was asked about volume, i remember the volume of blocks, only because there is 1 block in the water r : do you have other ways besides this s2 : no this interview snippet shows that the subject realizes and then plans strategies that make it easier for him to solve problems. this is included in the metacognition knowledge component, especially individual variables and strategy variables. in relation to the metacognitive experience used, it can be seen that there is monitoring of the cognitive processes that occur by deleting and deleting as well as an evaluation process that raises awareness, for example, lack of confidence in what is done and have no other way than the way that has been made. 3.2. discussion from the results of the analysis of the mathematics teacher candidate literacy level, it can be seen that from the 5 questions given 3 questions related to the quantity content, 2 questions related to the content of space and shape. quantity content is concerned with understanding the relationships and patterns of numbers, including the ability to understand size, number patterns, and everything related to numbers in everyday life, such as counting and measuring certain objects. included in the content of this quantity is the ability to reason quantitatively, present something in numbers, perform systematic calculations. according to prince et al. (2021), the ability students need in quantitative literacy is the ability to: (a) volume 10, no 2, september 2021, pp. 259-270 265 identify and express relationships in an effective symbolic form, (b) use computational tools to process information, and (c) interpret results this calculation. based on the results of the analysis of the level of literacy skills, it can be seen that the average level of literacy skills is still low (because it's less than 30%). this can be seen from the fact that there are no subjects who occupy a special multidimensional level. there are less than 50% of subjects at each literacy level and are more dominant in nominal literacy. this shows that their ability is limited to recognizing symbols in the problem, not understanding relevant information and not understanding basic mathematical concepts. this indicates that there is an incomplete understanding of the problem being solved which is known as instrumental understanding. instrumental understanding is a type of understanding related to the use of methods or rules without knowing (realizing) the reasons for the use. gough (2004) state that instrumental understanding as rules without reasons. percentage of literacy nominal that is higher than other literacy shows that undergraduate students have a higher ability to solve problems using calculations or numbers. laamena, nusantara, irawan, and muksar (2018) mention that students are able to solve problems involving numbers (inductively) but if they are faced with problems that require deductive reasoning then they will have difficulty. so according to laamena and nusantara (2019), if the problem is presented in a statement, students tend to use examples of numbers to test the truth of the statement (numerical backing). they understand the questions but are unable to compare what is understood with the relevant mathematical content. for example, the difficulty in applying the different denominated fraction operation concept. in the functional literacy a group they try to use formulas to solve problems but then experience difficulties in the process of solving them, for example the concept of comparison to be used, but in the process they have difficulty equating the two forms of fractions so that they subtract the variables. this shows that knowledge about a procedure does not always guarantee that someone understands the concepts that underlie the material, it really depends on the metacognitive knowledge one has (akben, 2020; desoete & de craene, 2019; lingel et al., 2019; yong et al., 2019). uncontrolled metacognitive knowledge can lead to errors, as argued veenman, van hout-wolters, and afflerbach (2006) that metacognitive knowledge about how we learn can be wrong or right and this knowledge about ourselves (self-knowledge) is likely to change. this change will occur when there is cognitive monitoring activity that raises awareness (desoete & de craene, 2019; kaune, 2006; smith & mancy, 2018; stillman & mevarech, 2010; veenman & van cleef, 2019). in the conceptual and procedural literacy groups, they try to link some of the concepts needed, for example problem number 1 (an equation involving fractions), the problem is symbolically represented but then cannot evaluate the results obtained with what is needed in the problem. the interesting thing was that some of these groups tried to represent the problem visually so that it was easier to find answers and match them with what was being asked. one example is how to conduct investigations through pictures to find answers to problems, but the problem faced is a lack of knowledge of other concepts needed, for example the concept of physics about the mass of objects. the interesting thing about one of the subjects is trying to interpret the problem by making a pattern of the relationship between the number of workers and the specified time. in the multidimensional literacy a group there is an understanding of mathematical concepts, especially spatial structures so that the spatial abilities of the subjects in this group apply mathematical concepts by symbolically representing problems in sketch form. here they carry out a mathematical process by trying to create a mathematical model (chao, liu, & yeh, 2018; muhammad, kumaidi, & mukminan, 2020; yong et al., 2019; zhong & xia, 2020). laamena & laurens, mathematical literacy ability and metacognitive characteristics … 266 based on the results of the analysis of the interviewed subjects and related to their work results, it can be concluded that almost all metacognition components appear in mathematical literacy, especially those related to metacognition knowledge. the component of metacognitive knowledge that emerges leads to awareness of the concepts they possess, for example the awareness that they do not understand the concept of fractional operations, they do not understand how to relate known geometric concepts to other concepts needed in relation to problem solving. in relation to the level of mathematical literacy, in general the use of metacognition in the illiteracy group and the nominal literacy group is strongly influenced by conceptual knowledge and procedural knowledge. the characteristics of metacognition are realizing that the solution strategy is not right but not improving it, planning the strategy that is made but not realizing the accuracy of the strategy, not showing monitoring activities and not sure what is being thought and tends to not master the concept. for the functional literacy group, the use of metacognition leads to awareness of their knowledge but still has difficulty connecting some related mathematical concepts (ali et al., 2020; özenç & dikici, 2016; zhussupova & kazbekova, 2016). in the use of metacognition activities, the characteristics that are raised are being aware of what is thinking, planning various strategies consciously to increase the accuracy of his thinking, but not always using these strategies, tending to monitor his thinking processes, showing a tendency to master the mathematical concepts underlying the problem. for the conceptual and procedural and multidimensional literacy group, the characteristics of metacognition that arise during problem solving are the use of various strategies to demonstrate or improve the accuracy of their thinking (making sketches, drawing), analyzing problems before solving them, understanding and mastering the mathematical concepts underlying the given problem, even though in some steps, it was difficult to check, but due to a lack of conceptual knowledge, the answers given were not correct (amin & mariani, 2017; bakar & ismail, 2020; kramarski & zoldan, 2008; salam et al., 2020; schneider & artelt, 2010; su et al., 2016; zepeda et al., 2019). 4. conclusion this study concludes that the average mathematical literacy ability of pre-service teachers is in the low category and if it is related to bybee's level (2008), the average is still at the level of nominal illiteracy and literacy, meaning that mastery of mathematical concepts is still low and only limited to introduction. symbols and mastery of mathematical procedures are still lacking. in relation to the use of metacognition, it can be said that those in the low group have difficulties in developing and utilizing their metacognition because of the lack of conceptual knowledge and procedural knowledge of mathematics. subjects in the high literacy group can take advantage of their metacognition in solving several problems by realizing their knowledge regarding mathematical concepts and strategies used in solving problems including monitoring and evaluating their cognitive processes. references akben, n. 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(2016). metacognitive strategies as points in teaching reading comprehension. procedia-social and behavioral sciences, 228, 593-600. https://doi.org/10.1016/j.sbspro.2016.07.091 https://doi.org/10.1016/j.sbspro.2010.12.020 https://doi.org/10.1007/s11858-018-1006-5 https://doi.org/10.1007/s11409-006-6893-0 https://doi.org/10.1016/j.jmathb.2014.08.002 https://doi.org/10.4018/ijgbl.2019010101 https://doi.org/10.1037/edu0000300 https://doi.org/10.1007/s10763-018-09939-y https://doi.org/10.1007/s10763-018-09939-y https://doi.org/10.1016/j.sbspro.2016.07.091 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 10, no. 1, february 2021 e–issn 2460-9285 https://doi.org/10.22460/infinity.v10i1.p133-148 133 marginal region mathematics teachers’ perception of using ict media trisna roy pradipta*1, krisna satrio perbowo1, afifah nafis1, asih miatun1, sue johnston-wilder2 1universitas muhammadiyah prof. dr. hamka, indonesia 2university of warwick, england, uk article info abstract article history: received aug 24, 2020 revised jan 29, 2021 accepted jan 31, 2021 the article presents a marginal region mathematics teachers' perception of ict as learning media and the type of ict media used in mathematics classrooms. a survey was designed including two domains: the usability and the importance of ict. a questionnaire was administered to 84 mathematics teachers in marginal regions. the respondents were chosen conveniently based on their accessibility and availability. about 50% of marginal region mathematics teachers do not use ict in teaching. the most common media used is microsoft office software to present teaching materials from internet or digital sources. using the rasch model, the data show that mathematics teachers' perception of the usage and importance of ict as a media of mathematics learning can be categorized as 'medium' level. mathematics teachers in the marginal regions consider ict as mathematics learning media to be fairly important. keywords: ict, marginal region, perception copyright © 2021 ikip siliwangi. all rights reserved. corresponding author: trisna roy pradipta, department of mathematics education, universitas muhammadiyah prof. dr. hamka, jl. tanah merdeka, pasar rebo, jakarta timur, jakarta, indonesia. email: troymath@uhamka.ac.id how to cite: pradipta, t.r., perbowo, k.s., nafis, a., miatun, a., & johnston-wilder, s. (2021). marginal region mathematics teachers’ perception of using ict media. infinity, 10(1), 133-148. 1. introduction only a few published articles were found talking about mathematics education in marginalised contexts (howley, howley, & huber, 2005). it means, more attentions are needed to improve the quality of mathematics education in marginal regions. more collaboration is needed, both practically and academically, in mathematics education in marginal contexts (bush, 2005; nicol, archibald, & baker, 2013). a small part to contribute in solving mathematics education issue in the marginal region is to depict mathematics teachers’ perception of using ict as learning media in their classroom. learning media is a tool to deliver learning information that is designed so that it can help students understand the subject (muhson, 2010), as well as a communication tool for interaction between teachers and students in the learning process (ahern, 2016). the purpose of learning media use is to stimulate the mind and attention of students (triyanto, anitah, & suryani, 2013). while, the function of learning media is to accelerate the learning process effectively, improve quality and concretise abstract material (nurseto, 2011). the use of https://doi.org/10.22460/infinity.v10i1.p133-148 pradipta, perbowo, nafis, miatun, & johnston-wilder, marginal region mathematics teachers’ … 134 varied and innovative learning media can increase the joy and love of learning mathematics (safitri, hartono, & somakim, 2013). the rapid development of technology in the modern age has become the latest innovation in the learning process. ict media is one of the learning media besides teaching aids that are often used in learning mathematics. the rapid development of technology has an impact on the world of education, creating expectations to integrate ict into the classroom; this can change conventional learning styles (directs-teaching & learning) into constructivist learning (donnelly, mcgarr, & o’reilly, 2011; hismanoglu, 2012; lin, wang, & lin, 2012; smith, shin, & kim, 2017). ict-assisted learning is an effective and efficient way of building knowledge so that it helps teachers create a modern learning context (eyyam & yaratan, 2014). learning by involving ict can facilitate students in understanding concepts in theoretical and practical approaches by using technology such as led tv, lcd projectors, laptops, tablets, computers, mobile phones, internet, etc. (gautam & agrawal, 2012). the forms of ict media used in the learning process are text, audio, video or images (blum & parette, 2015). ict plays the most important factor in creating enjoyable and efficient learning to achieve learning effectiveness so that it can improve learning outcomes. ict media software in learning mathematics includes geogebra, sketchpad, microsoft mathematic, autograph, and others (bakar, ayub, & tarmizi, 2010). learning via the internet is rampant nowadays (limayem & cheung, 2011) because the internet is a place of learning to obtain information and knowledge anywhere and anytime, following various forms of media via the internet such as ruang guru, zenius, youtube, brainly, and edmodo. there are many benefits obtained by using ict (ali, haolader, & muhammad, 2013), most teachers recognise the importance of using ict in learning so training is needed so that teachers can integrate ict effectively in the teaching and learning process. ict becomes one of the important factors in a country's development process depending on the readiness of infrastructure and the spread of ict (alghamdi, goodwin, & rampersad, 2011). in indonesia, the progress of ict has developed rapidly. the tim indikator tik pusat litbang ppi (2015) surveyed conditions within households, in indonesia, with the use of ict as follows: (1) have computers in urban regions 41.9% while rural 19.9% (2) use the internet in urban regions 47.9% while rural 24.7% (3) have mobile phones in urban regions 90.9 % while rural 78.8%. based on the survey results, the use of ict was still relatively low in rural regions compared to urban regions. this finding has been supported by several studies; ict can be experienced throughout indonesia. amin (2016) found the use of the internet in the education sector in the eastern border region using mobile broadband is as much as 50.4%, while 40.2% of schools are using fixed broadband. based on the ministry performance report (afidah, doom, & putri, 2017), a strategy for the availability of ict infrastructure and the development of ict ecosystems has been worked with villages in the border areas, disadvantaged areas, including local transportation services available in 4.02% of 222 locations and 3 piloting villages. the development of ict in the marginal regions is one of the active missions carried out by the ministry of research and technology since 2000 among others in the form of warung informasi dan teknologi (warintek), community access points (cap), and mobil pusat layanan internet kecamatan (mplik), which by 2013 had a number of 84 stalls scattered in 28 of 34 provinces in indonesia (kusnandar, 2013). all statements above show that only some marginal regions are occupied with information and technology services. however, the use of ict as a learning media in marginal regions has not been realised comprehensively in almost schools in indonesia. this is because human resources and marginal region governance have not contributed fully in the context of developing their regions (chaerul & aisyah, 2014), so that there are many limitations of facilities and infrastructure owned by marginal regions including the difficulty of getting access to basic volume 10, no 1, february 2021, pp. 133-148 135 services, such as education, health, water, infrastructure, transportation, electricity, and telecommunications (kementerian ppn/bappenas, 2016). despite the problems of the marginal regions, there are very few marginal regions that have experienced the use of ict. limited access to ict in marginal areas raises a question about mathematics teachers' perception of the use of ict media in learning mathematics in marginal regions. 2. method this research was conducted by a survey with a quantitative descriptive approach. data were collected by a questionnaire adapted and translated from albalaw (2017). the questionnaire was translated and checked by an expert from english department of university of muhammadiyah prof. dr. hamka, indonesia. the instrument contained statements of perception of mathematics teachers toward the use of ict. it consists of two domains or variables: the use of ict as a learning media (19 items) and the importance of ict as a learning media (27 items). the validity and reliability of the instrument were checked with the rasch model. the instrument is valid due to the high ptmea corr score for each item (x > 0.2), and raw-variance more than 40% and unexplained-variance less than 15% for each domain (linacre, 2011). the reliability of the instrument is high with person reliability 0.93, item reliability 0.98 and alpha cronbach 0.98 (bond, yan, & heene, 2020). data from the questionnaire were processed using the rasch model assisted with winstep application to convert ordinal data into interval data (sumintono & widhiarso, 2014). the respondent perception and the item responses are represented on the wright map logit (log odds unit) scale such as those given in figure 1 and figure 2. the results of respondents' responses are converted into the form of measure scale values with standard deviation calculations so that each domain has a different scale as seen in table 1. table 1. item logit categories domain 1: the use of ict domain 2: the importance of ict mean measure range decision mean measure range decision 0.765 < 𝑥 never existed 0.75 < 𝑥 unimportant 0.255 < 𝑥 ≤ 0.765 rarely 0.25 < 𝑥 ≤ 0.75 fairly important −0.255 < 𝑥 ≤ 0.255 sometimes −0.25 < 𝑥 ≤ 0.25 somewhat important −0.765 < 𝑥 ≤ −0.255 mostly −0.75 < 𝑥 ≤ −0.25 important 𝑥 ≤ −0.765 always 𝑥 ≤ −0.75 very important due to the limitation to reach population of mathematics teachers in marginal regions of indonesia, this research was using convenience sampling that consisted of 84 mathematics teacher respondents in the marginal regions with levels of schools ranging from elementary (d), junior high (p), to high school (a) spread from western to eastern indonesia; the number of respondents in each region can be seen in table 2. the geographical locations in western indonesia include sumatra, java, kalimantan, and bali province. geographical locations in eastern indonesia include sulawesi island, maluku province, west nusa tenggara province, east nusa tenggara province, and papua island. pradipta, perbowo, nafis, miatun, & johnston-wilder, marginal region mathematics teachers’ … 136 table 2. grouping data based on respondent geographical location and level of school geographical location level total d p a east 2 24 8 34 west 27 17 6 50 total 29 41 14 84 3. results and discussion 3.1. results 3.1.1. types of ict as a learning media the type of ict used in mathematics learning activities in marginal regions based on geographical location in table 3 shows that microsoft office is most used in western indonesia with 11 people compared to eastern indonesia with four people with a percentage of 17.86% users. this is different from eastern indonesia, where the type of ict media most used is mathematics software with a total of 8 people while in western indonesia there are 5 people with a percentage of users of 15.48%. however, there are still many mathematics teachers in marginal areas who did not use ict media in mathematics learning, with a percentage of 50.00% of the total respondents. the majority of marginal regions mathematics teachers are not using any ict or even digital media during teaching mathematics. this seems due to the constraint of facility and communication access. table 3. types of ict media based on geographical location media location total percentage east west electronic book 1 0 1 1.19% social media 0 2 2 2.38% microsoft office 4 11 15 17.86% online media 3 8 11 13.10% mathematics software 8 5 13 15.48% not using 18 24 42 50.00% total 34 50 84 100.00% the most common media used within the regions is microsoft office, especially in the western part of indonesia. the teachers use powerpoint to present their works, or they use word to show the teaching materials they wrote or took from internet/digital sources to their students. meanwhile, mathematics software is more prevalent in eastern indonesia. the type of ict based on the level of education used in learning mathematics in the marginal regions in table 4 shows that the use of ict media in mathematics learning for the elementary school level (d) is widely used, namely six people use online media. for the junior high school level (p), the use of ict media which is widely used in learning mathematics is mathematics software, as many as 10 out of 13 users. whereas for the high school level (a) there are two ict media which are widely used in mathematics learning, as many as 3 out of 15 users of microsoft office and 13 users of mathematics software. volume 10, no 1, february 2021, pp. 133-148 137 table 4. types of ict media based on school levels media level education total percentage d p a electronic book 0 1 0 1 1.19% social media 1 1 0 2 2.38% microsoft office 4 8 3 15 17.86% online media 6 4 1 11 13.10% mathematics software 0 10 3 13 15.48% not using 18 17 7 42 50.00% total 29 41 14 84 100.00% the types of ict used in mathematics learning are grouped based on geographical location and education levels in table 5. it can be seen that the ict media that are widely used in western indonesia are online media with 6 users found in d. while for eastern indonesia, mathematics software is most widely used with 6 users in p. table 5. types of ict media based on geographical location and school level media ict east west total d p a d p a electronic book 0 1 0 0 0 0 1 media social 0 0 0 1 1 0 2 microsoft office 0 3 1 4 5 2 15 online media 0 3 0 6 1 1 11 mathematics software 0 6 2 0 4 1 13 not using 2 11 5 16 6 2 42 total 2 24 8 27 17 6 84 3.1.2. the usage of ict as a learning media the questionnaire data distribution consisted of 19 items of statements regarding the use of ict as a learning media. the variable map in figure 1 shows the item that was most difficult to be agreed upon by respondents is item number 6. in comparison, the items that were most approved were item numbers 17 and 3. pradipta, perbowo, nafis, miatun, & johnston-wilder, marginal region mathematics teachers’ … 138 figure 1. variable map of the use of ict as a learning media table 6 shows the logit standard deviation values according to the item logit category of respondents' responses in table 1. from table 6, it is known that there are six items in the category of ‘rarely’ use (numbers: 4, 6, 12, 13, 14 and 16). while the ‘always’ usage category contained three items (no: 3, 5 and 17). in addition, it can be seen that there are 14 items that are categorised as ‘rarely’ and ‘sometimes’ and five items that are categorised as ‘always’ and ‘mostly’. table 6. domain 1: the use of ict as a learning media no items logit value most responses 1. i use ict as one of my methods in teaching mathematics -0.17 sometimes 2. i give students my social media contact information at the beginning of the semester -0.17 sometimes 3. i encourage students to learn mathematics through ict -0.83 always 4. i encourage students to follow an online learning forum 0.60 rarely 5. i give students an idea about the necessary websites and apps for learning mathematics -0.77 always h ig h m id l o w volume 10, no 1, february 2021, pp. 133-148 139 no items logit value most responses 6. i recognise students’ academic improvement through ict 0.71 rarely 7. by the use of ict, i implement the concept of cooperative learning 0.15 sometimes 8. i deliver the content of the courses to my students through ict 0.19 sometimes 9. i give students a chance to cooperate learning through the use of ict 0.06 sometimes 10. i solve students’ learning problems through ict -0.04 sometimes 11. i teach some parts of the math course using ict -0.23 sometimes 12. i give students extra-curricular activities assigned through ict 0.32 rarely 13. i assign students in groups to discuss and solve math problems through ict 0.57 rarely 14. i prepare quizzes for students and tell them to do it through ict 0.64 rarely 15. i design courses using ict 0.25 sometimes 16. i train students to discuss and explore the concept of mathematics through ict 0.60 rarely 17. ict gives me other ways of teaching math -0.89 always 18. i give students the chance to search for information using ict -0.38 mostly 19. i use social media in exchanging mathematics teaching strategies with my colleagues -0.62 mostly the value distribution in general of the perception of mathematics teachers in the marginal area towards the use of ict media in figure 1 shows that by using ict the way of teachers teaching became more varied and not monotonous. the distribution of data based on school levels shows that those who have high perceptions of ict are found in junior high schools (p) by 61.54% of a total of 13 people. at the most moderate perception, there is 54.55% of the total of 44 people in junior high school (a). whereas, the lowest perception is at elementary school (d) level that is 48.15% of 27 teachers, as shown in table 7. table 7. perception of the use of ict based on school level category level total d p a high 4 8 1 13 15.48% medium 12 24 8 44 52.38% low 13 9 5 27 32.14% total 29 41 14 84 100.00% the perception of mathematics teachers in the marginal area towards the use of ict media based on geographical location is that those who have a high perception are located pradipta, perbowo, nafis, miatun, & johnston-wilder, marginal region mathematics teachers’ … 140 in western indonesia (w) by 69.23%. likewise, for medium and low perception is also the case in by western indonesia (w) by 61.36% and 51.85%. this can be seen in table 8. table 8. perceptions of the use of ict based on geographical location category location total e w high 4 9 13 15.48% medium 17 27 44 52.38% low 13 14 27 32.14% total 34 50 84 100.00% the perception of mathematics teachers in the marginal area towards the use of ict media based on school levels and geographical location (see table 9) illustrates that high perceptions were found in junior high schools (p) in western indonesia (w) by 38.46% of respondents. the medium perception category lies in junior high school (p) level in eastern indonesia (e) by 34.09%. whereas for the low category owned by elementary school (d) respondents in western indonesia (w) as much as 40.74%. table 9. perception of the use of ict based on school level and geographical location category d p a total e w e w e w high 0 4 3 5 1 0 13 15.48% medium 0 12 15 9 2 6 44 52.38% low 2 11 6 3 5 0 27 32.14% total 2 27 24 17 8 6 84 100.00% 3.1.3. the importance of ict as a learning media questionnaire data distribution consisted of 27 items of statements regarding the importance of using ict as a learning medium, and there were 84 respondents of mathematics teachers in the marginal regions ranging from elementary school (d), junior high school (p) and high school (a) scattered from western indonesia (w) to eastern indonesia (e). the variable map in figure 2 shows that the items that are most difficult to be agreed upon by respondents are items number 17 and 2. in contrast, item that is highly approved is item number 9. volume 10, no 1, february 2021, pp. 133-148 141 figure 2. variable map the importance of ict as a learning media while table 10 shows the standard logit deviation values according to the item logit category of respondents' responses in table 1. from table 10, it is known that there are three items in the ‘unimportant’ category (no. 2, 17 and 18). while the category of usage is ‘very important’ there is 1 item (no. 9). in addition, it can be seen that there are 15 items that are categorised as ‘fairly important’ and ‘somewhat important’ and nine items that are ‘important’ and ‘very important’. table 10. domain 2: the importance of using ict as a learning media no items logit value most responses 1 i use ict in teaching math -0.67 important 2 i give students my social media contact information at the beginning of the semester 1.09 unimportant 3 i encourage students to use ict more than the other ways 0.44 fairly important h ig h m id l o w pradipta, perbowo, nafis, miatun, & johnston-wilder, marginal region mathematics teachers’ … 142 no items logit value most responses 4 ict makes it easy for students to communicate within groups 0.31 fairly important 5 i give students an idea about necessary apps and math learning website -0.04 somewhat important 6 some students advance/improve because of their use of ict -0.22 somewhat important 7 ict is important for students’ learning advancement/improvement -0.33 important 8 i encourage students to seek inspiration when they used ict -0.15 somewhat important 9 using ict makes learning to be more amusing -0.99 very important 10 using ict helps to build students’ collaborative methods and skills -0.36 important 11 ict helps students by delivering the content of math’s courses -0.55 important 12 ict helps me to facilitate the presentation of