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.p21-30 21 THE EFFECTIVENESS OF REALISTIC MATHEMATICS EDUCATION TO IMPROVE STUDENTS’ MULTI- REPRESENTATION ABILITY Muhtarom* 1 , Nizaruddin 2 , Farida Nursyahidah 3 , Nurina Happy 4 1,2,3,4 Universitas PGRI Semarang Article Info ABSTRACT Article history: Received Sept 30, 2018 Revised Jan 28, 2019 Accepted Jan 30, 2019 This research aimed to evaluate the effectiveness of Realistic Mathematics Education (RME) to improve students' multi-representation ability. A quasi- experimental design was used in this research. Sixty-four samples from the seventh-grade students of Junior School were randomly selected and divided into two classes: experimental class was treated using RME and control class was treated using conventional learning, with each class consisting of thirty- two students. The essay test was used to measure the multi-representation ability of students and the questionnaire was used to measure students' responses in RME learning. The data from the essay test were analyzed by N-Gain test and t-test in which normality and homogenity test were conducted previously, while the students' learning completeness and student responses were presented descriptive quantitative. The result of the research concluded that the multi-representation ability of students who get RME learning is better than the multi-representation ability in students who get conventional learning. 87.25% of students who get RME learning with the developed device have completed the KKM, and many students are very enthusiastic and interested in RME based learning, thus increasing their learning spirit in a learning process. Keywords: Multi-Representation RME Copyright © 2019 IKIP Siliwangi. All rights reserved. Corresponding Author: Muhtarom, Departement of Mathematics Education, Universitas PGRI Semarang, Jl. Sidodadi Timur No. 24, Semarang, Indonesia. Email: muhtarom@upgris.ac.id How to Cite: Muhtarom, M., Nizaruddin, N., Nursyahidah, F., & Happy, N. (2019). The effectiveness of realistic mathematics education to improve students’ multi-representation ability. Infinity, 8(1), 21-30. 1. INTRODUCTION Guided discovery, didactic phenomenology, and the principle of mediation model are the three basic principles of Realistic Mathematics Education (RME). Lessons are developed through mathematical concepts that originate from the real world in accordance with the Indonesian cultural context. The selected context is easily recognized by the students and can be imagined by students, languages, and diagrams presented very clearly to provide support in the development of mathematical concepts (Sembiring, Hadi & Dolk, 2008). RME is more effective in improving student learning outcomes than conventional learning (Laurens et al., 2018; Ginting et al., 2018; Zakaria & Syamaun, 2017). Laurens et mailto:muhtarom@upgris.ac.id Muhtarom, Nizaruddin, Nursyahidah, & Happy, The effectiveness of realistic mathematics … 22 al. (2018) stated that Realistic Mathematics Education (RME) improve students’ mathematics cognitive achievement; improving the reasoning ability of elementary school student (Ginting et al., 2018) and improving students’ achievement and attitudes towards mathematics (Zakaria & Syamaun, 2017). However, this study has not focused on multi- representation skills of students. This is possible because learning tools that contain multiple representations trained to students are rarely found. Whereas RME should be developed in accordance with the needs of students there is no exception for the development of multi-representation skills of students (Sembiring et al., 2008). The development of multi-representation skills of students also reinforced by Neria & Amit (2004) study which states that only 153 students (44%) answered correctly with verbal representation, 131 students (37%) correctly answered with symbol representation. In addition, Nizaruddin, Muhtarom & Murtianto (2017) study states that the majority of students tend to use symbol representations to solve math problems, rather than using other representations. Even when using verbal representation, students find difficulties composing sentences while students have not been able to solve problems when using visual representations. Students are not able to accommodate to reconstruct their cognitive structure (Muhtarom, Murtianto & Sutrisno, 2017), including in the process of translation between representations. It shows that basically students still do not have multi- representation skills, students are still focused on one of the representations they think are suitable. Table 1. Focus of Multi-Representation Ability Representation Description Visual  The ability to represent data or information in the form of diagram, graphics or table.  Able to use visual representation to solve the problem.  Able to draw to clarify and facilitate its solution Verbal  Able to identify the problem based on data or given representation  Able to write the representation of given representation  Able to write steps of math problem solving Symbol  Able to make math equation or model from other given representation  Able to solve a problem by involving math expression (Milrad, 2002) On the other hand, Keller & Hirsch (1998); Bransford & Schwartz (1999) and Ainsworth (2006) strongly recommend a teacher to use more than one representation in the learning process of mathematics. The use of representations of more than one type at the same time is said to be multi-representation (Brenner et al., 1997). It is further emphasized that the ability of multiple mathematical representations is very important for students because they can develop mathematical concepts, relationships between concepts, using varied representations and help in communicating their way of thinking (NCTM, 2000). Hwang et al., (2007) divide the representations used in mathematics education into five types, i.e representations of real-world objects, concrete representations, symbol representations, verbal representations and visual representations. Among the five representations, the last three are more abstract and have higher difficulty levels. The representation of symbols is the skill of presenting the mathematical problems in the formula. the verbal representation is the skills of translating the nature and relationships in mathematical problems into the language or vowel, the visual representation is the skill of presenting math