Infinity Journal of Mathematics Education p–ISSN 2089-6867 Volume 6, No. 1, February 2017 e–ISSN 2460-9285 DOI 10.22460/infinity.v6i1.236 77 THE ANALYSIS OF DIAGNOSTIC ASSESSMENT RESULT IN PISA MATHEMATICAL LITERACY BASED ON STUDENTS SELF-EFFICACY IN RME LEARNING Khaerunisak 1 , Kartono 2 , Isti Hidayah 3 . Ahmad Yusril Fahmi 4 1 Universitas Selamat Sri, Kendal East Java, Indonesia 2,3 Mathematics Education Semarang State University, Semarang East Java, Indonesia 4 Teacher MTs Walisongo, Pekalongan East Java, Indonesia 1 igetmydreams@yahoo.co.id, 2 pakarunnes@yahoo.com, 3 isti.hidayah@yahoo.com, 4 fahmiahmad@madrasah.id Received: January 2, 2017 ; Accepted: January 29, 2017 Abstract This research aimed to test RME learning with an effective scientific approach to improving mathematical literacy and self-efficacy, obtaining an overview of the mathematical literacy diagnostic assessment results that has high, medium and low self-efficacy as well as student difficulties in learning RME with a scientific approach. This research using mix method concurrent embedded with the subject of research is students class VIII. The research begins with a mathematical literacy diagnostic assessment and self-efficacy inventory then performed RME learning in experimental class and conventional learning in control class. Quantitative analysis was conducted to test the effectiveness of learning and deepened with the interview as a qualitative analysis. Learning RME with a scientific approach effective is marked by the achievement of classical completeness, the proportion of students' mathematical literacy, self-efficacy and the difference in pre-post students’ mathematical literacy on RME learning better than conventional learning. The results of students’ mathematical literacy diagnostic assessment fit the criteria of self-efficacy students except for medium mathematical literacy that having high self-efficacy. Student difficulties in RME learning with the scientific approach are based on the results of mathematical literacy diagnostic assessment, namely language skills problem, the capacity to understand, create strategies, and create the algorithm. Keywords: Mathematics Literacy, Self-efficacy, RME, Diagnostic Abstrak Penelitian ini bertujuan untuk menguji pembelajaran RME dengan pendekatan saintifik efektif meningkatkan literasi matematika dan self-efficacy, memperoleh gambaran hasil penilaian diagnostik literasi matematika yang memiliki self-efficacy tinggi, sedang dan rendah serta kesulitan siswa dalam pembelajaran RME dengan pendekatan saintifik. Metode penelitian ini menggunakan mix method cuncurrent embbeded dengan subyek penelitian siswa kelas VIII. Penelitian diawali dengan penilaian diagnostik literasi matematika dan inventori self-efficacy selanjutnya dilakukan pembelajaran RME pada kelas eksperimen dan pembelajaran konvensional pada kelas kontrol. Analisis kuantitatif dilakukan untuk menguji keefektifan pembelajaran. dan diperdalam dengan wawancara sebagai analisis kualitatifnya. Pembelajaran RME dengan pendekatan saintifik efektif ditandai dengan tercapainya ketuntasan klasikal, proporsi literasi matematika siswa, self-efficacy siswa dan selisih literasi matematika awal-akhir pada pembelajaran RME lebih baik daripada pembelajaran konvensional. Hasil penilaian diagnostik literasi matematika siswa sesuai kriteria self-efficacy siswa kecuali untuk literasi matematika sedang yang memiliki self-efficacy tinggi. kesulitan siswa dalam pembelajaran RME dengan pendekatan saintifik berdasarkan hasil penilaian diagnostik literasi matematika, yakni kesulitan kemampuan bahasa, kemampuan memahami, membuat strategi, dan membuat algoritma. Kata Kunci: Literasi Matematika, Self-efficacy, RME, Diagnostik Khaerunisak, Kartono, Hidayah & Fahmi, The Analysis of Diagnostic Assesment … 78 How to Cite: Khaerunisak, Kartono, Hidayah, I. & Fahmi, A. Y. (2017). The Analysis of Diagnostic Assesment Result in Pisa Mathematical Literacy Based on Students Self-Efficacy in RME Learning. Infinity, 6 (1), 77-94. INTRODUCTION Education has an important role in educating the human resources to be able to compete globally in the development of science and technology. This is in accordance with national education goals outlined in ACT Number 20 Year 2003 on National Education System. Through education, students are equipped with knowledge and skills needed in school and its application in real life. Students have certain aspects that can be measured and the results can provide useful information for improving the quality of education through the study. For example, the study Programme for International Student Assessment (PISA), the international literacy study is a form of skills and knowledge evaluation that are designed for students aged 15 years, were carried out every 3 years under the auspices of the Organization for Economic Co-operation and Development (OECD). PISA aims to assess the 15-year-old students in OECD countries and other countries in the achievement of reading proficiency, mathematics literacy, and science to make a contribution towards its member of his country (Wilkens, 2011). The results of PISA study in 2003, Indonesia was ranked 39 out of 40 countries and the following year was also not encouraging. PISA results in 2009 showed that the mathematics literacy score for Indonesia students ranked 61 out of 65 participating countries and the results of the latest PISA in 