information -0.67 important 13 ict helps in considering individual differences among students 0.17 somewhat important 14 ict gives students the chance to cooperate in learning 0.14 somewhat important 15 ict gives me a chance to solve students’ problems about learning mathematics -0.04 somewhat important 16 i teach the content of some courses through ict 0.07 somewhat important 17 i give students extracurricular activities through ict 1.09 unimportant 18 i assign students in groups to discuss and solve mathematics problems through ict 0.90 unimportant 19 ict helps me in preparing quizzes and conducting them through ict 0.54 fairly important 20 i designed the math course using ict 0.38 fairly important 21 using ict helps students gain more confidence 0.07 somewhat important 22 using ict gives students important life experiences -0.36 important 23 using ict equips students with the skills for discussion and debate -0.07 somewhat important 24 ict equips students with the skill of self-learning -0.25 important 25 ict helps in creating a variety in math-teaching methods -0.33 important 26 ict pushes students to learn -0.18 somewhat important 27 ict helps students gain social skills 0.03 somewhat important based on responses shown in table 10, it can be seen that the teachers mostly agree that ict plays an important role to make the learning process to be more interesting and enjoyable for students. volume 10, no 1, february 2021, pp. 133-148 143 the distribution of data based on school levels shows that those who have a high perception of the importance of using ict as a learning media are found at the junior high school level (p) by 72.73% of a total of 11 people. at the most moderate perception, it has at the junior high school level (p) 46.43% of the total of 56 people. likewise, the lowest level of perception was in junior high school level (p), namely 41.18% of 17 people, as shown in table 11. table 11. perceptions of the importance of ict based on school category level total d p a high 3 8 0 11 13.10% medium 21 26 9 56 66.67% low 5 7 5 17 20.24% total 29 41 14 84 100.00% the perception of mathematics teachers in the marginal area towards the importance of ict media based on geographical location is that those who have a high perception are located in western indonesia (w) by 72.73%. likewise, for moderate perception found in western indonesia (w) which is 67.86%. whereas in the low perception owned by eastern indonesia (e) was 76.47%. this can be seen in table 12. table 12. perceptions of the importance of ict based on geographical location category location total e w (n) (%) (n) (%) (n) (%) high 3 27.27% 8 72.73% 11 13.10% medium 18 32.14% 38 67.86% 56 66.67% low 13 76.47% 4 23.53% 17 20.24% total 34 100.00% 50 100.00% 84 100.00% mathematics teachers’ perception in the marginal area on the importance of ict media based on education level and geographical location as seen in table 13 illustrates that high perceptions were found in junior high schools in western indonesia by 45.45%. on the perception at the elementary school level in western indonesia by 35.71%. whereas for low perception, there is a junior high school level in eastern indonesia that is 41.18%. table 13. perceptions of the importance of ict based on education level and geographical location category d p a total e w e w e w high 0 3 3 5 0 0 11 13.10% medium 1 20 14 12 3 6 56 66.67% low 1 4 7 0 5 0 17 20.24% total 2 27 24 17 8 6 84 100.00% pradipta, perbowo, nafis, miatun, & johnston-wilder, marginal region mathematics teachers’ … 144 3.2. discussion this study found that the majority of marginal regions mathematics teachers are not using any ict or even digital media during teaching mathematics. the constraint of facility and communication access are common limitations in marginal regions (kementerian ppn/bappenas, 2016). this can be understood by looking at the situation in the regions that many mathematics teachers do not utilise ict in mathematics classrooms. in addition, a study by perbowo, maarif, and pratiwi (2019) shows that the perception of marginal regions mathematics teachers on the use of manipulative tools is higher than on the use of ict. most marginal region mathematics teachers are choosing microsoft office to help their teaching since microsoft holds the biggest office software market over the globe (gandal, markovich, & riordan, 2018); obviously, microsoft office software becomes the most common bundle for a personal computer or laptop unit and does not require internet access to be operated. this software is sometimes considered as the standard software for the requirements for successful e-learning (waterhouse & rogers, 2004). in line with lawrence and tar (2018), the utilisation of ict provides more opportunities for teachers to improve the quality of teaching and learning environment. in addition, the findings show that the teachers would promote the use of ict to students to help them learn mathematics. the use of ict media as a medium of mathematics learning is dominated by western indonesia because there has been more developement and improvement for the access of the community to ict, compared to eastern indonesia, especially in garut district and riau province (djuwendah, hapsari, renaldy, & saidah, 2013; syahza & suarman, 2013). according to tossavainen and faarinen (2019), ict adds more positive value in mathematics classroom while traditional teaching of mathematics is more or less boring. on the contrary, teachers tend to mind giving students their social media contact information. they see this as an unimportant matter in mathematics teaching and learning. in addition, teachers also assume that giving extra activities for students to discuss and doing mathematical activities through ict as another unimportant case. teachers must be aware that ict not only can increase student motivation (tossavainen & faarinen, 2019), but also can enhance students’ understanding and mathematics proficiency (drijvers, boon, & van reeuwijk, 2011; widodo et al., 2019). the rapid development of digital media, especially ict, is affecting the way in which humans live and learn (voogt & roblin, 2012). mathematics teachers, especially in marginal regions, need to continuously transform and adapt in order to comply with the competencies needed for industrial revolution 4.0 in the 21st century. the findings of this study show that marginal regions mathematics teachers do not have a high perception of adopting ict in their teaching. in addition, they do not have enough concerns about the role of ict in promoting students' performance and proficiency in mathematics. we assume that it is because of all barriers and limitations they face in their region. yet, they must be able to deal with the situation. the challenge for the future is to give a handful of designs to teach mathematics in marginal regions; a design that can optimise the learning environment within the regions. thus, further studies for teaching and learning designs that are suitable in marginal regions are needed; whether it involves digital media, hands-on manipulative tools or any media that can help teachers to teach mathematics as concrete as possible. thus, at least there are two factors that needed to be considered in order to create the most suitable teaching design for mathematics classrooms in marginal regions which are learning environment and realistic mathematics context. volume 10, no 1, february 2021, pp. 133-148 145 4. conclusion the study findings indicate that most marginal regions mathematics teachers are still not utilising ict or any other digital media in their teaching. most teachers who use ict are using microsoft media since this software is common and does not require internet access to be operated. in specific, online media is mostly used in teaching mathematics for primary school, while mathematics software for secondary school and microsoft office for senior high school. the perception of mathematics teachers in the marginal regions towards the domain of the use of ict can be categorised as ‘medium’ which is dominated by secondary school mathematics teachers in marginal regions of eastern indonesia. the teachers are used to adopting ict in teaching mathematics regularly. in comparison, the perception of mathematics teachers in the marginal area on the importance of ict can be categorised as ‘medium’ which is dominated by elementary mathematics 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(2019). visual media in team accelerated instruction to improve mathematical problemsolving skill. in proceedings of the 1st international conference on science and technology for an internet of things. european alliance for innovation (eai). http://doi.org/10.4108/eai.19-10-2018.2281297 https://doi.org/10.1080/00220272.2012.668938 http://doi.org/10.4108/eai.19-10-2018.2281297 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 10, no. 1, february 2021 e–issn 2460-9285 https://doi.org/10.22460/infinity.v10i1.p93-108 93 profile of prospective teachers' mathematical communication ability reviewed from adversity quotient muhtarom*, adelia dian pratiwi, yanuar hery murtianto universitas pgri semarang, indonesia article info abstract article history: received sep 14, 2020 revised jan 15, 2021 accepted jan 16, 2021 communication skills are an essential aspect that students need to possess by students who want to succeed in their studies, where students' mathematical communication can organize mathematical thinking both orally and in writing. while aq is intelligent in facing difficulties, a student must face the problems that exist in them. this study aims to determine the profile of prospective mathematics prospective teacher's mathematical communication skills in terms of adversity quotient. this study was conducted on mathematics education students in the 6th semester of universitas pgri semarang. this research is a descriptive qualitative study. subjects taken from 57 respondents were three students in the category of climbers, campers, and quitters. written tests and interviews do data collection. indicators of mathematical communication skills used in this study include drawing, writing, and mathematical expression. the results showed that the subject climber can meet all the indicators of mathematical communication skills and can be said to be good. subject campers tend to meet all indicators of mathematical communication skills, have the power of communication in indicators drawing, and be quite useful. quitter's subject tends not to meet all the communication indicators. the subject does not answer the drawing indicator's problem, and the writing and mathematical expression indicators are still wrong. keywords: adversity quotient, mathematical communication ability copyright © 2021 ikip siliwangi. all rights reserved. corresponding author: muhtarom, department of mathematics education universitas pgri semarang, jl. sidodadi timur no. 24, dr. cipto semarang, central java 50232, indonesia. email: muhtarom@upgris.ac.id how to cite: muhtarom, m., pratiwi, a. d., & murtianto, y. h. (2021). profile of prospective teachers' mathematical communication ability reviewed from adversity quotient. infinity, 10(1), 93-108. 1. introduction the 21st century is a century marked by the occurrence of a massive transformation from an agrarian society to an industrial society and continues to a knowledgeable society (soh, arsad, & osman, 2010). life in the 21st century requires a variety of skills that must be mastered by someone, education is becoming increasingly important to ensure students have learning and innovation skills, skills to use technology and information media, and can work, and survive using life skills (wijaya, sudjimat, & nyoto, 2016). https://doi.org/10.22460/infinity.v10i1.p93-108 muhtarom, pratiwi, & murtianto, profile of prospective teachers' mathematical communication … 94 scott (2015) states in the international commission on education for the twentyfirst century proposes four visions of learning, namely knowledge, understanding, competence for life, and competence to act. in addition to this vision, four principles known as the four pillars of education are formulated, namely learning to know, lerning to do, learning to be and learning to live together. fridanianti, purwati, and murtianto (2018) state that strengthening character education in schools must be able to foster student character to be able to think critically, creatively, be able to communicate, and collaborate, who are able to compete in the 21st century. this is in accordance with the four competencies that students must have in the 21st century which is called 4c, namely critical thinking and problem solving, creativity, communication skills, and the ability to work together. communication is one of the skills in learning to do, oral and written communication skills contribute to career development in the 21st century. the results of an analytical study conducted by wardhani & rumiati (salam, 2017), the cause of the low mathematics achievement of indonesian students in the 2015 timss results is due to the weakness of indonesian students in working on questions that require several abilities, one of the abilities needed is the ability to communicate in mathematics. this can be caused by student confusion in presenting ideas or ideas in the form of symbols, graphs, tables or other media to clarify math problems. the results of the 2018 pisa assessment (nugrahanto & zuchdi, 2019) show that the mathematical abilities of students in indonesia are still low. one of the low mathematical abilities is mathematical communication skills, this can be caused by student confusion in presenting ideas or ideas in the form of symbols, graphs, tables or other media to clarify mathematical problems. ulfa, buchori, and murtianto (2017) stated that in general the process of learning mathematics in the classroom is teacher-centered. this is in line with hampson, patton, and shanks (2011) who state that high-quality teachers are those who have a strong influence on student achievement. the ability to communicate in learning activities is said to be good if the ability of a teacher and lecturer to create a communicative climate, where between lecturers and students or teachers with students as subjects are actively involved in learning activities, both verbally and nonverbally, in other words this communicative climate as a vehicle for the implementation of learning in accordance with the design and achieving learning objectives (son, 2015). it would be better if the provision of mathematical communication skills is integrated in every lecture. to realize good students’ mathematical communication skills given by the teacher, trained or prepared since becoming prospective teacher. son (2015) also adds, of course it is not effective and efficient if prospective mathematics teacher students only get a theory of mathematical communication in a subject without getting enough opportunities to practice it, it would be better if the provision of mathematical communication skills is integrated in every lecture. hapsari, nizaruddin, and muhtarom (2019) state that teachers play a very important role in improving the quality of learning and learning outcomes that will be achieved by students before going to a higher level. many students still have imperfect mathematical communication skills. paradesa and ningsih (2017) states that the ability of students in the aspect of mathematical communication seen from the ability to provide mathematical evidence in the form of facts and data is still experiencing difficulties. if it is related to the problem of mathematical communication skills, the type of intelligence can be used, namely adversity quotient (aq). aq is often identified with fighting power against adversity. aq is considered to be able to support student success in increasing achievement motivation (hidayat & husnussalam, 2019; hidayat, noto, & sariningsih, 2019; hidayat, wahyudin, & prabawanto, 2018). many studies have been conducted to see the effect of aq, including: hidayat, herdiman, aripin, yuliani, and maya (2018) who try to improve aq and student teacher student mathematical creative reasoning, stating that aq has a positive influence on the volume 10, no 1, february 2021, pp. 93-108 95 development of students' mathematical creative reasoning abilities prospective teacher. kartika and yazidah (2019) also tried to analyze the ability of mathematical proof in real analysis courses based on aq, stating that climbers’ students are more able to compile direct evidence than quitters and campers students. paramita (2017) also conducted research on mathematical communication skills in terms of aq through the application of the scss learning model in students class viii, showing that quitters tend not to be able to meet all indicators of mathematical communication skills, campers subject tends to be able to fulfill two indicators, namely the ability to state a situation to in mathematical language and the ability to visualize mathematical ideas, the climbers subject was able to fulfill all indicators. yuniarti (2015) also conducted research on the analysis of the results of the diagnostic assessment of mathematical communication skills in osborn learning based on aq, and the results showed that the quitter category student subjects had not been able to fulfill almost every mathematical communication indicator, the camper category was quite capable in several indicators of mathematical communication, and the climber category. based on the above explanation that aq has a significant effect in determining the success of students' mathematical communication skills, therefore the mathematical communication skills of students who have high aq or students with climbers level will be different from the mathematical communication skills of students who have aq at the campers and quitters level. thus the purpose of this study is to determine and investigate in depth the aq profile of prospective mathematics teacher students on mathematical communication skills. 2. method the method used in this research is descriptive qualitative research method using written and oral data. because when the research was being carried out, it was during the covid-19 pandemic, social distancing, and work from home, so this research was carried out online, where the aq questionnaire was filled out via google form, and a written test of mathematical communication was carried out via the whatsapp group video call, while interviews were conducted via whatsapp call. the subjects defined in this study were 3 students at 6th semester of the mathematics education study program of the universitas pgri semarang class of 2017 including one student with aq quitters, one student with aq campers, and one student with aq climbers. this study used purposive sampling. sugiyono (2008) states that purposive sampling is a technique of sampling data sources with certain considerations, with the consideration that the person we choose is considered to know best about what we expect, making it easier for researchers to explore the object or social situation under study. the instruments used in this study included the aq questionnaire, the mathematical communication skills test sheet, and the interview guide. the aq questionnaire for sixth semester mathematics education students was given to two classes via google form and obtained 57 respondents. the aq questionnaire instrument was adapted by stoltz (2000) and has been validated by one counseling lecturer and three mathematics lecturers at the universitas pgri semarang. this questionnaire was conducted to select 3 students with the categories quitters (mm), campers (kal), and climbers (ndc). in this study, the climber subject was taken with the highest questionnaire score in the climbers category, the camper subject was taken with the middle questionnaire score in the campers’ category, and the quitter subject was taken with the lowest questionnaire score in the quitters’ category. after determining each subject in the aq category, then an online written test was carried out through the whatsapp video call group for students who had the intelligence of quitters, campers, and climbers. the questions given consist of one story item on calculus muhtarom, pratiwi, & murtianto, profile of prospective teachers' mathematical communication … 96 material, which has been validated by three mathematics lecturers. indicators of mathematical communication skills used include: 1) writing, which is to provide answers using your own language or problems using writing and algebra, listening to, discussing and writing about mathematics, and being able to explain ideas or situations from a picture or graphic with words itself in writing; 2) drawing, namely reflecting real objects, pictures, and diagrams into mathematical ideas and vice versa, and expressing a situation with pictures or graphs; 3) mathematical expressions, namely expressing mathematical concepts by expressing everyday events in mathematical language or symbols, and expressing a situation in the form of a mathematical model. before conducting the interview, the researcher checked back one by one the answers of each subject and checked the location of the truth and error in each indicator of mathematical communication. interviews were conducted online via whatsapp calls to get more in-depth information about the mathematical communication forms possessed by these students. the interview instrument was validated by three mathematics lecturers. the interviews were conducted for approximately 10-20 minutes. to maintain the validity of the data in this study, triangulation was used. the triangulation used was method triangulation. after obtaining the results of the analysis of the written test answers and the interview data analysis, then a comparison is made to determine whether the data obtained is valid or not. and the result states that all data for climbers, campers, and quaitters subject can be said to be valid. 3. results and discussion 3.1. results the first step was to determine the students as categories climbers, campers, and quitters. from the aq questionnaire that has been distributed, it was obtained from 57 respondents that 3.51% of students with aq quitters, 0% of students with aq quitters to aq campers, 31.58% of students with aq campers, 57.89% of students with aq campers to aq climbers, and 7.02% of students with aq climbers as in the following figure 1. figure 1. graph of the number of students for each aq 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% quitters quitters to campers campers campers to climbers climbers volume 10, no 1, february 2021, pp. 93-108 97 after selecting 3 students with the categories climbers, campers, and quitters, then the three students were given questions on communication skills tests and interviews. instruments used for mathematical communication skills include drawing, writing, and mathematical expression. 3.1.1. ndc subject the ndc subject fulfills following the indicators of mathematical communication drawing skills as shown in figure 2. ndc subject can state the problem in the form of an image correctly and accurately and provide information on the length, width, and height of the problem in the question. figure 2. answers to drawing the ndc subject based on the results of the interviews conducted, the ndc subject is able to meet the indicators of mathematical drawing communication skills and can smoothly explain problems into the form of images correctly and accurately and is able to smoothly explain the length, width, and height of the drawings he has made in his answer sheet. an excerpt from the interview with the ndc subject is presented as follows: researcher : what steps do you take? ndc : this is what is asked for the maximum volume, so the first thing to do is to draw a square first, there are 4 edges, so all of them are cut, so it turns out to be a picture that is 24-2a in length, 9-2a in width and a height. the ndc subject fulfills following the indicators of mathematical communication writing skills as shown in figure 3. ndc subjects can use mathematical language appropriately and correctly, and are able to explain ideas or situations from images that have been made previously in their own words in writing. the subject takes his own side in written form, the subject considers the side of the square which is cut off with the symbol "a", and also write an explanation in determining the interval "a"correctly. muhtarom, pratiwi, & murtianto, profile of prospective teachers' mathematical communication … 98 figure 3. answers to writing the ndc subject based on the results of the interviews conducted, the ndc subject is able to meet the indicators of writing mathematical communication skills and can explain fluently an idea or situation from a previously made image and can also explain the example of the square side used, and be able to state and explain how to determine the interval to meet the volume maximum sought. here are excerpts of interviews with the subject ndc: researcher : yes... then after that? ndc : so after that, suppose the square side is cut identically is “a”, then the length is 24-2a, the width is 9-2a and the height is “a”. researcher : then how to determine the maximum volume how? ndc : to determine the maximum volume with v''= 0 researcher : yes... continue? ndc : to determine the a interval it is 0 < a < 4.5 researcher : the reason? ndc : you see, so there is a value, sis, the height is a, then the “a” is less than 0. researcher : where did you determine the 4.5 from? ndc : that's from the width, the width is 9-2a = 0, we move the segment so 9/2 = a, so 4.5 = a. the ndc subject fulfills the following indicators of mathematical communication mathematical expression skills as shown in figure 4. ndc subjects can state mathematical solutions in writing clearly and precisely, are able to use mathematical symbols and perform calculations or get complete and correct solutions. the subject is able to determine the length of the shape she has previously made with the values 24 2a, and for the width 9 2a, and the height a. then the subject is able to write the volume formula used with v = p.l.t, the subject is also able to apply the first derived properties with v' = 0 and is able to determine the value "a" that meets the maximum volume sought, and performs calculations correctly both in calculating the initial volume, determine the equation v', find the value of a, and determine the maximum volume. volume 10, no 1, february 2021, pp. 93-108 99 figure 4. answers to mathematical expression the ndc subject based on the results of the interviews conducted, the ndc subject is able to meet the indicators of mathematical expression and can explain mathematical solutions clearly and precisely, and is able to explain mathematical calculations and correct answers. an excerpt from the interview with the ndc subject is presented as follows: researcher : what do you do after that? ndc : i determine the volume first, the volume formula is p.l.t, now enter the length is 24-2a, the width is 9-2a, the height is a, after that we operate the volume, the result is 4a3-66a2+216a. researcher : then what is the next step? ndc : so after that, determine the maximum volume with v'= 0, now determining v'= 0, we will derive it from the result of the volume which was 12a2132a+216=0, so continue to divide by 12, now the result is it is equal to 2 or a is equal to 9, now for a = 9 it does not meet. researcher : why not fulfill that for what reason? ndc : because the interval was less than 4.5. researcher : how do you continue to determine the maximum volume? ndc : now the maximum volume uses the formula, which is length times width times height, now we enter the one that is known to be 24-2a in length, 9-2a in width, the height is “a”. that's what v''= 0 has already been obtained which is equal to 2, continue to be added to the formula so the maximum volume is 200 cm3. 3.1.2. kal subject the kal subject fulfills the following indicators of mathematical communication drawing skills as shown in figure 5. kal subjects can state the problem in the form of an image correctly and precisely and are able to provide information on the length, width, and height of the problem in the question. muhtarom, pratiwi, & murtianto, profile of prospective teachers' mathematical communication … 100 figure 5. answers to drawing the kal subject based on the results of the interviews conducted, the subject of kal is able to meet the indicators of mathematical communication skills of drawing and can explain problems into the form of images correctly and accurately and is able to explain the length, width, and height of the drawings he has made. an excerpt from the interview with the ndc subject is presented as follows: researcher : explain the picture that you have made. kal : you draw it, the length is 24, now the width is 9, cut into a square, for example, the square is x, the right and left square is 2, so 24-2x is the length, now the width is the same, it makes 9-2x, keep making the height earlier was the x. it is clearly figure 6 shows that the results of the written work of the kal subject on the indicators of mathematical communication writing skills. kal subject can use mathematical language correctly, and is able to explain ideas or situations from images that have been previously made in their own words in written form but are still incomplete. the kal subject takes the cut side of the square with the symbol “x”. however, the kal subject did not specify the interval of “x”. figure 6. answers to writing the kal subject based on the results of the interviews conducted, the kal subject was able to meet the indicators of writing mathematical communication skills and was able to explain ideas or situations from images that had been previously made but were still incomplete, because the kal subject only explained for example the cut side of the square, namely x, but had not explained the interval from x itself. an excerpt from the interview with the ndc subject is presented as follows: volume 10, no 1, february 2021, pp. 93-108 101 researcher : explain the picture that you have made. kal : you draw it, the length is 24, now the width is 9, cut it into a square, let's say that a square is x. it is clearly figure 7 shows that the results of the written work of the kal subject on the indicators of mathematical communication expression skills. the subject of kal can clearly state mathematical solutions in writing, can use mathematical symbols, and perform calculations but is still incomplete. the subject is able to determine the length of the shape he made previously with the values 24 2x, and for the width 9–2x, and the height a. then the kal subject is able to write the volume formula used with v = p.l.t and its calculations, the subject is also able to apply the first derivative with v'= 0, but the kal subject cannot determine the maximum volume of the given problem. figure 7. answers to mathematical expression the kal subject based on the results of the interviews conducted, the kal subject is able to meet the indicators of mathematical expression communication skills and can explain the solution, but the kal subject cannot determine the maximum volume of the given problem, the subject has tried to calculate the maximum volume but the result is negative, this is because the subject did not previously specify the x interval. an excerpt from the interview with the ndc subject is presented as follows: researcher : after you draw, what steps do you take? kal : finding the volume. researcher : how? kal : use that formula, it means that the length times the width times the height, put in (24-2x) (9-2x) (x). now the result is 4x3-66x2+216x, now it's lowered. researcher : continue kal : the result means12x2-132x+216. researcher : then what is the next step? kal : that can be simplified, so it's x2-11x+18. researcher : continue muhtarom, pratiwi, & murtianto, profile of prospective teachers' mathematical communication … 102 kal : so, you get x = 2 or x = 9. researcher : then after that? kal : so, i just got there, sis. researcher : why is the deck just that way? kal : the problem was that i tried to enter it, but the results were both negative. researcher : that means what you are doing only up to here? kal : yes, miss. it means that the maximum volume has not been obtained. it hasn't reached the final result value. 3.1.3. mm subject the subject of mm did not fulfill the mathematical communication indicators of drawing in solving the problem. subject did not present the data or information from the question in the form of an image. mm subject could not write an explanation of the answer to the problem mathematically and did not use mathematical language or symbols appropriately and correctly. figure 8 showed that mm subject is less able to express mathematical solutions in writing, and perform calculations but is wrong, because the mm subject solves the problem not with the volume block formula but by using the rectangular formula and the determination of the length and width values is still wrong. figure 8. answers to mathematical expression the mm subject based on the results of the interviews conducted, the mm subject is not able to meet the indicators of mathematical communication skills in mathematical expression and the mm subject explains mathematical solutions according to the answer sheet but the answer is still wrong, the mm subject is also still hesitant in answering what shapes roughly correspond to the problem in question. an excerpt from the interview with the ndc subject is presented as follows: researcher : what is the next step after you know what was being asked? mm : i multiplied the length times the width. researcher : what do you think it is up to? mm : square researcher : square? square or shape? mm : square ... rectangle. researcher : then you count the volume of the rectangle how it is? mm : length by width. the maximum volume is 216 cm2. data were also collected through in-depth interviews with the subjects of climbers (ndc), campers (kal), and quitters (mm). written test results data were compared with interview data to obtain valid data. from the research results written tests and interviews conducted by climbers subjects met all indicators of mathematical communication skills used, campers subjects tended to be able to meet all indicators of mathematical volume 10, no 1, february 2021, pp. 93-108 103 communication skills used, while quitters subjects were unable to meet all indicators of mathematical communication skills used. 3.2. discussion from the results of the tests and interviews, the researcher observed that the data obtained was sufficient, so the written test and interview were not continued to the next stage. from the analysis of written tests and interviews of mathematical communication skills, the following results are obtained: 3.2.1. mathematics prospective teacher with aq climbers based on the results of the description and analysis of the written test results, the prospective teacher with the aq climbers category can meet all indicators of mathematical communication skills used by the researcher, including drawing, writing, and mathematical expression. prospective teacher with aq climbers are able to express and describe mathematical ideas in the form of pictures, aq climbers are able to provide answers using their own language or problems using writing and algebra, and are able to explain ideas or situations from an image or graph with own words in written form. prospective teacher with aq climbers is able to state a situation in the form of a mathematical model, and is able to perform mathematical calculations correctly. this is in line with nartani, hidayat, and sumiyati (2015) improving the communication skills of mathematics indicated by students are able to express ideas or ideas with mathematics verbally sentence, students are actively involved in discussions about math, students can formulate definitions and generalizations about the math, students can formulate a definition of mathematics by using its own words. mathematical communication skills are shown by students being able to express ideas or ideas with mathematical sentences verbally, students are actively involved in discussions about mathematics, students can formulate definitions and generalizations about mathematics, students can formulate mathematical definitions using their own words. this is also in line with ansari (2012) who states that drawing communication skills are reflecting real objects, drawings and diagrams into mathematical ideas, writing is stating and explaining a mathematical drawing or model into a mathematical idea form, mathematical expression is express a situation or mathematical idea into a symbol or mathematical model and solve it. it can be concluded that the prospective teacher aq climbers is able to meet all indicators of mathematical communication skills of drawing, writing, and mathematical expression. stoltz (2000) states that the subject of climbers is a group of people who always try to reach the peak of success, are ready to face any obstacles, and always raise themselves to success. this research is in line with the research of paramita (2017), kartika and yazidah (2019), and yuniarti (2015). in paramita's research (2017) which states that the climbers subject is able to meet all indicators of mathematical communication skills including the ability to state a situation in mathematical language, the ability to describe mathematical ideas visually, the ability to explain mathematical ideas in writing, and the ability to evaluate mathematical ideas in writing. in kartika and yazidah's research (2019), which states that climbers students are more able to compile direct evidence than quitters and campers students. in research yuniarti (2015) also states that the climber category is capable of almost all indicators of mathematical communication. muhtarom, pratiwi, & murtianto, profile of prospective teachers' mathematical communication … 104 3.2.2. mathematics prospective teacher with aq campers based on the results of descriptions and analysis of written test results, prospective teacher with the aq campers category tend to be able to meet all indicators of mathematical communication skills used by researchers, including drawing. writing, and mathematical expression. prospective teacher with aq campers are able to state, express and describe mathematical ideas in the form of images. aq campers tend to be able to provide answers in their own language or problems using writing and algebra, and are able to explain ideas or situations from an image or graphic in their own words in written form. prospective teacher with aq campers tend to be able to state a situation in the form of a mathematical model, but have not been able to complete it completely in finding the maximum volume value requested in the problem. this is in line with nartani, hidayat, and sumiyati (2015) improving the communication skills of mathematics indicated by students are able to express ideas or ideas with mathematics verbally sentence, students are actively involved in discussions about math, students can formulate definitions and generalizations about the math, students can formulate a definition of mathematics by using its own words. this is also in line with ansari (2012) who states that drawing communication skills are reflecting real objects, drawings and diagrams into mathematical ideas, writing is stating and explaining a mathematical drawing or model into a mathematical idea form, mathematical expression is express a situation or mathematical idea into a symbol or mathematical model and solve it. it can be concluded that the aq campers tends to be able to meet all indicators of mathematical communication skills of drawing, writing, and mathematical expression. stoltz (2000) stated that campers are a group of people who still have the desire to respond to existing challenges, but do not reach the peak of success and easily give up on what has been achieved. stoltz (2000) also adds that campers do not fully exploit their potential, campers have a limited ability to change, especially major changes, campers live with the belief that after several years or after making a number of efforts, life should be relatively free of difficulties. in this study, new things were found because the subject of aq campers tended to meet all indicators of mathematical communication skills of drawing, writing, and mathematical expression. this is not in line with previous research conducted by paramita (2017) and yuniati (2015). in paramita's (2017) research which states that campers tend to be able to fulfill two indicators, namely the ability to express a situation in mathematical language and the ability to visualize mathematical ideas only. yuniarti's (2015) study which states that the camper category is quite capable in several communication indicators. mathematically and the category of campers make process errors and conclusion errors. 3.2.3. mathematics prospective teacher with aq quitters based on the results of descriptions and analysis of written test results, the prospective teacher with the aq quitters category cannot meet all indicators of mathematical communication skills used by researchers, including drawing. writing, and mathematical expression. aq quitters is not able to meet all indicators of mathematical communication skills of drawing, writing, and mathematical expression. stoltz (2000) states that quitters are a group of people who prefer to avoid and reject opportunities, easily give up, give up easily, tend to be passive, and are not enthusiastic about reaching the peak of success. stoltz (2000) also adds that quitters have limited abilities in facing adversity, quitters tend to resist change and claim its every success, or to avoid it and actively walk away from it. the subject of quitters tends to think that the difficulties that arise will continue to occur, so that they are volume 10, no 1, february 2021, pp. 93-108 105 constantly overshadowed by obstacles that often arise, every difficulty, the cause is also considered something that will continue to appear again in the future (hidayat & husnussalam, 2019; hidayat, noto, & sariningsih, 2019; hidayat, wahyudin, & prabawanto, 2018). it is proven in this study that the quitters subject is not able to meet all the indicators requested by the researcher. this study is in line with the research of paramita (2017), and yuniarti (2015). in paramita's research (2017) which states that quitters are not able to fulfill all indicators of mathematical communication skills, including the ability to express a situation in mathematical language, the ability to visualize mathematical ideas, the ability to explain mathematical ideas in writing, and the ability to evaluate mathematical ideas in writing. yuniarti's research (2015) also states that the quitter category has not been able to meet almost every mathematical communication indicator and almost all types of errors occur in the quitters category. this is consistent with the results of this study where the quitters subject is not able to meet all indicators of mathematical communication skills including drawing, writing, and mathematical expression. the results of this study finally produce a summary of the understanding of mathematical communication skills of prospective mathematics teachers in terms of aq, as shown in the following table 1. table 1. summary of mathematical communication skills no aspect indicator category aq climbers aq campers aq quitters 1. drawing the ability to express, express and describe mathematical ideas in the form of pictures, graphs or visual mathematical models. fulfilled fulfilled not fulfilled 2. writing the ability to provide answers using your own language or problems using writing and algebra, and to explain an idea or situation from a picture or graphic in your own words in written form. fulfilled fulfilled not fulfilled 3. mathematical expression the ability to express mathematical concepts by expressing everyday events in mathematical language or symbols, and expressing a situation in the form of a mathematical model fulfilled almost fulfilled not fulfilled table 1 shows that the results of the study show that the subjects of prospective mathematics teachers who have aq climbers and aq campers are able to meet all indicators of mathematical communication skills, indicators of mathematical communication skills used include drawing, writing, and mathematical expression, while the subject of mathematics prospective teacher. those who have aq quitters are not able to meet all indicators of mathematical communication ability. the indicators of mathematical muhtarom, pratiwi, & murtianto, profile of prospective teachers' mathematical communication … 106 communication abilities used include drawing, writing, and mathematical expression. the results of each individual in communicating the problems obtained are in accordance with their aq. this is in line with syarifah, sujatmiko, and setiawan (2017), mathematical communication is the process of expressing mathematical ideas and understanding verbally, visually, and in writing, using numbers, symbols, pictures, graphs, diagrams, and words. someone. the results of this study are also in line with nopiyani, turmudi, and prabawanto (2016), mathematical communication is the ability to express mathematical ideas or ideas either in writing or in pictures. this is also in line with murtafiah (2016) that mathematical communication is the ability to express mathematical ideas through speech, writing, demonstrations, and visually depicting them in different types for each person. 4. conclusion based on the results of research and discussion that has been done with the subject of climbers, the conclusion is that students are able to solve problems using mathematical communication properly and correctly. the three indicators of communication the subject is able to meet all the indicators of mathematical communication used. the subject of campers is quite capable of solving mathematical communication problems properly and correctly, but there are calculations in resolving incomplete problems. the three indicators of communication the subject tends to be able to meet all the indicators of mathematical communication used. the subject of quitters has not been able to solve problems using mathematical communication properly. the three stages of communication, the subject tends not to be able to meet all the indicators of mathematical communication used. based on the results and conclusions of this study, the following 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(2015). analisis hasil penilaian diagnostik kemampuan komunikasi matematis dalam pembelajaran osborn berdasarkan adversity quotient (tesis). semarang: universitas negeri semarang. https://doi.org/10.30651/must.v2i2.888 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 9, no. 1, february 2020 e–issn 2460-9285 https://doi.org/10.22460/infinity.v9i1.p15-30 15 ontological misconception in mathematics teaching in elementary schools imam kusmaryono* 1 , mochamad abdul basir 2 , bagus ardi saputro 3 1,2 universitas islam sultan agung 3 universitas pgri semarang article info abstract article history: received oct 28, 2019 revised jan 29, 2020 accepted jan 30, 2020 elementary school teachers in indonesia are required to master many subjects to be taught to their students. it is undeniable that the teachers’ mastery of knowledge (material) in some subjects inadequate. therefore, it is worth to argue that there was a misconception in mathematics teaching in elementary schools. this research was designed using a qualitative approach. the participants of this study were 30 elementary school teachers in semarang city area, central java province, indonesia. the research data were obtained through questionnaires, and interviews. the purpose of the study was to discuss the types and causes of the misconception of mathematics teaching in elementary schools. alternative solutions were also presented to problem-solving so that misconceptions do not occur anymore in mathematics teaching. the findings show that, teachers evenly experience types of misconceptions: (1) pre-conception, (2) under-generalization, (3) over-generalization, (4) modelling error, (5) prototyping error; and (6) process-object error in teaching mathematics in elementary schools. some misconceptions have taken root and are difficult to remove, called "ontological misconceptions" because of teachers' years of belief that the knowledge they received was true when in fact it was not quite right. keywords: elementary schools, misconception, ontology, teaching mathematics copyright © 2020 ikip siliwangi. all rights reserved. corresponding author: imam kusmaryono, department of mathematics education, universitas islam sultan agung jl. kaligawe raya no.km. 4, terboyo kulon, semarang, central java 50112, indonesia email: kusmaryono@unissula.ac.id how to cite: kusmaryono, i., basir, m. a., & saputro, b. a. (2020). ontological misconception in mathematics teaching in elementary schools. infinity, 9(1), 15-30. 1. introduction teaching math is a difficult task under any circumstances. this is because of the complexity, characteristics and nature of mathematics itself. when beginning to study mathematics, students learn it themselves and or learn from others, especially with their teachers (skott, 2019). often, in mathematics learning misconceptions occur that hinder students' cognitive development. therefore the teacher must provide a careful explanation followed by opportunities that create opportunities for students to understand and absorb ideas that are presented clearly, so students become proficient in mathematics (sullivan, clarke, clarke, farrell, & gerrard, 2013). mailto:kusmaryono@unissula.ac.id kusmaryono, basir, & saputro, ontological misconception in mathematics teaching … 16 the results of the survey in the last ten years conducted by the program for international student assessment (pisa) and the survey by trends in the international mathematics and science study (timss) stated that student achievement in learning mathematics in indonesia is still at a lower level compared to several countries surveyed in the world (oecd, 2019). talking about the low performance of indonesian students in the field of mathematics, can not be separated from the existence of misconceptions in teaching. many research have focused on analyzing students' misconceptions in learning mathematics (aliustaoğlu, tuna, & biber, 2018; gooding & metz, 2011; mohyuddin & khalil, 2016; sarwadi & shahrill, 2014). however, the authors have not discussed yet about teacher mistakes in mathematics learning in school. then a questionarised: did the teacher involve as a causal factor of misconception in mathematics learning? findings in this research are very important to analyze the misconception in mathematics teaching by teachers in elementary schools in indonesia and analytical alternatives for problem solving to get rid of misconception a teacher has a key role and position in the entire education process. the teacher is the main factor of students' learning success. moreover, in elementary schools, teachers are required to master teaching materials and to develop teaching methods in accordance with the subjects taught (anwar, 2012). elementary school teachers have the most heavy responsibilities in their professional duties compared to grade teachers middle school and high school level. an elementary school teacher in indonesia is required to master many subjects, including language, mathematics, geography, history, cultural arts and skills. therefore, it is undeniable that their mastery of knowledge (material) in some subjects is not edequate. on one hand, teachers master subjects and are proficient in the field of language learning, but on the other hand, mastery of the material by the teacher is inadequate and are not proficient in mathematics learning. if the teachers do not have mathematical skills in teaching, it will hinder the achievement of learning goals, and affect students' positive dispositions towards mathematics learning (kusmaryono, suyitno, dwijanto, & dwidayati, 2019). the results of observations of mathematics learning of elementary school teachers in the central semarang area, there are still many learning misconceptions. they lack mastery and are not proficient in mathematics. therefore this research is very important to do, considering elementary school teachers are the first people to instill knowledge of mathematical concepts in formal education. mathematical proficiency is a skillfull quality that shows skills, competencies, knowledge, beliefs, and fluency in working on and teaching mathematics and being problem solvers who are proficient with high productive dispositions (groves, 2012; kilpatrick, swafford, & findell, 2001). it is important for teachers to understand, that mathematical proficiency in teaching will have implications in learning that misconceptions will not occur, so that the teacher can become a facilitator who encourages students to become constructors of "constructive knowledge" for themselves students (kistner, rakoczy, otto, & klieme, 2015). the misconception of mathematics by teachers in a teaching process in elementary schools can result in misconceptions or misunderstanding of a sustainable basis which lead to higher education level. this is because the characteristics of mathematics learning materials are interrelated and continuous with other materials. to learn one of the mathematics topics at the advanced level must be based on reasoning from basic knowledge or prior prerequisite knowledge. if someone experiences a conceptual error (misconception) of mathematics in lower classes learning and is not immediately volume 9, no 1, february 2020, pp. 15-30 17 addressed, it will have an impact on the learning of mathematics in high classes (flevares & schiff, 2014). misconceptions include understanding or thinking which is not based on true information. misconceptions occur because of errors in transferring concepts from information obtained into a framework. so, the concept understood may not be in accordance with the actual concept. teacher naturally forms ideas from everyday experience, but not all ideas developed are true in connection with evidence in a given discipline. in addition, some mathematical concepts in different content areas are very difficult to understand. even teachers sometimes can have misconceptions about materials (burgoon, heddle, & duran, 2017). for them, it may be a very abstract concept, counter intuitive or quite complex. therefore, changing a teacher's framework is the key to improving mathematics teaching for the better (skott, 2019). this paper outlines some of the misconceptions of teaching mathematics in elementary schools. in addition, it also provides alternative solutions to the problem, so that conceptual errors (misconceptions) do not occur anymore in mathematics teaching. basically, every teacher has the potential to successfully carry out his/her duties as a reliable learning agent. teacher’s success can be clearly seen from the teaching skills and students’ success in following the process and achieving learning goals (oecd, 2019). 2. method 2.1 research design this research used a qualitative approach. in this research, the hypothesis was not determined to be tested because the researcher wanted to get research findings that flowed and described the results of systematic observations (creswell, 2014; mcmillan & schumacher, 2014). this research was conducted during the active period of learning activities in elementary schools, precisely in january february 2019. 2.2 participants the participants of this research were 30 elementary school teachers of first to sixth grades, representing 10 elementary schools in central semarang sub-district, semarang city, central java province, indonesia. the teachers have had teaching experiences in primary schools for 4 to 20 years. 2.3 procedure at the beginning of the research, observations of the mathematics teaching process were conducted in several elementary schools. then, teachers completed questionnaires in the form of mathematical questions with answers written in the questionnaires. responses of answers from questionnaires were identified and analyzed in terms of types of errors, then grouped into types of misconceptions: (1) pre-conception, (2) under-generalization, (3) over-generalization, (4) modelling error, (5) prototyping error; or (6) error processes (ben-hur, 2006; diyanahesa, kusairi, & latifah, 2017; saputri & widyaningrum, 2016). based on the misconception data, teacher representatives were then selected through a purposive snowball technique to get the subjects interviewed (naderifar, goli, & ghaljaie, 2017). the following is the flow of research implementation in figure 1. kusmaryono, basir, & saputro, ontological misconception in mathematics teaching … 18 figure 1. research flowcart 2.4 instruments instruments for retrieving research data include questionnaires and a list of interview questions. the following is the flow of research implementation in figure 1. the instrument was validated by experts in the field of mathematics learning, namely dyana wijayanti, ph.d.the questionnaires contained six questions related to mathematics teaching materials and the teachers’ perspectives on mathematics teaching. the questionnaire instruments in the form of questions were designed to explore responses of teachers’ answers, types of errors and misconceptions in mathematics teaching in elementary schools. the list of interview questions was to reveal the causes of errors and misconceptions in mathematics teaching. the topics of mathematics teaching becoming the focus of this study were integers, flat geometry, rational numbers, and algebraic equations. following are some examples of questionnaires used in this research instrument (table 1). table 1. example of research questionnaire no. question capable not capable give answers and reasons 1 are you able to read the mathematical statement below? (a) 7 + (4) = 3 (b) -10 – (-6) = -4 2 are you able to prove that 1.252525 ... is a rational number? 3 are you able to solve problems ... 3 1 : 9 4  with procedures that you know about? 