2012, Indonesia was ranked 64 out of 65 survey participants countries. Although the results of PISA 2015 have elevated points with Indonesia was ranked 64 out of 72 countries. This indicates a mathematical literacy SMP/MTs students in Indonesia is still low. According to Dzulfikar, Asikin & Hendikawati (2012), mathematical subjects for many students still considered as a difficult lesson, scary, and less useful in everyday life, such as for many students a math lesson seemed difficult and unattractive. This case makes many students became less motivated to learn math and have an impact on student difficulties in solving mathematical problems caused by the inability of students to understand or remember the basic concepts of mathematics ever learned before. Particularly with the condition of students in Indonesia are not familiar with modeling form question, which requires the ability to translate everyday problems in the form of formal mathematics to completing it. Thus, students’ mathematical literacy skills need to be cultivated so that the result of student learning outcomes increased in mathematics learning. Cases that are often encountered by mathematics teachers, especially in SMP N 2 Wonopringgo, many students have not reached the minimum completeness criteria in math tests despite being held remedial against students who do not achieve completeness. Based on the interview with one mathematics teacher at SMP N 2 Wonopringgo, the percentage of students who scored pure mathematics in daily tests above 67 is not more than 25%. Thus, the proportion of students who achieve completeness learning is still low. This occurs when students are faced with a math problem associated with real problems, students have difficulty in interpreting the real problems into mathematical models or can be said mathematical literacy SMP students is low. Volume 6, No. 1, February 2017 pp 77-94 79 Student difficulties in interpreting the real problem into a mathematical model needed to be diagnosed the source of the problem and held a follow-up to resolve the issue. One of them by having a diagnostic assessment. The diagnostic assessment in the form of diagnostic tests are given to know the strengths and weaknesses in learning (Hughes in Suwarto, 2013) so that learning can be improved and the learning objectives are achieved. Sion & Jingan (Suwarto, 2013) States the diagnostic test as a test that provides information to teachers on students' prior knowledge and misconceptions before starting the activity. With the diagnostic assessment can know things that need to be repaired and improved and things that need to be maintained in the implementation of learning. Assessment obliges teachers to gather information as complete as possible for the purpose of decision making of teaching so that teaching decisions can be precisely targeted, one of them is diagnostic assessment (Hidayat, Sugiarto & Pramesti, 2013). According to Shute, Graf & Hansen (2006) There are three aspects in the diagnostic evaluation that includes diagnostic process of determining the nature of a child's ability in a learning activity, the diagnostic process should be able to classify the students' cognitive abilities, diagnostics is part of a larger learning process with the main aim to identify problems and help overcome learning problems. Based on the results of diagnostic assessments, needs to be followed in determining the strategies and appropriate learning methods about mathematical literacy. Judging from the characteristics of mathematical literacy that is often associated with contextual issues appropriate if applied with a Realistic Mathematic Education (RME) learning. In addition to the application of RME, need to hold scaffolding for some students who do not meet the KKM. In this process, the teacher explains the material that has not been mastered by students without looking at the concepts, principles, and procedures that are not yet fully understood by students. The application of the scientific approach that adopted scientists measures to build knowledge through scientific methods, 2013 Curriculum can help students' skills in reasoning subject matter based on the evidence of the observable, empirical and measurable object. 2013 Curriculum were applied in SMP N 2 Wonopringgo because included in the pilot schools (pilot project) from Kemendikbud Pekalongan. RME learning can be applied at SMP 2 Wonopringgo due to suitable with curriculum 2013 regarding RME characteristics that in line with the character of a scientific approach (implementation of 2013 curriculum). The pessimistic tendency of students in learning mathematics because students' views of mathematics that are still considered difficult and scary subjects make the daunting obstacles when students solve a math problem. Students who thus have a timid soul, less bold in making decisions, and less daring responsible for the actions that have been carried out. Therefore, it takes a strong self-efficacy on students so that they can succeed in learning mathematics. Self-efficacy beliefs influence the choice of duty, endurance and persistence efforts and achievement. According to Hacket & Betz (Nicolaidou & Philippou, 2003) stated that the influence of self- efficacy on performance in mathematics as strong as the effect of general mental ability. Self-efficacy has an impact on motivation, so it is also related to the success of students. A student who has high self-efficacy, if given the learning they will be enthusiastic/strive to demonstrate its ability to achieve success or otherwise (Wigfield & Eccles, 2001). Many researchers report that self-efficacy (SE) students correlated with the construction of the motivation, performance and student achievement. One of them is research done by Zimmerman, Bandura & Martinez-Pons (1992), that self-efficacy influences academic Khaerunisak, Kartono, Hidayah & Fahmi, The Analysis of Diagnostic Assesment … 80 achievement directly by increasing the value of students interest. Pintrich and De Groot (1990) found that students who believe that they can perform academic tasks using cognitive and metacognitive strategies more and keep doing better than students who do not believe. Self-efficacy is making a difference in the way people act, as a follow-up of feelings and thoughts. People who believe that 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 one believes can perform the actions required by certain situation. Learning certainly requires the right strategy for learning optimally implemented. Although learning has been applied, the need for improvement of learning to optimize student learning outcomes, the next step to improve learning by taking into account the results of a diagnostic assessment of Realistic Mathematic Education (RME) learning approaches. RME developed by Hans Freudenthal have two views, i.e. mathematics must be connected to reality and mathematics as human activity (Gravemeijer in Tandililing, 2010). Based on that idea, mathematics should be close to the students and should be relevant to everyday life situations. The situation that is relevant to everyday life will help the learning process that is meaningful to students so that students were able to find their own concepts and ideas of mathematics, must be mapped. In addition, he also emphasizes that mathematics as a human activity, so students should be given the opportunity to learn to perform activities of all the topics in mathematics. As a consequence, teachers must be able to develop interactive teaching and give students opportunities to contribute to their learning process. In connection with the background that has been described, presented some of the research questions as follows: (1) Is the RME learning with scientific approach effective against to mathematical literacy and self-efficacy? (2) How do the results of the students' mathematical literacy diagnostic assessment in RME learning with scientific approach that has high, medium and low self-efficacy students? (3) How do the results of the students' mathematical literacy diagnostic assessment in conventional learning with a scientific approach that has high, medium and low self-efficacy students? (4) How is the student's difficulties on RME learning with a scientific approach based on the results of the mathematical literacy diagnostic assessment? METHOD This study is a combination of qualitative and quantitative research. Combinations model used in this study is the type of concurrent embedded strategy. In this study, quantitative research as the primary method while quantitative research as a secondary method. The population in this study were students of SMP Negeri 2 Wonopringgo the second semester of the academic year 2014/2015. From classes VIII in SMP Negeri 2 Wonopringgo 3 classes randomly selected as samples in accordance with the study design, the first experimental class, which in the classroom experiment applying the RME learning model. Secondly, the control class where the learning applying the learning model used by their teacher and the third is a trial class is a class that is used for the analysis of test trials. The scaffolding application is given when students are in the ZPD. It is aimed so that is actual ability can be increased to a potential ability. Determination of the students who are in ZPD area through the calculation of an average student and a standard deviation of class, with intervals of the mean-SD z_ (0.5-α), then the mathematics literacy of experiment class students reaches a minimum completeness criteria for more than 75%. Based on the calculation, the Khaerunisak, Kartono, Hidayah & Fahmi, The Analysis of Diagnostic Assesment … 88 value for z_value = 5.36. At α = 5% was obtained z_critical = 1.64. Because z_value> z_critical, then the proportion of mathematics literacy diagnostic test results experimental class students is better than the proportion of mathematics literacy diagnostic test of control class. Based on the calculation, the t¬value = 2.025 and t-critical = 1.67. Because 2.025>1.67 so t-value> t-critical. This information shows that self-efficacy of experiment class students better than the control class. t-value = 1.913 and t-critical = 1.67. Because t-critical > t-critical then the difference between preliminary and final mathematical literacy value of experimental class students better than difference between preliminary and final mathematical literacy value of control class. RME learning model with scientific approach effective against students' mathematical literacy. This is because (1) the percentage of students in RME learning has reached completeness, i.e. more than 75%; (2) the proportion of diagnostic mathematical literacy tests results of experimental class is better than the diagnostic mathematical literacy tests results of control class; (3) Students' self-efficacy