2.5 data collection, analysis, and triangulation the research data were collected through questionnaires and interviews. subject as informants were the first to sixth-grade teachers teaching mathematics in elementary schools. this qualitative research data analysis was described as an interactively connected cycle through the stages of data collection, data reduction, data presentation, and conclusion (miles & huberman, 2012; moleong, 2007). to ensure the validity of the data, the researcher used the triangulation theory and source triangulation (moleong, 2007). learning observation formulate the problem instrument preparation and validation questionnaire distribution data analysis and triangulation identification of misconceptions conclusion interview volume 9, no 1, february 2020, pp. 15-30 19 3. results and discussion 3.1. results in the early stage of the study, observations of mathematics teaching processes were carried out in several elementary schools. the observations were conducted when teachers gave explanations of how to overcome problems experienced by students. the results of the observations showed that the teacher's explanation was more on conceptual or procedural categories and/or both. successfully noted that the explanation from the teacher was sometimes illogical and not in accordance with the rules or mathematical principles. whereas, based on the results of the responses to the questionnaire responses, several misconceptions related to mathematics teaching in elementary schools were found. the following are the misconception of mathematics teaching found (table 2). table 2. types of misconceptions in mathematics teaching topic misconceptions types type 1 type 2 type 3 type 4 type 5 type 6 integers  ----- rational number -    - linear equation ---- - geometry field  ---- note: type 1=pre-conception type 2=under-generalization type 3=over-generalization type 4= modelling error type 5= process-object error type 6=prototyping error answer to problem 1 problem 1 is the problem related to the teachers’ understanding of symbol (+) and (-) as a sign of a count operation or integer name. most respondents (teachers) had the same answers when it came to reading math sentences. pay attention to the duplication of the respondents’ answers in figure 2a. misconceptions the alternative solution (a) 7 + (4) = 3 read: seven plus minus four equals to three (b) -10 (-6) = -4 read: minus ten substracted by minus six equals to minus four (a) 7 + (4) = 3 read: seven plus negative four equals to three (b) -10 – (-6) = -4 read: negative ten minus negative six equals to negative four figure 2a. respondent's answer (r.02) figure 2b. alternative solution to clarify the information from the respondent (r.02), let us consider the following excerpt from the interview. kusmaryono, basir, & saputro, ontological misconception in mathematics teaching … 20 researcher : do you understand the difference between of symbol (-) as a sign of a count operation and (-) as an integer name? respondent (r.02) : symbol (-) is read minus. so symbol (-) can be a count operation or number name. researcher : in an integer system, there is a positive number (4) and a negative number (-4), but there is no minus number. respondent (r.02) : oh yeah, it's different. now i understand symbol (-) as a sign of a count operation and (-) as a negative integer name answer to problem 2 the problem to prove that 1.252525 ... is a rational number is a very important thing to explain thoroughly. pay attention to the answer of the respondent in figure 3a. misconceptions the alternative solution answer: numbers 1.252525… . = 100 125 rational numbers so, 1.252525 ... = 100 125 it will be proven that 1.252525 ... is a rational number. for example: y = 1.252525 ... and 100y = 125.252525 ... then 100y = 125.252525… . y = 1.252525… . _ 99y = 124 y = 99 124 so 1.252525… . = 99 124 a rational number. figure 3a. respondent's answer (r.27) figure 3b. alternative solution the findings of the questionnaire analysis showed that the answers from the respondent were false. the following is an excerpt from the interview with one of the respondents (r.27). researcher : do you understand this number 1.252525 ... ? respondent (r.27) : number 1.252525 ... is an infinite number of repeated decimal places researcher : is the number 1.25 = 1.252525 ... ? respondent (r.27) : yes, 1.25  1.252525 … ... but this is difficult to prove in rational numbers. researcher : pay attention, please, to the solution presented in figure 3b. now, do you understand? respondent (r.27) : yes, i do. thanks for the explanation. volume 9, no 1, february 2020, pp. 15-30 21 answer to problem 3 the teaching of rational number division operations is always a serious concern in the procedural context. there are irregularities in the problem-solving process of all of the respondents' answers for solving this problem were correct and no need to question. but the problem was the respondent could not explain why the fraction division operation was changed to a multiplication operation and the divider is reversed (figure 4a). misconception the alternative solution 3 1 1 9 3 1 9 12 19 34 1 3 9 4 3 1 : 9 4  x x x there is a change in the distribution operation mark into a multiplication operation (a) 3 1 1 3 4 3:9 1:4 3 1 : 9 4  (b) 3 1 1 3 4 1 3:4 9:9 3:4 9 3 : 9 4 3 1 : 9 4  consistent and no changes in the operation marks figure 4a. respondent's answer figure 4b. alternative solution based on the finding of the questionnaires, it was found that the teacher’s answer to the problem was correct (figure 4a). however, the mathematical modelling presented as the solution to the problem could not precisely be explained with reasons given. the following interview excerpt is to strengthen this statement. re researcher : why 3 2 : 9 4 when you completed the division operation, did it turn into a multiplication operation and the dividing number becomes like this 2 3 9 4 x ? respondent (r.02) : i can't describe it correctly. i did a problem solving, as i understood. researcher : are you sure there is no other way to solve this problem? respondent (r.02) : i pretty am, there is no other way. all teachers solve this problem as i did. researcher : since when did you understand how to solve this? respondent (r.02) : since i studied in elementary school 25 years ago. i followed the teacher's instructions and i have been doing it until now. answer to problem 4 figure 5a is an example of an erroneous understanding of teaching turning ordinary fractions into decimal fractions. paying attention to the respondent's answer (r.11) that the decimal form of ¼ is 0.25 is correct (figure 5a). it was identified that the teaching process to get a 0.25 result kusmaryono, basir, & saputro, ontological misconception in mathematics teaching … 22 was deemed inappropriate. then the respondent confirmed (r.11) through the following interview. researcher : why do you always add zero (0) number to each number which is not divisible by four? respondent (r.11) : number 1, if added to zero (0) will be ten so that 10 can be divided by 4 researcher : supposedly, 1 + 0 = 1, it is not correct if 1 + 0 = 10? how do you explain this to students? respondent (r.11) : i learned from mathematics teaching at previous schools. if a number cannot be divided, then borrow zero (0) and the result of the division is zero points (decimal). researcher : are you not aware, that there has been a conceptual error in this learning? respondent (r.11) sorry, i can't explain correctly. i realized that there has been a teaching error, because all this time, i have only followed the books and habits applied and carried out by all the teachers at schools. below is shown the results of the subject's work in solving problem number 4. misconception the alternative solution change ordinary fractions 4 1 change ordinary fractions. the solution is by stacking as follows: 0.25 4 10 8 _ 20 20 _ 0 so, the decimal fraction of 4 1 is 0.25 the solution should be as follows: 4 1 = 100 100 4 1 x 4 1 = 4 100 x 100 1 4 1 = 25 x 100 1 4 1 = 100 25 4 1 = 0.25 so, the decimal fraction of 4 1 is 0.25 figure 5a. respondent's answer (r.11) figure 5b. alternative solution answer to problem 5 a process-object error was identified in the case (problem 5) of this study, namely the occurrence of an error in the completion process of a single variable linear equation (figure 6a). 1). borrow zero number 3). borrow zero number 2). written zero point volume 9, no 1, february 2020, pp. 15-30 23 misconception the alternative solution determine the value of x, so that 2x + 5 = 17 is correct 2x + 5 = 17 2x = 17 – 5 ??? 2x = 12 x = 2 12 x = 6 so, the solution 2x + 5 = 17 is x = 6 determine the value of x, so that 2x + 5 = 17 is correct 2x + 5 = 17 2x + 5 + (-5) = 17 + (-5) step 1 2x = 12 2x . 2 1 = 12 . 2 1  step 2 x = 2 12 x = 6 so, the solution 2x + 5 = 17 is x = 6 figure 6a. respondent's answer (r.08) figure 6b. alternative solution if we look at figure 6a, the result of the response answer is correct. however, the completion process in the second step on the right side displays a reduction operation with number 5. then the answer is confirmed through the interview below. researcher : is the completion process that you did right? respondent (r.08) : i'm sure, it is. value of x = 6 researcher : why is that in the second step 2x = 17 5, like this? respondent (r.08) : number positive 5 on the left segment is moved to the right segment to be negative (-5). answer to problem 6 the misconception problem arises when the teacher was confronted with a flat square image. the teacher was asked to show the name of the parallelogram. question: which form of a quadrilateral is the parallelogram? a b c d respondent's answer: model b is a parallelogram. model a, c, and d are not. figure 7. quadrilateral models the result of the respondent's answer stated that only one of the four images available was figure b (figure 7) considered a parallelogram. then the respondent confirmed (r.02) through the following interview. kusmaryono, basir, & saputro, ontological misconception in mathematics teaching … 24 researcher : why did you choose image b as a parallelogram? respondent (r.02) : because image b has a parallel hypotenuse researcher : why are image a, c or d not? respondent (r.02) : a is a rectangle, c is a square, and d is a cube. researcher : would you explain the definition of the parallelogram? respondent (r.02) : the parallelogram is a quadrilateral that has two pairs of sides facing the same length, there is an inclined side, and with equal angles. 3.2. discussion problem 1: pre-conception it was identified that respondents experienced pre-conception, namely problems in reading integer symbols. they were not able to distinguish between symbol (+) or (-) as a count operation or integer name. pre-conception is an initial mistake before someone understands the concept correctly (diyanahesa et al., 2017). based on the interview excerpts with the respondent (r.02), it can be said that the teacher failed to give an interpretation and interpreted the minus sign (-) as an operation to calculate the subtraction and negative in (-4) as the name of the number four negative. according to cockburn and littler's findings, integer material is one of the topics that is difficult to teach in embedding integer concepts (cockburn & littler, 2008). problem 2: under-generalization under-generalization is a more specific part of pre-conception. undergeneralization is expressed as a limited understanding and ability to apply the concepts (saputri & widyaningrum, 2016). this limited understanding explains various circumstances regarding teacher’s knowledge during all mathematical ideas develop. cases in rational and irrational numbers may be one of the most problematic in mathematics teaching in elementary school. many teachers only understand rational numbers as ordinary fractions, decimal fractions, and percent. in fact, fraction interpretation as a part-whole relationship is only a sub concept or one way of understanding rational numbers. the following under-generalization is identified from the response of the teacher's answer. teacher's mastery of the concept of rational numbers has not developed perfectly, the teacher only understands in a limited way. the alternative solution shown in figure 2b is the right step as a problem-solving instruction. then the instructions on the number system must be able to answer the problem of under-generalization because there is an assumption that certain characteristics in the number system inhibit general understanding (ben-hur, 2006). problem 3: over-generalization over-generalization is a case of misconception, where the application of concepts is not understood and the rules applied are considered irrelevant. figure 3a is an example of an erroneous understanding of teaching in turning ordinary fractions into decimal fractions. based on the interview excerpt, it was indicated that the respondent (r.11) had misrepresented an illogical interpretation which caused a false understanding. techniques for solving a mathematical problem can vary in ways, but the interpretation must generally volume 9, no 1, february 2020, pp. 15-30 25 be explained or understood by students (others). the solution in figure 3b shows that the strategy was chosen because equals to 1. in accordance with the algebraic law that all numbers, if multiplied by 1 are fixed, so that they are obtained . through interviews with respondents (r.11), information was obtained that there had been an error (misconception) on mathematics teaching. during this time, the teaching of mathematics conducted by teachers only following books and habits that had been valid for many years. so it can be interpreted that there has been a rooted misconception that the concept of teaching believed to be true turns out that the concept of teaching is false (ontological misconception) (ben-hur, 2006). ontological misconceptions in teaching mathematics occur because of the lack of mathematical knowledge from elementary school teachers. problem 4: modelling error modelling errors were identified when students (teachers) only imitated examples of wrong work from representations of rational number counting operations. in teaching rational number division operations, the teacher failed to give reasons through mathematical modelling displayed. an example of problems . mathematical modelling presented as a solution to the problem could not be explained precisely with given reasons. apparently, the way of the respondent’s (r.02) completion was obtained from their teacher while studying at the elementary level. they answered that the work process was obtained because of the teacher’s beliefs and doctrines that had to be followed. a doctrine that they had just to accept without reasons because they assumed that mathematics is an exact science and the teacher never went wrong. the method of completion was replicated by students without knowing the reasons for the steps (figure 4a). such misconceptions are grouped as modelling errors. compare it to the alternative solution in figure 4b, it appears that the proposed alternative solution is very logical and consistent in accordance with mathematical principles. some teachers’ answers in the questionnaire illustrate how limited understanding undermines the conception of key mathematical ideas. there is an opinion stating that maybe when the teachers experience a modelling error, the teachers have their own version of the model in the situation (blazar & kraft, 2017). so, it can be interpreted that in this case, there is also a deep-rooted misconception, that is, the teaching concept which was believed to be true turns out that the teaching concept is false (ontological misconception) (ben-hur, 2006). problem 5: process-object error process-object errors are identified in the case (problem 5), namely the occurrence of a process error completion from a single variable linear equation. if we look at figure 5a, the final result of the respondent's answer was correct. however, the completion process in the second step on the right side appeared a reduction operation with number 5. confirmation was carried out through interviews, some teachers were very confident and believed that the process of solving a single variable linear equation was completed as in figure 5a. they believed that the positive number on the left side, if moved to the right side, would change to a negative number. so it can be concluded that they do not understand the laws of algebra. the alternative solution in figure 5b is the best process for solving a single variable linear equation. the first step, the two segments get the same kusmaryono, basir, & saputro, ontological misconception in mathematics teaching … 26 treatment, which is added to the same number (-5), so that it still has the same value. the second step, multiplying the two segments with the same number (½). problem 6: prototyping error in the case (problem 6), the respondents refused to recognize that rectangles, squares, and rhombus are parallelograms. they did not understand the definition of parallelograms so it can be classified in the type of pre-conception. there were few respondents who could explain the definition of a parallelogram, that parallelogram is a quadrilateral which has two pairs of parallel equal sides and the opposite angles are equal. but in their minds, they still considered that image a, c, and d were not parallelograms. this misconception is classified in prototyping error. the teachers only understood the eternity of forms through a standard example of a parallelogram. the teacher considered the standard example of a concept to be the only type of example. the teacher did not understand the definition of a parallelogram, but only did representation through standard visual images. based on the explanation of the research findings discussed, it can be said that the things we have learned are sometimes not helpful in learning new concepts or theories. this happens when a new concept or theory is inconsistent with the material previously studied. thus, it is very common for students, teachers, and adults to have misconceptions in different domains (content knowledge fields). teachers evenly experience types of misconceptions: (1) pre-conception, (2) under-generalization, (3) over-generalization, (4) modelling error, (5) prototyping error; and (6) process-object error in teaching mathematics in elementary schools (ben-hur, 2006; ryan & williams, 2007). misconceptions in teaching mathematics in elementary schools occur for several reasons. teachers generally do not realize that the knowledge they have is incorrect. the teachers interpret new experiences through this erroneous understanding, thus disrupting the ability to understand new information correctly. understanding incorrect mathematical concepts for years has been stable, permanent and rooted (desstya, prasetyo, susila, suyanta, & irwanto, 2019; hughes, lyddy, & lambe, 2013). the stable, permanent and rooted misconceptions are called "ontological misconceptions," in teachers’ thinking. the ontological misconceptions relate to ontological beliefs, that is, beliefs about the category and nature of the world (burgoon et al., 2011). citing the opinion of harisman et al that teaching experience (duration of teaching) is not a determinant of teacher professionalism, but the level of education and experience attending training is a factor that influences teacher proficiency in problem solving (o'leary, fitzpatrick, & hallett, 2017). so, it should be argued that the misconceptions that students have actually originated from their teacher "ontological misconception" in mathematics teaching in elementary schools. based on the research findings, to eliminate errors and misconceptions in mathematics teaching in elementary schools, it is recommended: (1) teachers always improve mathematical skills in terms of understanding learning theory, and mastering the core material of each subject of mathematics; (2) the mathematics ability to change the framework in mathematics teaching can be improved through workshops, seminars, discussions with mathematical experts and teacher working groups; (3) applying mathematical concepts in daily life, especially the use of reasons and thought to solve life problems in society so as to support changes in logical and critical thinking. volume 9, no 1, february 2020, pp. 15-30 27 4. conclusion the findings show that, teachers evenly experience types of misconceptions: (1) pre-conception, (2) under-generalization, (3) over-generalization, (4) modelling error, (5) prototyping error; and (6) process-object error in teaching mathematics in elementary schools. the findings of this research reveal that the math skills of elementary school teachers need to be improved. various errors and misconceptions are oriented to conceptual and procedural errors in mathematics teaching. the misconceptions have been stable, permanent and rooted in "ontological misconception," in teacher thinking. the causes of misconceptions are (1) the teachers do not realize that the mathematical knowledge they have got because of teachers' years of belief that the knowledge they received was true when in fact it was not quite right.; (2) the mathematical knowledge possessed by the teachers have been accepted as rigid doctrines without any reasons to deny it for years. (3) the teachers’ confidence in the knowledge they receive, is stable, permanent and rooted in "ontological misconception," in the teacher's thinking. (4) the teachers interpret new experiences through incorrect understanding, thus inhibiting the entry of new information correctly. misconceptions tend to be very resistant to teaching and difficult to improve. therefore, learning requires replacing or reorganizing the teacher’s knowledge radically. through math skills training, misconceptions can be replaced or eliminated by changing the framework of teaching mathematics. acknowledgements the authors would like to thank for the support to elementary school teachers in semarang tengah sub-district and lppm universitas islam sultan agung who have helped smooth the research and funding assistance. references aliustaoğlu, f., tuna, a., & biber, a. ç. 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(2019). incomprehension of the indonesian elementary school students on fraction division problem. infinity, 8(1), 57-74. 1. introduction fractions are one of the topics studied in elementary mathematics which serves as a cornerstone for comprehending further mathematics topics such as arithmetics, algebra, probability, data analysis, geometry, and measurements. they are also capitalized on for communicating and solving daily life problems. nevertheless, fractions and the operation are the most challenging elementary mathematics topics as they are difficult to understand. in addition, most elementary school students are presented with meaningless instruction mailto:yoppy.w.purnomo@uhamka.ac.id purnomo, widowati, & ulfah, incomprehension of the indonesian elementary school … 58 (geller, son, & stigler, 2017; lin, becker, ko, & byun, 2013; wang, chen, & lin, 2014), especially in fractions division (kribs-zaleta, 2006; sidney, hattikudur, & alibali, 2015; tirosh, 2000). fractions division learning emphasizing heavily on algorithms acquisition inevitably tends to be accepted and dominated teaching and learning process. the most common procedures used in coming to grips with fractions division problems are the invert and multiply (or keep-flip-change) strategies. these procedures are perceived as the most mysterious rules in elementary mathematics topics (van de walle, karp, & bay-william, 2010) as they are not frequently understood by the teachers and the students. skemp (1987) name these procedures as rules without reason. the ability to manipulate symbols and implement rules without understanding may create trouble in making sense and students may make mistakes when encountering problems which have to be solved using unfamiliar procedures (purnomo, kowiyah, alyani, & assiti, 2014). 1.1. procedural and conceptual knowledge of fraction procedural knowledge has been described as knowledge about how to do something (hallett, nunes, & bryant, 2010). it refers to students’ ability to implement, calculate, and execute symbols representation system and algorithms to solve problem accurately, efficiently, and appropriately (lauritzen, 2012; rittle-johnson, siegler, & alibali, 2001). skemp has identified this knowledge as an instrumental understanding which is described as rules without reason. procedural knowledge deals with symbols, rules, formulas, and algorithms in a discrete manner while conceptual knowledge refers to a knowledge that is rich in connections (rittle-johnson et al., 2001). skemp (1976) label it as a relational understanding. connection or relation between mathematical concepts and integration to a contextual situation is the heart of conceptual knowledge. it is able to assist students in making sense of the fraction concept. conceptual knowledge and procedural knowledge may support each other. concept-first and procedures-first were acknowledged by kinds of literature (rittlejohnson et al., 2001). development of students’ conceptual knowledge at the outset of a lesson may contribute to the ability to address varieties of mathematical tasks successfully. moreover, students are able to build conceptual knowledge by establishing various types of algorithm initially. focusing heavily on procedures in fraction learning may impede students to engage with the real-world context used as a bridge for developing conceptual knowledge. without context, students may encounter puzzlement in coming to grips with the concept of fraction and its application in various situations (sharp & adams, 2002; yim, 2010). traditionally, in the case of fraction division, students mostly are presented by procedure-oriented, memory-based, and meaningless instructional approaches. the common algorithm used for fraction division is by multiplying the dividend by the reciprocal of the divisor. this algorithm is straightforward. hence, students are able to use it easily in dealing with routine problems that have been exemplified by their teachers. however, they get trouble in an attempt to solve unfamiliar problems such as word problems and non-routine problems. the difficulties can be caused by students’ lack to understand the concept of fractions. therefore, procedural knowledge and conceptual knowledge should be interwoven and integrated with each other (kilpatrick, swafford, & findell, 2001). volume 8, no 1, february 2019, pp. 57-74 59 1.2. interpretation of fraction division traditionally, fraction division is able to be explained by the extension of the division interpretation of whole numbers, namely, partitive and measurement concepts (alenazi, 2016; purnomo, 2015a). furthermore, recent studies have discussed others interpretation of fraction division, namely, the determination of a unit rate, the inverse of multiplication, and the inverse of a cartesian product (alenazi, 2016; sinicrope, mick, & kolb, 2002). in our study, we focus on the traditional concepts of fraction division that are partitive and measurement concepts because these concepts are typically introduced to learn the fraction division in first because of related concept whole number division. in addition, these concepts are considered to be relevant and appropriate for developing the understanding of elementary school students on fraction division problem. 1.2.1. fractions division as measurement (repeated subtraction) this model explains fraction as the number of times we can subtract the denominator from the numerator before we attain 0 (zero). this meaningful interpretation can be applied in case of fraction division. for instance, in the case of division of 1/2 by 1/4, students may reason it as a quarter goes into 1/2 two times. it can be interpreted contextually, for instance, if someone has half of a cake and she/he wants to divide it into quarters, then you have two pieces of 1/4. 1.2.2. fractions division as partitive (equal share) this model is mostly known as partitioning or equal sharing. it represents to share activity which distributes a collection or quantity equally among some number of people. in the case of fraction division, for example, division 1/2 by 1/4, students may reason it contextually as a process of distributing half of a cake to several numbers of people in order that each person gets 1/4 of cake equally. 1.3. the present study in indonesia, the elementary school consists of classes from 1st grade up to 6th grade. it is commonly classified into a lower elementary (1st – 3rd grade) and an upper elementary (4th – 6th grade). indonesia has two simultaneously applied curricula, namely the school-based curriculum (known as kurikulum tingkat satuan pendidikan; in abbreviated as ktsp) that has been implemented since 2006 and the curriculum of 2013. one of the fundamental differences of both curricula is a pattern of material organizing. at the ktsp, a relationship among subjects is more mutually exclusive, while for the curriculum of 2013, it is integrative thematic. nevertheless, the implementation of the 2013 curriculum is still a limited trial phase applied in selected schools. at the elementary school level, this curriculum is only applied in grade 2 to represent the lower elementary and grade 4 to represent the upper elementary. in indonesia and most of the international curriculum, fractions are firstly introduced in the third grade of the elementary school (wijaya, 2017), while the divisions are introduced in the fifth grade of elementary school (see also purnomo, widowati, aziz, & pramudiani, 2017). further, wijaya (2017) states that the introduction of the fractional concept as parts of the whole becomes the only construct having a space to learn from both mathematical textbooks and the teacher's teaching method, while the fractional operations are dominated by rigid rules to solve problems. purnomo, widowati, & ulfah, incomprehension of the indonesian elementary school … 60 in indonesia, some previous studies have mentioned that the fractions topic becomes a difficult topic for the students and a serious concern because of the weakness of the students' performance on this topic (purnomo et al., 2014; trivena, ningsih, & jupri, 2017; wijaya, 2017). in his study, wijaya (2017) has analyzed students' difficulties on the fractions topic from timss results in 2015 and attributed it to the students' opportunities to study the fractional at school. based on the analysis of timss results, his research has found that indonesian students have a weakness on the understanding of fractions, particularly in story problem cases. students do not have space to explore their ideas because teachers resist getting out of the content and sequence of material in the book. similarly, trivena, ningsih, and jupri (2017) also have found that elementary school students are oftentimes misconception the concept of addition and subtraction of fractions. these studies show the fraction is one of the materials requiring attention and handling. however, those studies and literature related to it have not focused on more specific content that is fractions division. focusing on more specific issues helps to handle the problems more precise at hand. in addition, it is also substantial to know how the students' strategy in dealing with the case of division and what the difficulties are. based on the above description, this study aims to explore the indonesian elementary school students’ performance in solving fractions division cases including the difficulties, relations, and implications for the classroom instruction. research questions may arise i.e. how is indonesian elementary school students’ understanding of fraction division? 2. method 2.1. context and participants the method of this research employed two phases. the first one was a descriptive study to gain insight into students’ performance in coming to grips with fraction division problems. the participant of this phase was 40 fifth grade elementary school students in jakarta. it was collected fifth-grade students as the participant because they had learned a fraction from the definition up to the operation of fractions division. the second one was a case study to investigate the students’ knowledge further about fraction division and its underlying epistemological factors. several participants were selected based on their achievement in the test and teacher’s suggestions such as their ability of verbal expression and confidence. according to these considerations, three students were selected and pseudonyms were used to address ethical issues. the first student was ummu, an 11-yearsold, javanese girl, she was an outstanding student being a top three in her class every academic year. she comes from a middle-income family. the second one was nunu, an 11-years-old, javanese boy, he was an average student. he comes from a low-income family. his salient characteristics are that he is an active student selected as a leader in his class. the last was cici, a 12-years-old, sundanese girl, she was a student categorized as a low-achiever. however, she is involved actively in several school activities such as flag hoisting troop. she comes from a low-income family. a similarity among them is that they have settled in jakarta city since they were born. 2.2. data colletion the data collection processes were done by using a written test and an interview. the written test was administered to obtain data from the participants’ performance in dealing with fraction division problems. meanwhile, the semi-structured interview was volume 8, no 1, february 2019, pp. 57-74 61 conducted to explore epistemological factors related to the understanding of fraction and its difficulty. the written test composed of three question items about fractions division with different indicators. table 1 below demonstrates the question items. table 1. indicators of the written test case descriptions 1. , with (this case relates to a measurement concept of the fraction division) you have 2 birthday cakes given to your friends, each of them is 1/2 parts. how do you know the number of your friends who will get the cakes? 