of experimental class is better than self-efficacy of control class; and (4) the average difference between preliminary and final students' mathematical literacy of experiment class better than the control class. Figure 5. Photo of Application of Using Realistic Mathematics Education This study supports previous research including by Dewanto (2008) conveys that the higher the students' self-efficacy, the higher the multiple representations of its mathematical ability, meaning that self-assurance was positively correlated with mathematical ability. Stacey (2011) said that the additional reporting category of PISA 2012 will enhance the usability of the results for the development of public policy and provide further insight into mathematics learning in schools that are expected to affect the mathematical literacy ability. This is also consistent with Wardono and Mariani (2014) that the realistic learning device that innovative with character education and PISA assessment that has been developed can be categorized as valid, practical, and effective way to enhance the mathematics literacy problem solving of SMP students, as well as quality of learning categorized good and students' character rise better. According to Tarigan (2006), the general approach of RME is oriented approach towards the students' reasoning that are realistic and aimed at the development of practical mindset, logical, critical and honest with a math-oriented reasoning in solving a problem. With PMR model learning, students gave more positive response and can develop creative solution of a problem (Krismiati, 2013) and students understand mathematical concepts through the completion of a problem (Haji & Abdullah, 2015). Volume 6, No. 1, February 2017 pp 77-94 89 2. Qualitative Analysis Mathematical Literacy diagnostic test results and interviews were used to analyze mathematical literacy students based on self-efficacy is divided into 7 indicators, namely communication, mathematising, representation, reasoning and argument, devising strategies for solving problems, using formal and symbolic, technical language and operation, and using mathematics tools. Here is a snippet of the students' answers on RME learning indicating that the student E-17 has the poor mathematising ability and low self-efficacy. Figure 6. Sample of Matematising E-17 From Figure 6 it is shown that students E-17 less able to change the real world problems into mathematical form or just the opposite, namely students E-17 are less able to interpret a result or mathematical models into the original problem. Figure 10 is a snippet of the students' answers on RME learning indicating that the student E-04 has the good mathematising ability and medium self-efficacy. From Figure 10 shows that the students E- 04 capable of changing the real world problems into mathematical form or just the opposite, namely student E-04 is able to interpret the results or mathematical model to the original problem. Figure 7. Sample of mathematising E-04 Khaerunisak, Kartono, Hidayah & Fahmi, The Analysis of Diagnostic Assesment … 90 Figure 7 is a snippet of students' answers on RME learning indicating that the student E-13 has the good mathematising ability and high self-efficacy. From the figure is seen that students E-13 capable of changing the real world problems into mathematical form or just the opposite, namely student E-13 is able to interpret the results or mathematical model into the original problem. Figure 8. Sample of mathematising E-13 In RME learning, group of students who have low self-efficacy largely can not reach seven indicators of mathematical literacy and contains low mathematical literacy category anyway. For most of the students who have medium self-efficacy was reached seven indicators of mathematical literacy, it's just only in his achievements on each indicator is insufficient e.g. in the achievement indicators number 6, students who have medium self-efficacy has reached indicator number six but could not understand between relationship of problem context with problem representation. medium self-efficacy was having medium mathematical literacy category and can only achieve level 3, while most of the students who have high self-efficacy has reached maximum seven mathematical literacy indicators. High self-efficacy has medium and high mathematical literacy and has reached level 5. In the study by Collins (Mukhid, 2009) about self-efficacy revealed that children that mathematical capable, has stronger self-efficacy beliefs. The same was stated by Somakim (2011) says that there is significance in increasing students' mathematical self-efficacy ability between learning using realistic mathematics approach and usual mathematical approach. Additionally, Dzulfikar (2013) shows that the importance of mathematically self-efficacy to be owned by each student is also mandated in the purpose of mathematics courses given to students is that they have respect for the usefulness of mathematics in life, i.e. have curiosity, attentive, and interest in learning mathematics, as well as a tenacious attitude and confidence in problem solving. Peters (2013), show that students who have high self-efficacy also have high mathematics achievement. Mathematical literacy in conventional learning, where the conventional application of the model in question is the Discovery Learning. Discovery Learning (DL) can be applied to achieve mathematical