2. , with and (this case relates to partitive concept of the fraction division) father has 1/2 pizzas given to 2 of his children named mila and damar equally. how do you know how big parts will damar get? 3. , with and (this case relates to measurement concept of fraction division) mrs. vivi has 3/4 kgs flavor. to make 1 donut, mrs. vivi spent 1/4 kgs flavor. how do you know that how many donuts can be made? the interviewing questions based on the items of the question above and responses of the students on each question. first, we re-questioned “how do they solve the problem”. then, we asked, “why do they choose those strategies”. the third was “where do they know the knowledge”. 2.3. data analysis we used a rubric to analyze participants’ written answers. the rubric (see table 2) took indicators into consideration that were, understanding the problems, planning, and the answer’s accuracy. each indicator had 2 for the maximum score and 0 for the minimum score, so the highest score possible for each item is 6. in total, the highest score possible is 18 and the lowest score possible is 0. table 2. assessment rubric for written test assessment criteria assessed indicators score problem understanding comprehensive and organized understanding 2 there is an effort to organize but some problems could not be figured out 1 do not understand the problems, are not organized and systematic 0 strategic planning the strategy used is relevant and well explained (if it is implemented, it will be valid) 2 some strategies are relevant but are not well explained 1 the strategies are irrelevant, unclear and difficult to get to the point 0 accuracy of calculation using the right strategy leading to the right answer 2 some algorithms applied are correct but there are errors found. as the result, the answer is not valid 1 there are no answer 0 purnomo, widowati, & ulfah, incomprehension of the indonesian elementary school … 62 the percentage of students’ correct answers on every item is counted and classified into the whole right answer, partly right answer, and wrong answer. the written test data also were analyzed descriptively including mean and standard deviation. the mean and standard deviation are used to determine selected students for a case study. the written test data is grouped into high, medium, and low category. the high category had a score more than ̅ . the low category had a score less than ̅ . the scores between both criteria are categorized as a medium category. one student of each category would be chosen for the case study. on the other hand, the interview result data were transcribed and coded based on pattern responses to explore further. triangulation was done by confirmation the written test data and interview result. we also used students’ worksheets as additional data. the students’ worksheets were taken during the interview when students explained their understanding to the interviewer. 3. results and discussion 3.1. results 3.1.1. profile of the fraction division performance the students’ written answers represented their understanding of each case given. descriptive statistic of students’ answers is shown in table 3. table 3. percentage of student responses for each case of fraction division no. item correct partially correct incorrect 1 10% 50% 40% 2 8% 25% 68% 3 15% 28% 58% based on table 3, most participants encountered difficulties when dealing with the presented items. item number 2 obtained the lowest response among others. this item was only whole right answered by 8% of students and 68% of them responded wrong. table 3 also shows that at most only 15% of respondents answered a whole right answer for each given item. overall, the number of participants who correctly answered the items was much less than that of those who obtained partially correct and incorrect answers. it might indicate that fractions division is a problematic and challenging elementary mathematics topic for students. the results of the data analysis on the written test have obtained a mean at 4.525 and a standard deviation at 4.391 with the highest score was 14 and the lowest score was 0. based on the criteria for each category that we had previously set, there were 7 students (18%) as the high category, 21 students (53%) as the medium category, and 13 students (33%) in the low category. 3.1.2. a case on the natural numbers divided by fractions ummu’s responses in accordance with her written response addressing the first case, ummu sliced each cake into two pieces equally, then four half-pieces were obtained from two cakes. in the interview, she said, “this cake is sliced into two similar parts, so does this (another volume 8, no 1, february 2019, pp. 57-74 63 cake) one. after slicing the two, we have four similar pieces. this one (by referring to the shaded part) is for one person. so, there will be four”. ummu tried to address the problem by considering the number of half piece of cakes. therefore, a strategy implemented by ummu is likely to be in line with the concept of division as repeated subtraction. nevertheless, we discern that ummu’s explanation in the interview session tends to be different from her written answer in the test. the same approach also she did when answering subsequent questions we gave. ummu was asked to give explanations of how to share twelve doughnuts with her friends in which each of them would get two doughnuts. she explained, “it will be two doughnuts for one person, two for the other, so do this, this, this (putting marks to every two objects)”. ummu’s strategy was that she tried to distribute two for each person so that it would end at twelve for the number of doughnuts and six for the number of the person. based on this, ummu’s knowledge of the concept of division tends to converge on the idea of division as an inverse of repeated addition. nunu’s responses when dealing with the first case, nunu employed invert-and-multiply rule. figure 1 describes nunu’s efforts to address the question given. figure 1. nunu’s response in written test through the interview, we tried to gain deep information related to nunu’s written response during the test. the following are excerpts of the interview with nunu conducted after the test. interviewer : nunu, could you explain your answer? nunu : this was division, i mean that 2/2 is divided by 1/2. interviewer : which 2/2 did you mean? nunu : as there were two cakes, so 2/2. because we divided this, the second one was reversed and then we multiplied.the result was 4/2. interviewer : so, you thought that 2/2 was two cakes, how about 5/5? nunu : there were five cakes. based on the excerpt above, it is obvious that invert-and-multiply rule is capitalized on by her to solve the question. however, even though she was able to solve it in a correct manner, she did not seem to have an accurate comprehension concerning a concept of fractional parts. this inaccuracy occurs as she tends to assume that the value of a fraction, whose numerator and denominator are equal numbers, is the same as its numerator and denominator. for instance, nunu presumed that 2/2 could be represented as two units. by this method, she also regarded that 5/5 could be represented as five units. based on this interesting fact, further queries were posed to find out about nunu’s comprehension of the concept of fractional parts. purnomo, widowati, & ulfah, incomprehension of the indonesian elementary school … 64 figure 2. nunu’s response in interview session fig. 2 shows that nunu’s understanding of the fractional concept parts is weak. nunu focused on how many parts are divided and then she presumes that each part b and part c are 1/3. she said, “because we have three parts from one cake”. however, this statement is in contradiction with nunu’s answer that is 1/2 for part a. nunu realized that she added up the three parts and turned out to produce more than 1. cici’s responses cici’s responses to the first case were similar to what ummu undertook. in the interview, she said, “this cake is cut into two parts. then, i get two 1/2s. the other is also divided by two, so i get 1/2 and 1/2. thus, 1/2 + 1/2 = 2/4. since there are two cakes, thus 2/4 × 2/4 = 4/4. so, the result is 4/4 person. 4/4 refers to four persons”. when we elaborated on an aforementioned explanation by posing a further question, unfortunately, she was not able to reveal her argumentation concerning the reason why she used addition and multiplication. “i don’t know why?” she replied. figure 3. cici’s response in written test figure 4. cici’s response in interview session based on the aforementioned description, we disclosed several mistakes and misconceptions made by cici’s work. firstly, cici did mistake when adding two fractions with like denominator, for instance, 1/2 and 1/2. secondly, cici was likely to have an inaccurate understanding of addition and multiplication conception of numbers. thirdly, volume 8, no 1, february 2019, pp. 57-74 65 similar to what nunu did, cici claimed that the value of a fraction with similar numerator and denominator were equal to its numerator and denominator. 3.1.3. a case on the fractions divided by the natural numbers ummu’s responses in the second case, ummu tried to respond by splitting pizza out into two equal parts and wrote 1/4 in each part. therefore, according to ummu’s responses, the result of a division of 1/2 by 4 is 1/4. the following figure presents ummu’s written response to this case. figure 5. ummu’s response in written test figure 6. ummu’s response in interview session ummu’s written response in the test was likely to reflect her understanding of division as equal sharing. however, its conception was not demonstrated when she was interviewed. she tended to present her procedural knowledge. it was obvious when she tried to solve the question presented. even though her procedures and obtained answer were correct, she seemed to express her puzzlement concerning her answer. the following was an excerpt from the interview with ummu. interviewer : could you explain the way how you get 1/4 as your final answer? ummu : by dividing. 1/2 is divided by 2 equals ¼. wait, it is divided by 2… it is 1/2, isn’t? interviewer : what do you mean by 1/2? ummu : this pizza is cut into two. it is 1/2, isn’t? damar has one part, and …… interviewer : your previous obtained answer was 1/4. why do you have the different answer? ummu : because a half pizza is cut into two. interviewer : could you show me, which part of the figure indicates 1/4? ummu : this one (she refers to damar’s part), but i am a bit confused because it is divided by two. but i am sure that 1/4 is the correct answer (by showing her written response) based on the above excerption, ummu was not able to convince herself that 1/4 was the result of division 1/2 by 2. ummu tended to rely heavily on her procedural knowledge and got confused when there was a contradiction between her work showing that 1/2 divided 2 equals to 1/4 and her mental image presuming that something divided by 2 equals to 1/2. the reason might lay in the fact that ummu’s primary focus was the result purnomo, widowati, & ulfah, incomprehension of the indonesian elementary school … 66 of division instead of paying attention to its dividend and divisor. in addition, a similar response was presented by ummu when she was asked further questions during the interview. ummu : each person gets one. the rest is cut into four like this. let me sign these, 1, 2, 3, and 4. then, i add one cake with this. so, each person will get . ummu : it’s the same. i divide this by three. as each person gets one, then we divide the rest by 3. so the answer is . figure 7. ummu’s response in interview session figure 8. ummu’s response in interview session it is apparent from fig. 7 that ummu was able to address a case in which the dividend of the fraction is whole numbers. however, she was likely to have difficulty in coming to grips with the division problem in which its dividend was a rational number. from fig. 8, ummu presumed that division of a half circle by three results in 1/3. in addition, ummu seemed to have a weak understanding of fractional parts concept. it was obviously observed when she was asked about the fraction representing each sector in fig. 2 and her answers were that sector b and c were 1/3 and sector a was 2/3. fractional parts concept is a fundamental aspect in comprehending division of fraction and other fraction operation. nunu’s responses nunu’s response to the second case indicated that nunu capitalized on procedural knowledge, yet her works were difficult to interpret. based on the interview response, it seemed that nunu’s concept of fraction and division of fraction were still weak. volume 8, no 1, february 2019, pp. 57-74 67 figure 9. nunu’s response in written test figure 10. nunu’s response in written test interviewer : nunu, could you explain this answer you have obtained during the test? nunu : 1/2 is divided by 2/2 interviewer : what does 2/2 mean? nunu : two children interviewer : was 3/4 the answer to the question? nunu : yes, it was. 3/4 for damar. but, wait. it is wrong. it should be 2, not 3. so, the correct answer is 2/4. the dominance of procedural knowledge over conceptual knowledge in fraction concept might lead nunu to make mistake as she was not able to catch on what the presented problem was. for instance, she presumed that 2/2 stood for two units. figure 11. nunu’s response in interview session figure 12. nunu’s response in interview session in the further interview, nunu said i got 1/4 as we divide a cake by four. then, 1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 5/4. therefore, each child will have 5/4 cake (see fig. 11). in this case, nunu was able to deal with division case whose dividend was whole numbers, yet from fig. 12 we knew that she encountered difficulty as the dividend was not whole numbers. purnomo, widowati, & ulfah, incomprehension of the indonesian elementary school … 68 cici’s responses on the third case, cici tried to solve the question by cutting the cake into two equal parts. according to cici’s statement during the interview, we found that cici was likely to focus her attention on the result of the fraction instead of noticing the dividend and divisor. figure 13. cici’s response in interview session figure 14. cici’s response in interview session based on the cici’s work and statements, one issue was paramount when it came to her misconceptions about the fraction, that was, she presumed that if all things were cut into three equal parts, then the result would be 1/3. she passed over the form of the thing being divided. another cici’s weaknesses were found when she assumed that a region c and d were greater than region a and b as illustrated in fig. 14. however, surprisingly this response was at odds with her statement when she was asked about the fraction unit that named each part of the divided whole. she claimed that each part represented 1/4. this state of an affair might be attributed to cici’s lack of understanding of equal sharing concept at the fractional parts. 3.1.4. a case on fractions divide by fractions ummu’s responses ummu tried to address the third case using the subtraction method. the following figures illustrate ummu’s written responses during the test and the interview session. figure 15. ummu’s response in written test figure 16. ummu’s response in interview session volume 8, no 1, february 2019, pp. 57-74 69 we were not able to identify ummu’s argumentation, as she viewed this problem as a case of subtracting 1/4 from 3/4. we tried to have ummu read the question meticulously, yet she was likely to stick with its stance in her opinion. nunu’s responses nunu’s responses tended to be similar to that of ummu in which the third case could be addressed using subtraction. it could be discerned clearly when interviewing nunu. her answer was 2/4 as a result of subtraction of 1/4 from 3/4. she accounted for it as 1/4 floor used for making a doughnut. she performed single subtraction in lieu of multiple subtractions. figure 17. nunu’s response in written test figure 18. nunu’s response in interview test cici’s responses cici’s response to the third case indicated that she made the use of her procedural knowledge to address the question. fig. 19 shows cici’s written response in the test. she multiplied 3/4 and 1/4 and during the interview, she was not able to uncover the reason behind her strategy. therefore, it seemed that cici encountered difficulty in grasping the problem presented thoroughly. figure 19. cici’s response in written test purnomo, widowati, & ulfah, incomprehension of the indonesian elementary school … 70 3.2. discussion tirosh (2000) has summarized that there are at least three main categories of mistakes made by children when solving fractions division problems, to wit: algorithmbased mistakes, intuition-based mistakes, and mistakes derived from formal knowledge. in our study, we explored how children knowledge solves fraction division regarding tirosh’s work and any possibility beyond his work. the findings of the study indicated that most of the participants encounter difficulties in solving problems of fraction division. they face difficulties in solving problems related to the case of dividing fractions by whole numbers. in other words, their equal sharing concept is still weak. this finding is not in accordance with our predictions who reveal that this case is the easiest case compared with other cases. nevertheless, the other cases also need an attention because 58% of the students provided an incorrect answer for the case of dividing fractions by fractions and only 10% answered correctly for the case of dividing of whole numbers by fractions. in addition to being weak in equal sharing’s conceptual knowledge, the majority of the students in this sample still depend on procedural knowledge which is not accompanied by a strong conceptual knowledge. this finding was also supported by purnomo et al. (2014) when examining primary school students number sense. in their study, purnomo found that the students encountered some difficulties in understanding the meaning and the concept of numbers, especially the fractions and decimals. students have a misconception about the fractional concepts and make some errors when performing calculations as they pay more attention to its rules and algorithms. the findings were clarified and reinforced by the response of the three case study samples, namely ummu, cici, and nunu. all three participants are weak in equal sharing concept in the division of fractions. the equal sharing concept is used to interpret divisions which involving whole numbers as divisors. more precisely, this difficulty occurs when they encounter the case of an incomplete part of an object and they asked to determine how much each part divides the incomplete part. they focus on how many parts have been divided regardless of the shared part. this case can be exemplified by ummu when responding to what part was received by three children when they shared the 3 1/2 cakes equally. ummu assumed that the 1/2 part divided by 3 is 1/3 (fig.8). this is also similar to cici's response to the problem (fig 13). we connect this equal sharing conceptual problem to an intuition-based mistake from tirosh (2000). the intuition-based mistake encounters stem from students’ tendency to generalize the concept of equal sharing overly. the students in the sample of this study think that "everything shared by a certain number of a part is one per part of a dividing part". we also recognize that the conceptual problem for equal sharing of these fractions is related to students' misconceptions on the concept of fractions part. the students often focus only on how many parts are shared but they do not notice whether a value of fractions is equal (see fig. 2; fig. 14). the concept of the fraction part is a foundation for children to learn a fraction meaning, fractions operations, and advanced concepts of fractions. therefore, when these fundamentals are not robust, it will affect the understanding of fraction operations including fraction divisions. in an attempt to reduce this problem, it is critical not only to focus on the meaning of the fractions as part-towhole, but also to emphasize other sub-fraction constructs in the learning process of fraction concepts (clarke, clarke, & roche, 2011; purnomo, 2015a; siebert & gaskin, 2006), among others fraction as division, fraction as ratio, fraction as operator, fraction as measure. this is also alluded to by wijaya (2017) in which most mathematics textbooks in indonesia only introduce the concept of fractions with the concept of fractions as part-to volume 8, no 1, february 2019, pp. 57-74 71 whole. the intuition-based mistakes and misconceptions about the concept of fractional parts also discourage students from using the correct terminology. we encounter these things when the child considers 2 as 2/2, 5 as 5/5, and so on (see fig. 1; fig. 3; fig. 4). concept issues for equal sharing are not stand-alone. there are other obstacles related to student difficulties when students face fraction divisions. moreover, we have found that most students still depend on procedural knowledge without being aligned with conceptual knowledge. some researchers agree that focusing only on procedural knowledge may block a development of intuitive sense and the conceptual knowledge itself (forrester & chinnappan, 2010; purnomo et al., 2014, 2017). these problems can be verified by participants' work on the fractions division case which most of the students did it using invert and multiple rules. these rules are not based on a comprehensive explanation, students employ these rules to obey and apply procedures properly. however, applying the rules by ignoring the conceptual knowledge often causes errors in calculations. one example of the errors in employing this strategy can be seen in nunu (see fig.1 and fig. 9) and cici work (see fig. 3 and fig. 19). this has been mentioned by tirosh's study (2000) that he has categorized it as an algorithm-based mistake. generally, obedience to the rules and how to perform procedures properly require the students to memorize them. when they forget a few steps then it will certainly lead them to make mistake. the last problem encountered is an inability of the children to comprehend the fraction division case, particularly the fractions divided by fractions. this makes sense because they are not accustomed to confronting-context related to sources in both teaching and learning process. in indonesia, context-based teaching is still unique because education systems still focus on performance and result (purnomo, 2015b, 2016; purnomo, suryadi, & darwis, 2016; wijaya, 2017). in addition, mathematics textbooks in indonesia tend to consist of a set of rules and the use of performance-oriented algorithms (purnomo et al., 2014; wijaya, 2017). consequently, students are more likely to cope with regular problems and they encounter hardness in dealing with context-based problems. 4. conclusion the results of this study indicate that most of the participants of this study still tend to grape with difficulties in working on the fractions division. there are at least three crucial problems creating students difficulties in working on the case of fractions division. first, students' struggles are based on a shortage of conceptual understanding about equal sharing and fraction parts. second, the difficulty is based on an overemphasis on procedural understanding but not guided by a solid conceptual understanding. the last is students' unfamiliarity on the context-based problems leading to difficulties in interpreting the problem. references alenazi, a. 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(2010). children’s strategies for division by fractions in the context of the area of a rectangle. educational studies in mathematics, 73(2), 105–120. https://doi.org/10.1007/s10649-009-9206-0 purnomo, widowati, & ulfah, incomprehension of the indonesian elementary school … 74 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 11, no. 2, september 2022 e–issn 2460-9285 https://doi.org/10.22460/infinity.v11i2.p325-348 325 “flipped classroom type peer instructionbased learning” based on a website to improve student's problem solving tuti azizah, ahmad fauzan, yulyanti harisman* universitas negeri padang, indonesia article info abstract article history: received aug 26, 2022 revised sep 28, 2022 accepted sep 29, 2022 this study aims to develop learning tools in the form of lesson plans, student worksheets, learning videos, and ppt, based on web for first-grade seventhschool material linear equations with flipped classroom-type peer instruction. the development of this web-based learning tool uses the plomp model. the steps for developing web-based learning tools include preliminary needs analysis, curriculum analysis, concept analysis, student analysis, and literature analysis. then product development and assessment. this research was carried out during the product development stage based on needs analysis, curriculum analysis, concept analysis, student analysis, and literature analysis and then self-evaluated. the preliminary analysis obtained information that teachers need learning tools that can help students improve problem-solving skills, students need engaging learning media, students are interested in using learning media using videos with a period of 10-15 minutes, and ppt, accessed in the web. then the product is compiled and evaluated on its own, related to the apparent error in using it. based on the preliminary analysis, learning lessons, student worksheets, learning videos, ppt based on web and selfevaluation have been produced, which can then be validated by experts. keywords: flipped classroom, peer instructions, problem-solving, website this is an open access article under the cc by-sa license. corresponding author: yulyanti harisman, department of mathematics education, universitas negeri padang jl. prof. dr. hamka, kota padang city, west sumatra 25171, indonesia. email: yulyanti_h@fmipa.unp.ac.id how to cite: azizah, t., fauzan, a., & harisman, y. (2022). “flipped classroom type peer instruction-based learning” based on a website to improve student's problem solving. infinity, 11(2), 325-348. 1. introduction mathematics as one of the basic sciences has an important role in the development of science and technology. the learning objectives of mathematics in the decree of the ministry of education and culture no 64 of 2013 are related to the learning objectives set by the nctm (palgunadi et al., 2021). one of the objectives is that students are required to have basic problem-solving skills. therefore, it is very important for students to have the ability to solve problems in order to achieve maximum learning outcomes in accordance with the objectives of mathematics learning (kasem et al., 2018; roheni et al., 2017). in fact, https://doi.org/10.22460/infinity.v11i2.p325-348 https://creativecommons.org/licenses/by-sa/4.0/ azizah, fauzan, & harisman, “flipped classroom type peer instruction-based learning” based … 326 the mathematical problem-solving ability of students in indonesia still requires improvement and special attention, as shown by the results of the 2018 pisa study; indonesia's mathematics score was 379 below the international average score of 489 and the 2015 timss results for indonesia reached 397 with an international score of 500 (guhn et al., 2014; oecd, 2019; palgunadi et al., 2021). the national council for mathematics teachers (nctm) also mentioned the importance of solving learning problems. according to nctm (palgunadi et al., 2021), the mathematical thinking process in mathematics education includes five basic standard competencies: problem-solving skills, reasoning skills, communication skills, and presentation skills. this low ability results in the low quality of human resources as indicated by low problem-solving abilities. this is because, until now, education has not provided opportunities for students to develop problem-solving skills. students can also integrate realworld problem-solving skills to solve real-world problems and competition (cahyani & setyawati, 2017). indicators of mathematical problem-solving ability in this research are based on the combination and modification of polya (sam & qohar, 2016; siahaan et al., 2019), which are: (1) understanding the problem by identifying the adequacy of the required data; (2) developing a problem-solving plan by presenting the problem in a mathematical model; (3) solving problems by selecting and implementing the strategy; and (4) inferring or interpreting the solution. the process standards, learning must be planned, assessed, and supervised (ramadhani, 2016). on the other hand, with the covid-19 pandemic affecting learning activities, teachers must innovate in learning, including using technology in learning (herliandry et al., 2020). based on observations conducted at one of the junior high schools in padang, it is known that the learning process is carried out 3 days face-to-face and 3 days at home by giving assignments, one hour of mathematics lessons at the school is only done for 25 minutes. assignments are developed from student worksheets which mostly contain routine questions, so students have not been able to develop problem-solving skills well. educators also find it difficult to catch up on materials not understood by students. based on these problems, it is necessary to design effective learning tools that can help students develop their problem-solving skills, according to the characteristics of students and the covid-19 pandemic situation. internet-based learning technology with the flipped classroom model is a solution for transitioning traditional learning to a virtual system. students feel familiar with the materials that will be discussed in class (gariou-papalexiou et al., 2017). in several types of the flipped classroom, peer instruction flipped learning models have the most potential to improve problem-solving skills. this is because when in class students are given learning that begins with contextual problems; students are trained to understand and formulate the problems given through the concept test which will be answered individually so that students will get used to answering the questions given independently. learning tools will be developed later in the form of lesson plans, student worksheets, learning videos, and power point media to put in the web. studies which use web as a means of providing material are still rare, even though web provides complete tools, thus helping students learn comprehensively. based on research conducted by nakamura (2011), the advantage of the web is that there is no limitation on the number of web pages and it is easy to insert new pages to accommodate the needs of students who need to improve or add material. research on the development of learning tools using flipped classroom and its effect on students' mathematical abilities has been carried out by researchers, such as the research conducted by prayitno and masduki (2016) focusing on the development of blended learning media with the flipped classroom model in mathematics education courses. in the research, volume 11, no 2, september 2022, pp. 325-348 327 learning media were produced in the form of learning videos, quizzes, e-modules, and learning videos suitable for students based on expert tests, and students could use these media as a supplement to lecture materials. the effectiveness of the flipped classroom on attitudes and skills in learning mathematics in vocational high schools showed an increase in aspects of students' attitudes and skills in applying the concepts of sequence and series as well as being more active in problem-solving activities (damayanti & sutama, 2016). the development of a flipped classroom-based mathematics learning model in class xi of smkn 1 gedangsari gunungkidul showed that the flipped classroom-based mathematics learning model can maximize learning with one-on-one interaction through learning videos uploaded online and offline (damayanti & sutama, 2016). research shafique and irwin-robinson (2015) on the study of the effectiveness of the flipped classroom in 9 mathematics classes showed that learning at the university becomes more effective when flipped learning is implemented. in addition, the flipped classroom will also create a good learning experience for students. furthermore, hayati (2018) focusing on the theoretical study of the flipped classroom in mathematics learning showed that the flipped classroom learning model can help students learn both inside and outside the classroom, resulting in students being directly involved in the learning process along with the development of information and technology which requires teachers to apply technology in teaching and learning based on the characteristics of mathematics learning. furthermore, research conducted by prayitno and masduki (2016) on a comparative study of the flipped traditional learning model with peer instruction flipped on problem-solving abilities showed that the average value of the problem-solving ability test results for class viii students who received learning using the peer instruction flipped learning model was higher than the average score of the test results from students who experienced learning using the traditional flipped learning model. in addition, research related to the use of flipped classroom model has been carried out by researchers, such as research conducted by thohir et al. (2021) and herliandry et al. (2020). based on the description above, this research is different in the products developed, namely learning tools in the form of lesson plans, student worksheets, learning videos, powerpoint slides, and web which is arranged using flipped classroom type of peer instruction to see the effectiveness of the problem-solving abilities of the first grade of junior high school students. 2. method this research employed the research and development design. product development was conducted through several stages adapted to the model chosen, namely the plomp (plomp, 2013) which has been simplified into three stages as follows (1) preliminary research phase. the analysis activities carried out include needs analysis. the activity carried out is to analyze what is needed and expected for development. the information collection was carried out by the method of interviews. the results of the needs analysis were considered in the design of learning tools in order to achieve learning objectives and meet the needs of students in improving problem-solving skills. in curriculum analysis, the activities carried out were identifying the topic or subject matter, and compiling them in the right order, aiming to study the scope of the material, learning objectives, and the selection of appropriate strategies. the method used is a documentation method using a checklist of learning tools in schools. analysis of learners, the activities carried out were collecting information on the characteristics of students, and adjusting to the preparation of learning materials and tools. the purpose of student analysis is to find out the product that students want and identify the students' understanding of ppt applications. the method used in the azizah, fauzan, & harisman, “flipped classroom type peer instruction-based learning” based … 328 student analysis stage is the provision of questionnaires. the next is concept analysis; the activities carried out were identifying the main concepts of the material, detailing, and compiling them with concept maps systematically. relevant teaching materials are to be taught based on curriculum analysis. in the literature analysis stage, an analysis was carried out on reading/book resources used at schools to see the suitability of books with the curriculum. the appropriate books will be used as a reference for the preparation of learning tools to improve the problem-solving abilities of the first grade of junior high school'. furthermore, relevant research journals that can be used as the basis for developing products were reviewed. the next was (2) development phase or prototyping phase; in this phase, tools were designed in the form of lesson plans, student worksheets, learning videos, ppt slides, and web-based flipped classroom type peer instruction based on the results of the analysis in the preliminary research phase. the result of the design at this stage is called prototype 1. each prototype was evaluated with reference to the formative evaluation of tessmer's development in figure 1. figure 1. formative evaluation of tessmer development in plomp and nieveen the formative evaluation steps used are outlined as follows: (a) self-evaluation were carried out to double-check the completeness of the device components. the method used was self-evaluation and discussion with colleagues. the result of the revision of the learning device is called prototype 2. (b) expert reviews; expert assessment aims to validate the device by providing assessments and advice according to the expert's field. the validators involved were five people consisting of three mathematics education experts, one linguist, and educational technologist. (c) one-to-one evaluation, the one-on-one evaluation was carried out by asking for suggestions from users of learning devices, namely an educator and three students. students were selected based on high, medium, and low ability levels. the purpose of this individual evaluation is to identify possible errors in the student worksheet, learning videos, and website in the form of material, implementation, and to see the technical volume 11, no 2, september 2022, pp. 325-348 329 quality and practicality of the learning tools compiled. (d) small group evaluation; the revised learning tools produced prototype 3, then an evaluation was carried out involving 6 students selected by mathematics educators. each of the two learners represents a high, medium and low ability group. in this evaluation, aspects of presentation, time allocation, andreadability of the device were assessed. the data collection methods used in small group evaluation are interviews and observations (e) field test; in this stage, a trial was carried out, called a field trial. the goal of this trial is to evaluate learning tools in actual classroom situations. after field tests were carried out, the students were given a practicality questionnaire. (3) assessment phase; the assessment phase was carried out to determine the level of effectiveness of the tools by looking at the process and test results of mathematical problem-solving questions of students who have learned using learning devices. tests were carried out before and after students used the learning tools. the test results were processed based on the rubric of scoring mathematical problem-solving ability. this research was carried out in the stage of preliminary research, product development, and self-evaluation, while expert validation and product effectiveness will be reported in a different article. 3. result and discussion in the preliminary research phase, identification or analysis was carried out to develop a peer instruction type flipped classroom-based learning tool and analyze the limitations of the subject matter to be developed. the purpose of this stage is to establish and define the conditions needed in the development of learning tools. this stage started in july 2022. 3.1. needs analysis results the needs analysis stage is carried out with the aim of producing a flipped classroombased learning device of the peer instruction type that can be adapted to the needs. a needs analysis was conducted by interviewing the seventh-grade mathematics educators. based on the results of the interview, the following conclusions were obtained; (a) learning activities carried out after post-covid are face-to-face learning; (b) the school has applied flipped classroom learning, but the implementation is fully virtual; so, the material given is not explained again in class. (c) educators need learning tools that can help students maximize learning time, due to less learning time in class. (d) the problem-solving ability of students is still low, shown by the way the students understand the problem, plan a solution, complete the settlement, and re-examine the answers. (e) students enjoy learning using technology and using a variety of media. based on the results of the analysis, learning tools are needed to adapt to the learning conditions at one of the junior high schools in padang. at the same time, the tools can help students in solving problems. one of the efforts to overcome the problems in the learning process is to develop a peer-instruction flipped classroom in the form of lesson plans, learning media (ppt, and learning videos), student worksheets, and web as pages for students to access materials designed in such a way with the aim of overcoming problems. 3.2. curriculum analysis results curriculum analysis was carried out by examining the curriculum used at one of the junior high schools in padang. based on the results of the curriculum analysis, it is known that the curriculum used in schools is an independent curriculum in the seven-grade class semester 1. the curriculum began to be implemented on july 17, 2022. curriculum analysis aims to find out what materials about linear equations are presented in the curriculum in azizah, fauzan, & harisman, “flipped classroom type peer instruction-based learning” based … 330 accordance with the expected competencies, whether the materials are adequate to achieve learning objectives, and whether the materials have been properly ordered. the results of this curriculum analysis are used as a basis for formulating learning objectives in developing linear forecasting topic learning tools based on flipped classroom type peer instruction classes for the first grade of junior high school students. curriculum analysis is focused on analyzing learning outcomes in order to obtain learning objectives that become a reference in the development of lesson plans, student worksheets, ppt slides, and learning videos (see table 1). table 1. curriculum analysis results element learning outcomes learning objectives linear equation at the end of phase d, learners can recognize, predict and generalize patterns in the form of an arrangement of objects and numbers. they can express a situation in an algebraic form. they can use the properties of operations (commutative, associative, and distributive) to produce equivalent algebraic forms. learners can understand relationships and functions (domain, codomain, range) and present them in the form of arrow charts, tables, sets of sequential pairs, and graphs. they can distinguish some nonlinear functions from linear functions graphically. they can solve one-variable linear equations and inequalities. they can present, analyze, and solve problems by using relationships, functions, and linear equations. they can solve a twovariable linear safekeeping system through several ways to problemsolving. 1. state the relationship between two magnitudes (<,>,=,≤,≥) in a problem. 2. understand the correctness of mathematical sentences of equations when letters are substituted with numbers in a problem. 3. determine the solution of an equation without substituting numbers into letters in a problem. 4. solve equations using the properties of equations in a problem. 5. solve equations using the idea of moving tribes in a problem. 6. solve equations in the form of decimals and fractions in a problem. 7. solve problems by using linear equations 8. understand ratio relationships by using linear equations in a problem. 9. solve problems related to ratios by using linear equations the elaboration of learning objectives is carried out so that the materials can be explained in an orderly manner. this aims to make the materials easy to understand by students. regarding inequality, the curriculum guidelines for junior high schools stipulate that "the relationship between the amounts is expressed using the inequality", while the nature and completion of the inequality are studied in the next class. then, the researcher also paid attention to the small school class time, which is 30 minutes for one class hour. therefore, it only studied how it was used between the two-class hour. this was also part of a discussion with educators at one of the junior high schools in padang. 3.3. concept analysis based on the curriculum analysis, there are 9 learning objectives. to achieve the learning goal, appropriate and relevant materials are needed. the results of concept analysis reveal that teaching on the topic of the system of linear equations so far has not developed volume 11, no 2, september 2022, pp. 325-348 331 the ability to build concepts from linear equations and solve these problems. teaching the topic of linear equations so far has been directed to the abstract form of the general form of linear equations without starting from concrete/ contextual problems that can be observed by learners. solving direct linear equations is explained by the steps in the book, such as the method of substitution. based on the results of concept analysis, the topic of this linear equation begins by stating the relationship between two magnitudes. presenting the relationship of two quantities in the form of equations and inequality is an initial concept that students must master before solving the form of linear equations, the use of calculating operations, properties, and the application of linear equations to the form of more complex problem situations. finally, the comparison material on linear equations is an additional concept that aims to provide students with an understanding of problems that uses a comparison ratio, including the ratio of the size of sugar to one cup of coffee. based on the results of the analysis, the main concepts are studied in the material of linear equations and systematically compiled according to the flow of their presentation. the materials and concepts needed in learning linear equations are arranged in the form of concept maps. the concept map can be seen in figure 2. figure 2. concepts maps 3.4. results of student characteristics analysis student analysis was carried out to determine the characteristics of students so that the design of the learning tools is in accordance with expectations in the mathematics learning process. the analysis of students was carried out by interviewing educators and distributing a questionnaire on the characteristics of first-grade seventh school of junior hight school. based on the results of the interview, students in the class have diverse academic abilities consisting of high, medium, and low abilities. the characteristics of the learners analyzed include academic ability, group work ability, experience background, charm for colors and images, and student attitudes. azizah, fauzan, & harisman, “flipped classroom type peer instruction-based learning” based … 332 based on the questionnaire given to students, some information about the students was collected. the results obtained using the questionnaire can be seen in table 2. table 2. results of student characteristic analysis aspect information conclusion constraints during the learning process learning activities carried out by students at school are going well of the 32 respondents, 20 voted against, 9 voted disapproving, 3 voted in favor, 3 voted in favor the teaching materials/teaching media used by students have varied and attracted students' interest in learning of the 32 respondents, 22 voted disapproving, 8 agreed, and two disagreed. learner abilities students are less able to solve problems in the form of problemsolving. of the 32 respondents, 25 voted in favor, and 5 voted overwhelmingly in favor. learning tools to be developed learners need student worksheets for engaging and easy-to-understand learning 32 respondents voted in favor learners use electronic media to search for material 32 respondents voted in favor students are interested in using learning videos and power point media to learn over and over again at home that can be easily understood 32 respondents voted in favor students are interested in the learning videos and ppt media provided are distributed through the website 32 respondents voted in favor students interested in using the learning tools used can improve problem-solving skills 32 respondents voted in favor based on the answers to the student questionnaire, it is known that students want more interesting learning resources at school; students want more learning time so that when they understand the material better; most students state that they have used and often use smartphones as learning resources, and most students stated that they are not able less able to solve problem-solving problems. based on the analysis of the characteristics during the researcher's time at school, a peer instruction type flipped classroom-based learning tool in the form of lesson study, student worksheets, learning videos, power point media, and the web can help students in learning at home needs to be developed so that the learning time is available more, and in face-to-face, it focuses more on group discussion activities and solving problems related to the materials that can be accessed on the web; also, learning videos and power point media as interesting learning media can motivate students to study harder. in addition, students volume 11, no 2, september 2022, pp. 325-348 333 with individual character prefer to learn individually in understanding the material and can use the learning tool anytime and anywhere. 3.5. literature review literature review; literature analysis was carried out by analyzing the learning resources used at one of the junior high schools in padang. the results of the analysis of learning resources are presented in table 3. table 3. literature analysis results no indicator valuation yes no 1 learning resources obtained from written sources. √ 2 learning resources are obtained from unwritten sources. √ 3 the learning resources used can be found in the library. √ 4 the learning resources used are in accordance with the indicators in peer instruction. √ 5 the learning resources used do not facilitate problem-solving skills. √ 6 the learning resources used are less attractive to students in learning. √ 7 the learning resources used are easy for learners to understand. √ based on the literature analysis carried out, it is known that the books used at one of the junior high schools in padang are mathematics books of the 2013 curriculum and student worksheets. the book and student worksheet have not facilitated students to solve problems and the question exercises presented on the worksheets have not facilitated problem-solving. educators are still looking for teaching materials that are suitable for use in learning, especially those that are in accordance with the independent curriculum but due to the constraints on the cost of procuring books, educators still use the 2013 curriculum books. in terms of appearance, the worksheets used have not been able to attract students' learning interest because the design is simple. in addition, the presentation of materials from the package books used is still difficult for students to understand, and the package books can only be borrowed for use in the school area. the boks cannot be brought home because they are limited. based on the literature analysis, student worksheets will be designed to attract the students and guide them in conducting an investigation and solving problems in learning mathematics, especially linear equation materials. the next is product development based on the analysis, curriculum needs, concepts, and students, a peer instruction-type flipped classroom-based learning tool was designed in the form of student worksheets, learning videos, power point media, and web on the topic of seven-grade linear equations. peer instruction type flipped classroom-based lesson plan is a learning tool specifically designed for junior high school students in seven grades. the lesson plan format is designed to contain components based on flipped classroom-type peer instruction. the flipped classroom-based lesson plan type of peer instruction is designed to consist of three components that have been arranged in the independent curriculum. (a) general identity. general information contains information about the identity of the author, initial competencies, facilities and infrastructure, target students, and the learning model used. (b) core competencies. core competencies contain learning objectives and learning activities. (c) appendix. the attachment contains the learner worksheet. the pictures of the lesson plan can be seen in figure 3. azizah, fauzan, & harisman, “flipped classroom type peer instruction-based learning” based … 334 figure 3. lesson plan characteristics of student worksheet based on flipped classroom type peer instruction the model used in the student worksheet developed is a peer instruction type flipped classroom learning model that has the following steps: pre-class activities (students watch learning videos at home), class activities where the teacher gives the first question test which should be done individually, discussions between students regarding the answers to the first question, then the second question test which is done in groups, measuring students’ understanding at the end of the lesson; all of which consist of questions from a problemsolving problem. the structure of the student worksheet that has been compiled can be seen in table 4. table 4. student worksheet structure no student worksheet section student worksheet structure 1 introduction 1. cover 2. title page 3. foreword 4. table of contents 5. learning objectives 6. instructions for using student worksheet 7. concept map 2 fill learning materials (meeting 1-5) 3 cover bibliography volume 11, no 2, september 2022, pp. 325-348 335 the writing of student worksheet based on flipped classroom peer instruction type is based on the arrangement of the student worksheet structure that has been made. the writing of student worksheet on prototype 1 that the researchers have designed can be seen in the figure 4. figure 4. student worksheet front cover the front cover page contains the student worksheet title, class, target user, and creator identity. the foreword page view can be seen in figure 5. figure 5. foreword in the foreword section, the introductory preface page contains a general review of the content of the student worksheet, forework acknowledgment from the author, and the azizah, fauzan, & harisman, “flipped classroom type peer instruction-based learning” based … 336 author's expectations. student worksheet based on flipped classroom type peer instruction compiled is expected to be a guide and help students in learning linear equation materials. the student worksheet usage instructions page can be seen in figure 6. figure 6. instructions for use of student worksheet instructions for use of the student worksheet contain things that need to be considered in studying the student worksheet. on the student worksheet, there is an explanation page for step-by-step peer instruction. this page contains an explanation of the steps of peer instruction which aims to make it easier for students to understand the steps of peer instruction. the step-by-step peer instruction can be seen in figure 7. figure 7. peer instruction steps volume 11, no 2, september 2022, pp. 325-348 337 the concept map contains a sequence of concepts or an overview of the material to be studied. the concept map can be seen in figure 8. figure 8. concepts maps in the mathematical figures of linear equations, to presents the history of mathematical figures of linear equations, related to biographies and experiences related to mathematics. the page view of the mathematical figures of linear equations can be seen in figure 9. figure 9. linear equation figure azizah, fauzan, & harisman, “flipped classroom type peer instruction-based learning” based … 338 learning materials. the learning materials in the student worksheet are designed in accordance with the peer instruction type flipped classroom component which is summarized as follows. test concept 1 this component is a problem in the form of the first test question regarding a basic concept of the material. learners are given this test to find out the extent to which they learners understand the material being studied. learners are given time to answer the questions individually. the test 1 concept view can be seen in figure 10. figure 10. concept test 1 discussion of test concepts 1 in this component, students are given the opportunity to discuss and argue with each other about the first test questions given. in this stage, the discussion is carried out in groups. after the students’ correct answer to the discussion is more than 80%, it is continued to the second question. the discussion page is shown in figure 11. figure 11. discussion of test concepts 1 volume 11, no 2, september 2022, pp. 325-348 339 test concept 2 in this component, the second test question is given to further strengthen the concepts that have been obtained by the students. the work on this question is carried out in groups. the test 2 concept page is shown in figure 12. figure 12. concept test 2 final assessment at the end of the discussion, students are given a final assessment test related to the evaluation of the linear equation material that has been studied. the final assessment can be seen in figure 13. figure 13. final assessment the design stage of learning videos, power point media, and wesite began by establishing the main concepts so that the preparation of the material can achieve learning objectives. the material is presented in the form of learning videos and also in powerpoint azizah, fauzan, & harisman, “flipped classroom type peer instruction-based learning” based … 340 media that is adapted to the independent curriculum and can help students develop problemsolving skills. the web was created by using google site which can be accessed at https://sites.google.com/view/tuti-azizahs-math-education/material site. the web that has been designed has several navigations, namely home navigation which contains the student's attendance list, menu navigation which consists of materials for each meeting (ppt slides contain learning objectives, materials, quizzes, and learning videos), and the student worksheet menu at each meeting which can be viewed directly or downloaded by students. here are some views of learning videos, power point media, and website that have been designed. the development of the homepage can be seen in table 5. table 5. learning video view, ppt, and web part footage homepage. the home page is a web start page that contains the identity of the author and there is a student attendance menu. learner attendance page. on this page, students can fill the attendance of the meeting according to the meeting carried out homepage. the home page is a web start page that contains the identity of the author and there is a student attendance menu. https://sites.google.com/view/tuti-azizahs-math-education/material volume 11, no 2, september 2022, pp. 325-348 341 part footage display materials on this page, students can select the material they want to learn at each meeting by clicking on the available meeting icon. meeting materials 1. on this page, students can learn about the material available in the ppt display by clicking on the ppt section. ppt displays. in the ppt, there is an identity menu, concept map, learning (containing materials), quizzes, and teacher profiles. ppt is equipped with audio that explains the functions of the available menus section. azizah, fauzan, & harisman, “flipped classroom type peer instruction-based learning” based … 342 part footage download ppt materials in addition, students can learn the material on ppt directly on the web. learners can also download ppt by clicking download learning videos. on this page, students can watch the learning video by clicking play. learners can also stop the video by clicking pause. students can also download videos by going to the video link uploaded on youtube student worksheet on this page, learners can view and download student worksheets at each meeting teacher profile on this page contains the identity and biography of the author volume 11, no 2, september 2022, pp. 325-348 343 based on the results of the evaluation with colleagues, there are revisions related to the preparation of menus; then, in the ppt, recorded audio is added by the researcher so that students are not confused in operating the menus on the ppt; then, improvements were made to the animations on the ppt slides, improvements on the explanations in the learning video that are a bit slow, and the web display. the results of the improvement can be seen in table 6. table 6. self-evaluation results repair suggestions before and after revision before the revision, there was only a linear equation menu that contained an introduction, ppt, learning videos after the revision, the menus provided are arranged according to the meeting, and are more complete before revision after revision before revision ppt cannot be accessed by other users after the ppt revision can be run on the web and the menu button is smooth before revision after revision azizah, fauzan, & harisman, “flipped classroom type peer instruction-based learning” based … 344 repair suggestions before and after revision before the revision, there was no student worksheet menu that students could download after the revision, the student worksheet menu is given for each meeting so that students can access it as needed based on the results of product development that have been described, it is hoped that this media can improve students' problem-solving abilities. student problem solving is influenced by how the teacher behaves (harisman et al., 2019b). if teachers can develop creative learning media such as videos, ppt, and the web, they will be able to change students' problem-solving to be more sophisticated (harisman et al., 2018, 2019a; harun et al., 2019). the background of teachers in teaching and the experience of the teachers in teaching also affect how the teachers develop media in the learning process (fauzan et al., 2019; harisman et al., 2020; kariman et al., 2019). the literature review was also carried out in previous research and found some information related to mathematics learning that can be used as a basis for designing peer instruction-type flipped classroom-based learning tools. flipped classroom-based mathematics learning model can maximize learning through one-on-one interactions through learning videos uploaded online and offline (abdelaziz, 2014; fraga & harmon, 2014; kim & jeong, 2016; rontogiannis, 2014). next, the effectiveness of the flipped classroom shows that learning at the university becomes more effective with flipped learning (ma et al., 2018; mccabe et al., 2017; wachira & absaloms, 2017; wong & chu, 2014). the theoretical study of flipped classrooms in mathematics learning shows that the flipped classroom learning model can help students learn both inside and outside the classroom, resulting in students being directly involved in the learning process and along with the development of information and technology that does require teachers to apply technology in learning activities and is based on the characteristics of mathematics learning (choi et al., 2015; iverson et al., 2017; lin & hwang, 2019; mccabe et al., 2017; wachira & absaloms, 2017). next, flipped learning model with peer instruction can improve problem-solving abilities (bokosmaty et al., 2019; gough et al., 2017; kim & jeong, 2016; matzumura-kasano et al., 2018; wang et al., 2019; zhang et al., 2018). 