literacy, just not so recommended to be applied in improving mathematical literacy because it's should be applied for higher education. The results of this Volume 6, No. 1, February 2017 pp 77-94 91 study support previous research conducted by Alfieri, Brooks, Aldrich & Tenenbaum (2011) in his research, he mentions that the DL model has the potential formation of misconception, because when students were left to find the information or facts and new knowledge itself, it is feared the lesson will undergo a series of mistakes, misconceptions, making them frustrated and confused about what is being studied. Discovey Learning also has the potential formation of cognitive overload (make it difficult for students who need more structured learning). It is accordingly presented by Kirschner, Sweller & Clark (2006) says "Cognitive load theory suggests that the free exploration of a highly complex environment may generate a heavy working memory load that is detrimental to learning". In the control class, group of students who have low self-efficacy largely can not reach all mathematical literacy indicators. Most of the students in this category still find it difficult to accept and act upon the given question. Low self-efficacy had lower math literacy category anyway and can only reach level 1 but some are not reaching the level of mathematical literacy. For medium self-efficacy, most of the students have achieved four of the seven mathematical literacy indicator are met with good although even in the achievement of the indicators of mathematical literacy is still less than the maximum. The results of his work looks less clear and not easy to understand. Medium elf-efficacy had medium mathematical literacy category and can reach level 3 but some are not reached the mathematical literacy level. For high self-efficacy, some defecate students who have high self-efficacy has achieved some mathematical literacy indicators properly. In this category students can provide answers and acceptable solution although less than perfect. High self-efficacy has medium or and low mathematical literacy category can only reach level 2. Diagnostic tests in this research also used to analyse the students difficulties. Four student difficulties in RME learning with scientific approach based on the results of the diagnostic assessment of mathematical literacy in each category of self-efficacy. First, the difficulty the ability to translate problems into mathematical language occurred in the group of students who have low self-efficacy. The reason is that students are less careful in reading the questions and students are less careful in expressing information that exists on the question, not uncommon among them did not write down any information that known from question given by teachers. Second, the ability to understand the difficulties occurred in the group of students who have low self-efficacy. Most of them are less able to write formulas or concepts used in determining the answer to the given question. The reason is that students do not understand the explanation given. Third, the difficulty in the ability to make the strategy happen on a group of students who have low and medium self-efficacy. The reason is that students do not understand the concepts and principles that have been studied and students are less thorough in completing the answer. Fourth, difficulties in the ability to perform troubleshooting steps occurred in the group of students who have low and medium self- efficacy. The reason is that students are less scrupulous and often students do not write a conclusion on the results of the answer, he just wrote the final results of the calculation operation. This is in line with previous studies, namely Hidayat, Sugiarto & Pramesti (2013) states that one of the common mistakes student made in solving the question is a misconception, meanwhile Satoto, Sutarto & Pujiastuti (2012), which also states that the mistakes of understanding the problem is a common mistakes made by students. (3) ability to create strategies/identify the stages of problem solving (strategy knowledge). The reason is that students do not understand the concepts and principles that have been studied and students are less thorough in completing the answer. (4) ability to carry out stages problem solving Khaerunisak, Kartono, Hidayah & Fahmi, The Analysis of Diagnostic Assesment … 92 (algoritmic knowledge). The reason is that students are less scrupulous and often students do not write a conclusion on the results of the answer, he just wrote the final result of the calculation operation. CONCLUSION RME Learning with scientific approach proven effective to mathematical literacy and self- efficacy. The results of the mathematical literacy diagnostic assessment fit the criteria of students' self-efficacy except for middle mathematical literacy that having high self-efficacy. Students' self-efficacy need to be inculcated through the creation of environmental conditions that are responsive and personal approach to students. Mathematical literacy is one of the most important skills in learning mathematics. Students' Mathematical literacy are not directly grown well and needed proper exercise to train this ability to develop properly. One way to practice math literacy and create a responsive environment is to adopt RME learning with scientific approach. 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