4. conclusion the development of this product is based on a preliminary analysis comprising needs analysis, analysis of student characteristics, curriculum analysis, concept analysis, and literature analysis. based on the preliminary analysis, the material arrangement of linear equations is arranged into 5 meetings, the first meeting is studying the relationship between two magnitudes (<, >, =, ≤, ≥) in a problem. understanding the correctness of mathematical sentences of equations when letters are substituted with numbers in a problem, the second meeting determines the solution of an equation without substituting numbers into letters in a problem; solving equations using the properties of equations in a problem, third meeting volume 11, no 2, september 2022, pp. 325-348 345 solves equations using the idea of moving tribes in a problem; fourth meeting solving equations in the form of decimals and fractions in a problem, solving problems by using linear equations; the fifth meeting is understanding ratio relationships by using linear equations in a problem and solving problems related to ratios by using linear equations. furthermore, based on the distribution of materials, a learning video with a duration of 1015 minutes was prepared based on the results of the preliminary analysis; the material is also provided in the form of ppt slides which have menus that are provided with audio features to make it easier for students to carry out ppt. in the end, there is a quiz that can be done by students to measure their ability of students after studying the materials, and the student worksheet contains practice problem-solving questions that are arranged based on a flipped classroom type of peer instruction which consists of the first test question, discussion of the first test, second test, and final assessment. the lesson plans are prepared following the curriculum used in schools and contain this activity with the steps of a flipped classroom type of peer instruction, namely pre-class students’ study first at home by accessing the web which includes learning videos, and ppt and providing the results of material resumes by uploading them to the menu. the main activities in the classroom are students completing student worksheets according to the steps of the flipped classroom type of peer instruction. acknowledgements we would like to thank the drpm directorate of research and community service of the republic of indonesia on a master's thesis scheme with a letter number 2076/un3513/lt/0022 and contract number 197/e5/pg0200pt/2022. references abdelaziz, h. a. 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(2018). spoc-based flipped classroom of college english: construction of an effective learning model. international journal of emerging technologies in learning (ijet), 13(1), 37-45. https://doi.org/10.15294/kreano.v7i2.7300 https://doi.org/10.1088/1742-6596/895/1/012079 https://doi.org/10.1109/icalt.2014.216 https://doi.org/10.15294/kreano.v6i2.5188 https://doi.org/10.33087/phi.v2i2.37 https://doi.org/10.1109/afrcon.2017.8095566 https://doi.org/10.1007/s10734-019-00366-8 https://doi.org/10.1007/978-3-319-08961-4_10 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 11, no. 2, september 2022 e–issn 2460-9285 https://doi.org/10.22460/infinity.v11i2.p237-254 237 development of teaching materials for elearning-based statistics materials oriented towards the mathematical literacy ability of vocational high school students in in supianti1, poppy yaniawati1*, siti zuraidah md osman2, jasem al-tamar3, niki lestari4 1universitas pasundan, indonesia 2universiti sains malaysia, malaysia 3kuwait university, kuwait 4smk negeri 2 baleendah, indonesia article info abstract article history: received aug 8, 2022 revised sep 13, 2022 accepted sep 14, 2022 the aim of this study is the development of teaching materials for statistical materials based on edmodo-assisted e-learning and how they impact students' mathematical literacy skills. the method used is the dick & carey development model. the research population is class xii catering, one of the vocational high schools in bandung city, with a sample of class xii catering 1. the instrument used a mathematical literacy test, validation sheet, student response questionnaire, and interview guidelines. the data collected were analyzed descriptively qualitatively through triangulation, q-cochran statistical test, and n-gain test. the results of this study indicate that the design of teaching materials for statistical materials based on edmodo-assisted elearning is very feasible to use in learning mathematics. furthermore, the results of the application of teaching materials have a positive effect on mathematical literacy skills with a reasonably good category. therefore, teaching materials must further develop animation, use communicative language, and utilize the latest technology. keywords: e-learning, edmodo, mathematical literacy ability this is an open access article under the cc by-sa license. corresponding author: poppy yaniawati, department of mathematics education, universitas pasundan jl. sumatera no. 41 bandung, west java 40117, indonesia email: pyaniawati@unpas.ac.id how to cite: supianti, i. i., yaniawati, p., osman, s. z. m., al-tamar, j., & lestari, n. (2022). development of teaching materials for e-learning-based statistics materials oriented towards the mathematical literacy ability of vocational high school students. infinity, 11(2), 237-254. 1. introduction today's education cannot be separated from the use of technology. most teachers and students already use technology in schools. according to information from 258 students, 50.8% often, 45% never, and 4.2% never mathematics teachers in west java apply ict in learning (supianti, 2018). online learning can be said to be an electronic learning system https://doi.org/10.22460/infinity.v11i2.p237-254 https://creativecommons.org/licenses/by-sa/4.0/ supianti, yaniawati, osman, al-tamar, & lestari, development of teaching materials … 238 called e-learning which uses a website and can be accessed anytime, anywhere. e-learning is a learning activity that uses electronic services, for example, telephone/mobile phone, video, audio, computer, laptop, tablet, internet access, and so on (alifia & pradipta, 2021; fisher et al., 2019; supianti et al., 2021; wahyuni & sugiharta, 2019). thus, the internet network as a supporting facility for e-learning must be fulfilled. students can use e-learning to learn independently. the role of teachers in modern learning systems is much as a facilitator, which results in a paradigm shift that prepares students to learn independently (yaniawati, 2012). in line with that, learning mathematics using e-learning is better than conventional (supianti, 2013). e-learning-based learning provides opportunities for students to learn freely and without being pressured, accessible in the sense of finding learning resources, free from embarrassment as in conventional learning when they cannot answer questions from the teacher, fail to learn, and so on (supianti, 2018). online learning or elearning is practical because it can be used anywhere and anytime (irfan et al., 2020). easy, safe, and simple e-learning media can help students set strategies. e-learning media is interactive, and the information delivered is more real-time (sugianto et al., 2022). media in the learning process delivers the source of the message and the recipient of the message and stimulates thoughts, feelings, attention, and willingness so that they are encouraged and involved in the learning process (hamid et al., 2020). learning media will overcome the limitations of time, space, and senses. the function of learning media is also to influence the climate, conditions, and learning environment (pratama & ismiyati, 2019). edmodo is a secure and free social media-based digital classroom that helps teachers manage virtual classes to connect students with other students (balasubramanian et al., 2014). thus, the edmodo application is suitable for teaching and learning activities because it supports what teachers and students need in the learning process. the edmodo application has a school environment-based network because it helps teachers in virtual classes according to learning conditions in the classroom, based on natural class divisions in schools, where classes contain assignments, quizzes, and final assignments in each lesson (putranti, 2013). learning through the edmodo platform needs to be applied to be more varied, active, interactive, and independent (pratama & ismiyati, 2019). the learning objectives will be achieved with suitable learning media, and the student's abilities are expected to increase. the ability that is expected to increase is the ability of mathematical literacy. mathematical literacy is a person's ability to formulate, use, and interpret mathematics in any context, including mathematical reasoning, mathematical concepts, procedures, facts, and tools to describe, explain and predict an event (sari, 2015). even johar emphasized that knowledge and understanding of mathematical concepts are essential, but more importantly, activating students' mathematical literacy skills to solve everyday problems (yudiawati et al., 2021). mathematical literacy is an individual's ability to effectively use his mathematical knowledge to solve real problems in everyday life (anwar, 2018). effectiveness in question is in solving one's problems, starting with understanding problems, formulating them, and using mathematical knowledge to solve them and interpret them. the mathematical literacy of students in indonesia is still below the oecd average. the average international score to determine the ability of mathematical literacy is 500 (level 3), and indonesian students' average mathematical literacy score is 375 (level 1). based on data from the national center for education statistics that the mathematical literacy ability of indonesian students in pisa 2015 it was still low, namely 37.9% at level 1, 30.7% at level 1, 19.6% at level 2, 8.4% at level 3, 2.7% at level 4, 0.6 at level 5, and no one was able to reach the value of 0.6%. in pisa 2015, the mathematical literacy results of indonesian students were 380 and 490, which are the average scores of all countries that took the mathematical literacy test (kafifah et al., 2018). thus, students' mathematical literacy skills volume 11, no 2, september 2022, pp. 237-254 239 need to be improved, with the development of teaching materials for statistics materials based on e-learning assisted by edmodo oriented towards mathematical literacy skills. therefore, based on the introduction, the research objectives were: (1) to analyze the design of the development of teaching materials for statistics materials based on e-learning assisted by edmodo; and (2) to analyze the mathematical literacy abilities of students who used these teaching materials. 2. method this type of research uses r & d (research and development) with the model dick & carey (gafur, 2012) through 10 stages in the figure 1. figure 1. dick & carey's learning design model (gafur, 2012) the figure 1 showed the first stage in this research is to identify the competencies and general learning objectives of the teaching materials developed, namely statistical material. the second stage is to identify the objectives of developing teaching materials and the strategies used in presenting the developed teaching materials. the third stage identifies the characteristics of the initial ability of the class xii culinary management smkn 2 baleendah as many as 36 students. the initial ability of students is seen from the average daily test results which show the average value is still below the minimum completeness criteria. the fourth stage is to formulate special abilities that must be mastered specifically during and after completing learning. the fifth stage is developing relevant research instruments, namely the development of 6 items of essay questions on mathematical literacy abilities. the sixth stage is finding researches and student characteristics that are carried out based on relevant learning theories. the seventh stage is choosing materials based on the strategies that have been set and the abilities to be improved. the material in the teaching materials includes competence, main content and practice questions. identify instructional goals conduct instructional analysis identify entry behaviours write performance objectivies develop criterion referenced test develop instructional strategy develop/ select intructionals materials develop/ conduct formative evaluation revice instructions develop/ conduct summative evaluation supianti, yaniawati, osman, al-tamar, & lestari, development of teaching materials … 240 the eighth stage is a formative evaluation with validation, limited trials and field trials. validators in this study are material & media experts, and student response questionnaires. limited trials were conducted on 6 students who had obtained statistical material selected by purposive sampling. field trials were conducted on class xii culinary administration students at smk negeri 2 baleendah, bandung regency. the sample was taken by 30 students and given learning using teaching materials for statistics based on elearning assisted by edmodo. the sampling technique is purposive sampling, which is tailored to research needs. namely, all students have gadgets. the study went through a limited trial with ten subjects and a field trial with 30 subjects using the one group pretestposttest research design. the instruments used in this study are in the form of tests and nontests. the test-shaped instrument consists of 6 mathematical literacy test questions in the form of a description, while the non-test is in the form of validation sheets, student response questionnaires, and interview guidelines. the collected data were analyzed using qcochran, n-gain, and triangulation by comparing validation results, questionnaires, and interviews. the ninth stage makes improvements to the evaluation results in stages three to seven. the tenth stage is the refinement of teaching materials based on input at the summative evaluation stage. 3. result and discussion 3.1. result 3.1.1. e-learning-based teaching materials the development of e-learning-based teaching materials is carried out through 10 stages of dick & carey with the following results: the first stage identifies instruction goals, teaching materials have not been accompanied by animation and the existing e-learning, learning media have not varied, the second stage of conduct instructional analysis, relevant knowledge is statistical material because this application plays a vital role in daily life. the third stage of identifying entry behaviors, students have not been able to manage and regulate themselves in thoughts, feelings and behaviors, so that students' self-regulated learning is low, the fourth stage of writing performance objectives, simple, easy and appropriate learning media is the use of the edmodo application, the fifth stage of developing criterionreferenced tests, it is necessary to develop relevant question items that improve mathematical literacy skills, the sixth stage of develop instructional strategy, teaching materials are arranged according to the components of e-learning, the seventh stage of develop and select instructional materials, the display of teaching materials prepared based on the provisions of the development of teaching materials, the eighth stage of design and conduct formative evaluation of instructional, statistical teaching materials have been designed equipped with contextual problems, exciting animations, drawings with examples as shown in figure 2. volume 11, no 2, september 2022, pp. 237-254 241 figure 2. display of teaching materials then the teaching materials were validated by six material experts and three media experts. the validation results by material experts obtained 90.78% on very valid criteria, the media experts obtained 88.52% on very valid criteria, and student response questionnaires obtained 76.47% on the criteria were entirely valid. thus, the teaching materials developed are said to be feasible and can be used in learning. the results of the validation of teaching materials by material experts and media experts, along with student response questionnaires, are listed in table 1. supianti, yaniawati, osman, al-tamar, & lestari, development of teaching materials … 242 table 1. data from the validation of material experts no criterion average grades (percentages) v1 v2 v3 v4 v5 v6 1 aspects of content eligibility 76.67 90 96.67 85 96,67 95 2 aspects of presentation feasibility 78 90 100 96 94 94 3 aspects of linguistic feasibility 80 86.67 93.33 100 93.33 95.56 4 aspects of mathematical literacy assessment 80 86.67 91.11 95.56 91.11 93.33 average 78.67 88.33 95.28 94.14 93.78 94.47 average validity 90.78 validity level very valid, or can be used without revision based on table 1, the difference in scoring was obtained for v1. the criteria with the most significant value were the feasibility of language and mathematical literacy. for v2, the most significant criterion was the content and presentation feasibility. followed by v3, the most significant criterion was the feasibility of the presentation. for v4, the most significant criterion is linguistic eligibility. for v5, the biggest criterion is content eligibility, and for v6, the most significant criterion is linguistic eligibility. next, the data from the validation results of media experts are presented in table 2. table 2. media expert validation data no criterion average grades (percentages) average v1 v2 v3 1 display 74.67 89.33 96 86.67 2 use 80 83.33 93.33 85.55 3 utilization 90 96.67 93.33 93.33 average validity 81.56 89.78 94.22 88.52 validity level very valid, or can be used without revision table 2 shows that the most significant criterion of teaching materials is utilization, with an average percentage of 93.33%. the difference between display and utilization was 6.66%, and between utilization and usage was 7.78%. next is the student response questionnaire presented in table 3. table 3. data on the results of the recapitulation of student response questionnaires no aspects statement number average value (percentage) 1 interest 1-6 75.67 2 material 7-11 74.40 3 language 12-14 79.33 average validity 76.47 validity level “quite valid, or usable but needs minor revisions” table 3 shows that the teaching materials assessed by students have a good language aspect because the scores obtained are more significant compared to the aspects of interest and material. the difference between the three aspects is not much different. in the ninth stage of revised instruction, improvement of teaching materials based on criticism and suggestions, input and suggestions are included indicators as triggers from making the content of the discussion, determining quiz material to the end on the post-test question into direct evaluation, whether through the media students can achieve the expected essential competencies. the teaching materials are then revised according to these inputs and suggestions. in the tenth stage of design and conducting summative evaluation, an evaluation is carried out to improve the effectiveness of teaching materials. volume 11, no 2, september 2022, pp. 237-254 243 based on the q-cochran test shows the validation of material experts with statistical results ρ = 0.010< α = 0.05 means that there are differences in the validation results of elearning-based teaching materials assisted by edmodo between material experts validators 1, 2, 3, 4, 5 and 6. as for the q-cochran test, media experts showed results of ρ = 0.007< α = 0.05, meaning that there are differences in the validation results of e-learning-based teaching materials assisted by edmodo between media expert validators 1, 2, and 3. 3.1.2. mathematical literacy skills based on the pretest and post-test results of students' mathematical literacy ability tests, the average student score before learning using edmodo-assisted e-learning-based statistics teaching materials is 30.23. then, using statistics teaching materials based on elearning assisted by edmodo obtained an average score of 74.30. based on the minimum completion criteria set by the school of 75. so in the results of the pretest, students have not been able to reach the minimum completion criteria, while in the post-tests results, students have almost reached the minimum completion criteria. of the 30 students who took part in the learning, 19 students reached the minimum completion criteria, and 11 students had not reached the minimum completion criteria, so 63.33% of students had reached the minimum completion criteria. based on the completeness of learning, it is said to be complete with good categories if the average is 60% 79%. based on the n-gain value, a result of 0.6 with moderate interpretation was obtained, meaning that there was an increase in mathematical literacy ability with moderate criteria. thus, the results of the analysis of pretest and posttest data obtained by students have achieved complete learning with good categories, and an increase in their mathematical literacy skills is moderate. a comparison diagram of the pretest and post-test values of the mathematical literacy test is shown in figure 3. figure 3. the value of pretes and postes of mathematical literacy ability one example of the results of superior student work and low related to mathematical literacy test questions (level 1) with indicators of students being able to build their knowledge by making their data and processing the data into a frequency distribution table is presented in figure 4. 0 20 40 60 80 pretes postes pretes postes supianti, yaniawati, osman, al-tamar, & lestari, development of teaching materials … 244 question class xii busana 2 is carrying out mathematics learning with the teacher. the task given is identifying information and using his knowledge to solve the problem. with the instruction, make a set of scores of 80 students, with the lowest test score being 35 and the highest score being 99, where log 80 = (1.9031). present in a group frequency distribution table. superior student answers translate: count of data = 80 range = r = 99 – 35 = 64 determine the number of classes: k = 1 + 3.3 log 80 k = 1 + 3.3 (1.9031) k = 1 + 6.28 k = 7.28 k = 7 class length = 64/7 = 9.1 = 10 asor student answers translate: 2. the income that students and their wood shop often earns is 141,912 rupiah figure 4. postest problem number 1 based on figure 4, the answers of superior students have been able to make their data with their knowledge. solve problems with already known formulas so that students can create a frequency distribution table from data that has been created by themselves. thus, students are considered capable of completing level 1 mathematical literacy skills. as for the answers, the students did not do the questions according to the instructions. the students did not write down the requested data and could not solve the problem using formulas, so the students were not able to make a frequency distribution table. thus, students are considered unable to complete level 1 mathematical literacy skills. volume 11, no 2, september 2022, pp. 237-254 245 3.2. discussion in the first stage of the development of teaching materials for statistics materials based on e-learning assisted by edmodo was found that in the process of teaching and learning mathematics, only package books are available in the library. in the learning process, teachers always use the old method, namely the one-way learning process, so the teacher explains or lectures more. the lecture method is straightforward for verbalism to occur. more visual students become at a loss, teachers find it challenging to conclude between students who already understand or not, and students become passive in the learning process (helmi, 2016). so student activity becomes less because students only listen, without opening up opportunities for students to think more broadly than what the teacher conveys. thus, students experience difficulties when learning mathematics, especially when faced with math problems that are not routine. these difficulties are further increased by learning from home due to the covid-19 pandemic. teachers and students often use whatsapp groups to give assignments or just provide youtube links already available on the internet and ask students to learn about it. so, it can be concluded that the learning media used has not been maximized. schools need to consider efforts and approaches to improve the quality of e-learning and the learning outcomes achieved (al-smadi et al., 2022). especially for mathematics, they were learning that students find challenging and cause students' grades to always be below the criteria of minimal completion. so that the design of teaching material products that are attractive, easy to understand, and can be studied anywhere, which is currently indispensable for students to learn remotely using e-learning-based teaching materials that are already well done and students feel interested. e-learning can be beneficial in mastering the material, which is expected to increase awareness that learning is essential and fun in mathematics subjects, will achieve maximum achievements and positively influence mathematics learning and even increase learning outcomes (utami & cahyono, 2020). in the second stage, the material in this study is statistics. statistics is the subject matter of mathematics related to data collection and concluding the results of observations in the field. statistics has become the basis for researchers, research, or observations in various fields of science (listiati, 2022). statistics material is significantly related to daily life. statistics will be needed by students, both in the field of work and in completing their studies. wahyuningrum (2020) states that by studying statistics, a person can explain the relationship between variables, make decisions for the better, overcome changes and make plans and predictions. therefore, the basic competence used is to determine and analyze the size of the centralization of data and the dissemination of data presented in frequency distribution tables and histograms. apart from that, by studying statistics, many students will be trained to think systematically, conscientiously, and understand more mathematical symbols, because many are faced with formulas and problems that are not routine. studying statistics will benefit students in their daily lives because statistics can be applied in everyday life. statistics are often used in everyday life, such as in the research of a study, and applied in disciplines such as astronomy, biology, economics, and industry (janna, 2020). the third stage is to identify the initial abilities of the students and the strategies used. at this stage, it is found that students' initial ability in mathematics is still low, both in terms of affective and cognitive. so, the right learning strategy uses the edmodo application, which can be accessed on mobile phones and computers and helps students learn independently from home. learning by using phones is used to access learning, materials, instructions, and questions related to student learning, when and wherever they want to learn (yunianta et al., supianti, yaniawati, osman, al-tamar, & lestari, development of teaching materials … 246 2019). edmodo's application can help students achieve affective and cognitive abilities for the better. the edmodo application is a digital application that looks very easy and simply because it is similar to social media applications. of course, students are used to social media. edmodo is a free and secure learning platform available on www.edmodo.com. this website looks similar to facebook but is much more private and safer for the learning environment (ompusunggu & sari, 2019). using the feature in edmodo encourages student involvement in responsible learning (balasubramanian et al., 2014). edmodo has complete learning features, including flowing features, a calendar, classes, discovery, and messages. thus, using edmodo can help teachers and students in learning activities carried out online can be more directed and organized. edmodo can help students in learning because edmodo is developed based on classroom management and social media principles. edmodo also makes it easier for teachers to track student abilities. grades and assignments are automatically stored in the system and easy to access (ekayati, 2018; hanifah et al., 2019; kristianti, 2016; putranti, 2013; wahyuni & sugiharta, 2019). the fourth stage is to formulate the developed procedure. at this stage is an explanation of the procedures for accessing edmodo. the first step that must be done is to create an account for both teachers and students and fill out the registration form and valid data. then the teacher arranges the edmodo account, such as forming classes according to the many classes taught and students joining the provided classes (ekayati, 2018). these steps are not an obstacle for students because students are used to accessing applications on the internet. however, when installing the application, some students experienced problems because their cellphone memory was full, so they could not install edmodo. however, this can be handled because creating an account on edmodo does not always have to install an application. edmodo can also be accessed from google directly. conditions like this do not hinder teaching and learning activities because students of any type now enjoy technology and are familiar with it (kristianti, 2016). overall, students feel that they do not mind learning using edmodo. even students feel happy because the learning process in edmodo is easy to access. so, it requires careful preparation when using the edmodo application. the use of edmodo requires training for students starting from how to use and create accounts, class codes, how to access materials, and abilities that students must have when using the edmodo application (sari, 2015). the fifth stage is to develop relevant research instruments. at this stage, the instrument developed is a question of mathematical literacy ability consisting of 6 questions in the form of a description, each question made based on indicators and levels of mathematical literacy ability. karmila (2018) state that indicators of mathematical literacy ability are level 1 students that can use knowledge to solve routine problems and problems with a general context. level 2 students can interpret problems and solve them with formulas. level 3 students can carry out procedures well in solving problems and can choose problem-solving strategies. level 4 students can work effectively with models, choose and integrate different reprints, and connect with the real world. level 5 students can work with models for complex situations as well as be able to solve complex problems. level 6 students can use their reasoning to solve mathematical problems and generalize, formulate, and communicate their findings. the question was compiled by the researcher and assessed by the supervisor, and has been tested. the results of the question trial based on statistical processing and mathematical literacy ability are feasible for field trials. the sixth stage is the components of this e-learning-based teaching material which consists of twelve components. the essential components of e-learning-based teaching materials are an attractive appearance, a display filled with many interesting images, colors, and animations, and explicit material content and contents that make it easier for students to volume 11, no 2, september 2022, pp. 237-254 247 understand learning material. because with teaching materials that follow what is needed by students, learning will be enjoyable and can help achieve learning goals very well. the elearning system requires technological support in the digital era as a mechanism and exciting content (elyas, 2018). the use of videos and files uploaded to edmodo's account makes students more enthusiastic about learning (hanifah et al., 2019). the seventh stage is the established strategy and the abilities to be improved. based on the results of the validation of teaching materials, it produces teaching materials worthy of trial with an outstanding level of validity. going through the validation stages of teaching materials will make the developed teaching materials very good and get various criticisms and suggestions from validators that will help improve teaching materials. validity determines the quality of the teaching materials, and it will be seen what should be measured (azis, 2019). the eighth stage is the trial stage of e-learning-based teaching materials to students who are used as research samples. eight meetings have been held in the field trial stage; the learning was carried out online and through the edmodo application. the first meeting was with the giving of pretests to students. the second to the seventh meeting is giving materials and quizzes from each sub-topic, consisting of 3 sub-topic. moreover, the eighth meeting was the giving of the post-test. the teaching materials that are compiled must be excellent and correct because teaching materials are an essential part of learning. through teaching materials, students will be more helpful and easy to learn (magdalena et al., 2020). according to students, the results of interviews using google forms by learning to use edmodo-based e-learning teaching materials throughout the secular state that the appearance is attractive, reasonable, understandable, concise, and straightforward. then based on the material's content, teaching materials are straightforward to understand but problematic when faced with complex calculations. most students feel happy learning with this elearning-based teaching material because it is straightforward to understand and understand. e-learning-based learning can improve maximum learning outcomes (hartanto, 2016). the last stage is inputs on the improvement of teaching materials rather than validators that the teaching materials that have been prepared have several inputs. first, the teaching materials covered should be given authentic images of the material discussed in the media. the second is to include indicators in each discussion so that students know what should be achieved in the learning process. researchers have tried to improve the results of these inputs and produce suitable teaching materials. based on all the stages that have been carried out, the design of the developed teaching materials for statistics based on e-learning is assisted by edmodo. teaching materials are prepared by paying attention to the components of teaching materials suitable for e-learning-based. teaching materials can be accessed through the edmodo application easily. the teaching materials developed have gone through the validation stage by expert validators, media, and teachers so that teaching materials have good validity with excellent categories and can be used in the learning process for students. e-learning can make students access teaching materials or structured assignments independently without being limited by distance and time. however, in this case, there are also several obstacles faced in learning mathematics using e-learning media related to how difficult the material is to deliver because some materials are not easy to deliver, even face to face (hulukati et al., 2021). mathematical literacy ability refers to the pisa mathematical literacy ability level (karmila, 2018), which consists of 6 levels. at level 1, with mathematical literacy skills, students can use their knowledge to solve routine problems and problems with general contexts. most students can solve this problem well because, with their knowledge, students are asked to make data, and the data created by themselves must be processed so that the answers that arise from students will, of course, be different. a small part of there are supianti, yaniawati, osman, al-tamar, & lestari, development of teaching materials … 248 students who do not finish working on the problem, and some students suddenly make the final result in the form of a frequency distribution table. students can guess the answer, or students forget how to solve it. in addition, the lack of students in solving these problems is that students do not provide conclusions on the answers that have been made. this situation happens based on the results of the researchers' analysis; students may forget, or students are not accustomed to making conclusions outlined in written form. according to pisa, students' mathematical literacy achievement is concerning; 42.3% of students have not reached level 1 of the lowest proficiency (styawati & nursyahida, 2017). therefore, here the role of the teacher is needed to continue to train students so that their mathematical literacy skills develop to the maximum. level 2 literacy skills, namely interpreting problems and solving them and solving them with formulas, some students have been able to solve this problem, read the problem, and change it into a mathematical context well so that students can solve the problems faced. students can change the data presented as a bar chart into a frequency distribution table which is then searched for the mode value of the question posed. however, as in the case of mathematical literacy skills at level 1, students do not give conclusions at the end of their answers. at level 3 literacy skills, namely carrying out procedures well in solving problems and choosing problem-solving strategies, students are given questions about a table containing information about reports of visitors to a swimming pool. in this question, students' answers can vary depending on which side the student will answer. because what is being asked in this question are deciles, students can answer deciles 1, 2, 3, 4, or 5 so that the answer can be five alternatives. most of the students also have solved this problem well, can read the data, and complete what is asked in the question. however, it remains the same as the level 1 and 2 mathematical literacy skills. students do not provide reviews or conclusions from the results of their calculations. level 4 literacy skills can work effectively with models, choose and interpret different representations, and then relate them to the real world. mathematical literacy in learning mathematics in pisa develops competencies directly related to the real world (umbara & nuraeni, 2019). the oecd states that mathematical literacy can help someone understand the role or use of mathematics in everyday life. in addition, mathematical literacy emphasizes the ability of students to analyze, give a reason and communicate ideas effectively in solving mathematical problems they encounter (muzaki & masjudin, 2019). some students have solved the questions given, but at level 4, some are wrong in the calculations. in this matter, accuracy is needed, and knowing the formula and how to calculate it must be used. because not a few students answered the questions, not to completion, and did not give conclusions at the end of their answers. at level 5 literacy skills, namely being able to work with models for complex situations and solving complex problems, and level 6, using reasoning in solving mathematical problems, making generalizations, and formulating and communicating findings. for this level, most students cannot solve this problem well. most of them are wrong in answering the questions given. the results of the 2012 pisa research state that none of the indonesian students can answer the pisa level 5 and level 6 questions (putra et al., 2016). based on the question posed is about the variance or variance and standard deviation, where the variance and standard deviation are related. meanwhile, the calculations require calculations that students feel to be very difficult because there are calculations with unmistakable signs, powers, and formulas that are difficult to remember. thus, mathematical literacy skills at levels 5 and 6 still need to be improved to achieve everything more optimally. based on mathematical literacy skills from level 1 to level 6 seen from the results of student work, the abilities that have been achieved are level 1 to level 4, meaning that volume 11, no 2, september 2022, pp. 237-254 249 students can use their knowledge to solve, interpret, and interpret problems to solve them with formulas. in addition, students can carry out procedures well in solving problems and choose strategies. students can work effectively with models and relate them to the real world. because students have not been able to achieve optimally at levels 5 and 6, it means that students have not been able to work with models with complex situations and have not been able to solve complex problems. then students have not been able to use their reasoning in solving mathematical problems, formulating and communicating their findings. mathematical literacy plays a vital role as a life skill. therefore, teaching mathematics in schools should aim to develop mathematical literacy and improve the ability of each student to use and apply mathematical knowledge to solve real-life problems or situations (sumirattana et al., 2017). mathematical literacy skills are essential because mathematical literacy is an individual's capacity to formulate, use, and interpret mathematics in various contexts. these skills include mathematical reasoning and using mathematical concepts, procedures, facts, and tools to describe, explain, and predict phenomena. these skills lead individuals to recognize mathematics's role in life and make sound judgments and decisions that are needed by constructive and reflective citizens (sari, 2015). mathematical literacy ability does not automatically grow in every child; it takes effort to grow these abilities. for example, literacy-based learning is one of the efforts that can be done. in addition to improving students' mathematical literacy skills, appropriate teaching materials are needed so that students are trained to solve mathematical literacy problems at a higher level by frequently practicing problem-solving (masfufah & afriansyah, 2021). 4. conclusion based on the processing results and findings in this study, the development of edmodo-assisted e-learning-based teaching materials is very valid and can be used in learning. the method of developing e-learning-based teaching materials uses the dick and carey model with the following stages: (1) identify the instruction goal, the existing teaching materials are not accompanied by animation and the e-learning learning media is not varied; (2) conduct instructional analysis, relevant knowledge is statistical material, because its application plays a vital role in everyday life; (3) identify entry behaviours, students have not been able to manage and regulate themselves in thoughts, feelings and behavior; (4) write performance objectives, formulate the ability to use edmodo application learning media; (5) develop criterion referenced test, it is necessary to develop relevant items that improve mathematical literacy skills; (6) develop an instructional strategy, teaching materials are arranged according to the e-learning component; (7) develop and select instructional materials, display of teaching materials that are arranged based on the provisions of developing teaching materials; (8) design and conduct formative evaluation of instructional, statistical teaching materials have been designed equipped with contextual problems, animations and exciting pictures; (9) revision instruction, improvement of teaching materials based on criticism and suggestions, and (10) design and conduct summative evaluation, making improvements to teaching materials to increase the effectiveness of teaching materials. statistics teaching materials based on e-learning assisted by edmodo give pretty good results on mathematical literacy skills, most students have achieved the minimum completeness criteria scores, and there is an increase in mathematical literacy skills in the medium category. these results cause by students that can use their knowledge to solve routine problems with general contexts, students can interpret problems with formulas, students can complete procedures well, and students can work effectively and integrate with supianti, yaniawati, osman, al-tamar, & lestari, development of teaching materials … 250 real problems. so that students feel more helpful in understanding the material and can follow the learning process well even though it is done online. acknowledgements the authors would like to thank the postgraduate of universitas pasundan and smk negeri 2 baleendah, who have given the 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(2019). development and comparison of mathematic mobile learning by using exelearning 2.0 program and mit inventor 2. infinity journal, 8(1), 43-56. https://doi.org/10.22460/infinity.v8i1.p43-56 https://doi.org/10.23969/symmetry.v6i1.3999 https://doi.org/10.22460/infinity.v8i2.p167-178 https://doi.org/10.33365/ji-mr.v1i1.252 https://doi.org/10.24256/jpmipa.v7i1.467 https://doi.org/10.21831/cp.v0i3.1137 https://doi.org/10.23969/pjme.v11i1.3691 https://doi.org/10.22460/infinity.v8i1.p43-56 supianti, yaniawati, osman, al-tamar, & lestari, development of teaching materials … 254 sebuah kajian pustaka: journal of mathematics education p-issn 2089-6867 volume 11, no. 2, september 2022 e–issn 2460-9285 https://doi.org/10.22460/infinity.v11i2.p193-210 193 effectiveness of flipped classroom model through multimedia technology in improving students’ performance in directed numbers haji muhamad hafizuddin haji mohamad ali, daniel asamoah*, masitah shahrill sultan hassanal bolkiah institute of education, universiti brunei darussalam, brunei darussalam article info abstract article history: received mar 20, 2022 revised apr 27, 2022 accepted may 04, 2022 the recent globalisation and the emergency of covid-19 require a teaching and learning environment that encourages the use of technology. through a mixed-method design and an action research approach, this study investigated the effectiveness of a flipped classroom model through multimedia technology in improving students’ performance in directed numbers, given the difficulty and misconceptions of students in this mathematical concept. a total of 30 year 9 students conveniently sampled from one of the secondary schools in brunei darussalam served as participants. the action taken involved a pretest, intervention, posttest, and interviews. the results of the paired sample t-test revealed that students’ performance in directed numbers significantly improved after the flipped classroom intervention. students had positive perceptions of the flipped classroom model as it encouraged their readiness, participation, and motivation. challenges such as time constraints and distractions when studying from home were reported. these results imply that amid covid-19, a flipped classroom through multimedia technology can be an effective and alternative way of teaching and learning directed numbers. it has the potential of encouraging student-centred learning and creativity, which are vital in teaching and learning mathematics. keywords: academic performance, brunei darussalam, directed numbers, flipped classroom model, multimedia technology this is an open access article under the cc by-sa license. corresponding author: daniel asamoah, sultan hassanal bolkiah institute of education, universiti brunei darussalam universiti brunei darussalam, bandar seri begawan, brunei darussalam. email: 20h9000@ubd.edu.bn how to cite: ali, h. m. h. h. m., asamoah, d., & shahrill, m. (2022). effectiveness of flipped classroom model through multimedia technology in improving student performance in directed numbers. infinity, 11(2), 193-210. 1. introduction education in the 21st century has witnessed several changes. approaches that encourage more student-centred compared to teacher-centred instruction continue to be developed and integrated into teaching and learning. globalisation, the development of technology, and the emergency of covid-19 have shown that traditional approaches to teaching and learning may not meet current educational needs and goals (jamil et al., 2022; https://doi.org/10.22460/infinity.v11i2.p193-210 https://creativecommons.org/licenses/by-sa/4.0/ ali, asamoah, & shahrill, effectiveness of flipped classroom model through multimedia … 194 shahrill, noorashid, et al., 2021; shahrill, petra, et al., 2021). this has called for a need to constantly create instructional environment that encourages the use of technology (bishop & verleger, 2013). in responding to the changing needs of education, one of the approaches that have attracted recent research attention is the flipped classroom model. baker (2000) introduced this approach to instruction as a component of blended and inquiry-based instruction. it is an approach in which homework and classroom activities are interchanged ash (2012), such that students study instructional materials at home with their peers and teachers, followed by the teacher giving feedback and engaging in directed conversations during class time (lin & chen, 2016; say & yildirim, 2020). it exposes the students to study and understand instructional materials out-of-classroom, and in the classroom, do activities that support learning with the help of the teacher (moravec et al., 2010). students mainly study and master instructional materials through multimedia technology by watching videos, listening to podcasts, and reading e-books (balu, 2020; dominic-ugwu & nonyelum, 2019). using a flipped classroom model is associated with high students’ performance, motivation and retention (busebaia & john, 2020; say & yildirim, 2020; sirakaya & ozdemir, 2018), and this is irrespective of subject areas and educational level (strelan et al., 2020). it promotes student-centred learning, leading to student engagement, active participation, and self-directed learning (pierce & fox, 2012; qader & yalcin arslan, 2019). students can learn instructional materials at their own pace, ensures effective use of classroom time because most of the instructional tasks are done by the students at home, and the classroom time is used to clarify the misconceptions of students (fulton, 2012; hew & lo, 2018; matzin et al., 2013). given that a flipped classroom model encourages collaboration among their peers, high-ability students can assist low-ability students in constructing their knowledge on a given topic (ferreri & o’connor, 2013; nielsen et al., 2018). using a flipped classroom model encourages students to think creatively within and outside the classroom (herreid & schiller, 2013). however, the approach to teaching and learning has some disadvantages. teachers are unable to know if students learned instructional concepts at home. the lack of internet and other devices such as mobile phones, tablets and computers that make learning possible are other notable challenges (jenkins, 2012). other demerits of the flipped model include the high cost that comes with technology and the failure to create an environment where students can ask questions when learning at home (jenkins, 2012). despite these demerits, a flipped classroom model inverts the traditional model of instruction. it has the possibility of increasing student readiness as the learning content is introduced to students before the physical class. this allows teachers more instructional time to guide students through practical, active, and innovative ways of learning. previous studies have emphasised the need to use multimedia technologies in flipped classrooms and provide the technical support needed for such multimedia (oliveira, 2018). integrating multimedia in flipped learning has gained considerable relevance in teaching and learning. therefore, previous research attempts have focused on technological and conceptual improvement in using a flipped classroom model, especially on monitoring student learning while they are at home (jovanović et al., 2017). a flipped classroom model does not necessarily need to be implemented in an online platform, as it can also be done using multimedia technologies where text, visuals, animation, video, and sound can be merged to improve teaching and learning (abdurasulovich et al., 2020). since multimedia triggers multiple senses of audiences at a time, using various media in a flipped classroom model can produce conclusive results in teaching and learning (rajendra & sudana, 2018; yohannes et al., 2016). using multimedia in a flipped classroom serves as a varied source volume 11, no 2, september 2022, pp. 193-210 195 of information for students, making learning content accessible to students based on their preferences (aprianto et al., 2020; cevikbas & kaiser, 2020). how multimedia is used in a flipped classroom model to meet student needs and how students handle multimedia resources are also essential to determine the success of the flipped classroom methodology. oliveira (2018), for example, indicated that flipping the classroom is not a sufficient condition for improvement in student learning and engagement. however, how instructional resources in different formats reach the students and how well students can understand such resources are relevant. although student perceptions about flipped learning model are generally positive, students who have positive perceptions are those who can access instructional materials on time and without difficulty. at the same time, they prefer traditional teaching methods that are more interactive and learner-centred compared to a flipped classroom model (oliveira, 2018; yohannes et al., 2016). to this end, this study investigates the effectiveness of using multimedia technology in a flipped classroom model in improving students’ performance in directed numbers. directed numbers or integers have both direction and size, with one direction being positive and the other negative. for example, in 4-(-3), both 4 and (-3) are directed numbers with the 4 and (-3) being positive and negative, respectively. having a sufficient understanding of these numbers are applicable in everyday life (fuadiah & suryadi, 2017). they are helpful in reading temperature. a temperature of (-10) degrees means that it is 10 degrees away from and less than 0, suggesting a high level of coldness compared to a temperature reading of 10 degrees. understanding directed numbers is also helpful in profit and loss. it helps to know how less or more can be done to achieve satisfactory results in all aspects of life. profit is denoted by positive numbers in business transactions, while negative numbers indicate losses. understanding directed numbers helps to check account balance (makonye & fakude, 2016). if money is added to one’s account and there are adequate funds in the account, it is denoted by a positive number. in contrast, money withdrawn from one’s account is represented by a negative number. in the health sector, directed number is also applicable. normal blood pressure will record a positive number, while blood pressure below normalcy can be negative. this suggests that directed numbers are significant in every life, and the failure of students to have a good understanding of such numbers may cause serious challenges when applying such numbers in their daily activities. students have inadequate understanding and several misconceptions, despite the relevance of directed numbers (bofferding, 2014; lamb et al., 2012; vlassis, 2008). mostly, they are unable to differentiate between a negative sign used as an operation and one used as a symbol (lamb et al., 2012). this creates difficulties for them when performing operations involving directed numbers. student difficulty in directed numbers and other mathematical concepts exists in brunei darussalam (hereafter referred to as brunei). previous research has consistently reported that students have difficulty understanding algebraic expressions, fractions, simultaneous, linear, and quadratic equations (chong et al., 2022; hamid et al., 2013; japar et al., 2021; johari & shahrill, 2020; rosli et al., 2020; sarwadi & shahrill, 2014; shahrill, 2018). in most studies, the predominant cause of low performance was attributed to factors such as over-reliance on past examination questions, anxiety and stress, and teaching approaches (latif, 2021; salam & shahrill, 2014; shahrill, 2018; zakaria et al., 2013) and inadequate understanding and misconceptions about directed numbers (levison, 2016). despite these gaps, interventions to improve students’ understanding and performance in directed numbers are scarce. therefore, this study that provides a flipped classroom intervention to evaluate its effectiveness in improving students’ performance in directed numbers is timely. for the studies that focused on secondary schools in brunei, emphasis was placed on geography ali, asamoah, & shahrill, effectiveness of flipped classroom model through multimedia … 196 (nawi et al., 2015) and history (latif et al., 2017). the paucity of studies that focused on secondary school mathematics did not consider directed numbers (manjanai & shahrill, 2016; toh et al., 2017). therefore, more studies are necessary to develop a more in-depth analysis of the effects of the flipped classroom model in the teaching and learning of secondary school mathematics. this present study provides a flipped classroom intervention to assess its efficacy in improving student performance in directed numbers using secondary school students in brunei. the following research questions were answered: (1) what is the effectiveness of a flipped classroom model through multimedia technology in improving students’ performance in directed numbers? (2) how do students perceive a flipped classroom model through multimedia technology as an instructional option? 2. method this study adopted a mixed-method design with an action research approach where both quantitative and qualitative data were collected sequentially (creswell & creswell, 2017). the quantitative data were collected through achievement tests before the qualitative data, which was collected through interviews. since this study sought to provide a flipped classroom intervention to address student difficulty in directed numbers (avison et al., 1999; mertler, 2013), the action included a pretest, an intervention, and a posttest. through a conveince sampling, 30 year 9 students were selected. they were from one of the government secondary schools in the belait district of brunei. the selected school had two year 9 classes. class a consisited of 14 students (fiv