problems in pictures or graphs (Kaput & Romberg, 1999; Milrad, 2002). Volume 8, No 1, February 2019, pp. 21-30 23 Furthermore, these three representations will be the focus of this research, in which the description of each representation has been described in Table 1. Thus, RME-based devices containing visual representations, verbal representations and symbol representations were developed to facilitate different student learning styles. This representation begins with a realistic situation close to the student so that they can develop other representations. Students build their confidence in problem-solving (Muhtarom, Juniati & Siswono, 2017) through their chosen form of representation, fearlessness, and beliefs in explaining the answers (Supandi et al., 2018). RME-based devices are expected to contribute positively to students in gaining understanding of mathematics, improving learning interactions, and developing multi-representation capabilities. Based on the above description, the problem in this research are: a. Is there any difference in the multi-representation skills of students with RME and conventional learning? b. How is the mastery of students with RME and conventional learning? c. How is the improvement of multi representation skills of students with RME and conventional learning? d. How is the student's response to RME-based tools developed? 2. METHOD 2.1. General Background of Research The first stage of this research is the development of RME based learning tools that include lesson plans, modules based multi-representation, media, test description and student response questionnaire. The overall stages of this study use the concept of analysis, design, development, implementation, and evaluation (Almomen et al., 2016), in which the tools are developed based on local Indonesian wisdom and contain several mathematical representations. Figure 1 clearly outlines the stages of device development up to the evaluation of the effectiveness of RME learning tools developed. 2.2. Sample of Research The sample of this research consisted of sixty four students grade VII Junior school in Pati Regency of Central Java Province, Indonesia. The sample is divided into two classes: experimental class was treated using the RME learning and control class was given treatment using the existing Learning strategy (conventional learning), with each class consists of thirty-two students. The research sample was selected using cluster random sampling technique to ensure the objectivity of the research, avoiding bias in the research and giving equal opportunity to a group of students who were collected in the class to be a research sample. Prior to treatment, the researchers tested the normality by the Lilliefors method to ensure that the sample came from a normally distributed population, tested homogeneity with Bartlett's test to ensure that both homogeneous samples, and t-test to show that both samples had the same initial ability. Muhtarom, Nizaruddin, Nursyahidah, & Happy, The effectiveness of realistic mathematics … 24 Figure 1. Research Step 2.3. Instrument and Procedures The learning device developed include lesson plans, media, and RME-based modules. Prior to use, the device has been validated by three validators. They conclude that the device is eligible to use, in condition provided the text size should be enlarged. Furthermore, comments and suggestions from experts should be considered to improve the device so that the quality of media and RME module get better. The essay test is structured referring to the syllabus of mathematics subjects in the 2013 curriculum in which the solution uses visual, verbal and symbol representations. Researcher uses RME-based long questions to measure students' multi-representation skills in experimental and control classrooms. Prior to use, the test question has been validated by three experts, already said three lines above then tested to determine the reliability, level of difficulty and the differentiation of the item. The analysis of essay test instrument result is presented in Table 2 which clearly indicates that there are five items used as pre-test and post-test in this study. Table 2. Analysis of Essay Test Instrument Question Reliability Difficulty level Differentiation of item Remark r Criteria Score Criteria Score Criteria 1 0.65 Reliable 0.93 Easy 0.25 Enough Used 2 0.70 Medium 0.59 Good Used 3 0.71 Medium 0.43 Good Used 4 0.42 Medium 0.45 Good Unused 5 0.29 Difficult 0.54 Good Used Students only master one skill representation The need of learning material that triggers multi-representation Producing learning devices that improve students’ multi- representation ability (verbal, picture and symbol) Analysis Design Learning devices based on RME to improve students’ multi-representation ability Learning device validation based on RME, reliability instrument test; differentiate item test and difficulty instrument test RME modules validation RME media validation Questionnaire student’s response validation Applying learning devices based on RME at school Knowing the effectively of learning device based on developed RME Development Implementation Evaluation Volume 8, No 1, February 2019, pp. 21-30 25 Question Reliability Difficulty level Differentiation of item Remark r Criteria Score Criteria Score Criteria 6 0.24 Difficult 0.50 Good Unused 7 0.36 Medium 0.48 Good Unused 8 0.88 Easy 0.39 Enough Used Student responses are needed to analyze the readability of RME devices that have been made and to know how the students respond to the RME-based devices. Quantitative data scoring obtained from the results of the questionnaires using Likert scale. Before the questionnaire was used it was validated by three validators who concluded that the questionnaire was worth using. The prerequisite test includes the normality test and homogeneity test, which aims to find out the statistical tests to be used in the data analysis process. Parametric statistical tests are used if samples from classes with conventional learning and RME classes come from normally distributed populations, and the variance of both homogeneous groups. If the normality test requirement is not met, it will be used non-parametric statistical test. The t-test is used to find out whether there is a difference of mean of multi- representation ability between RME class and conventional class. The data tested is the post-test result, in the following way: H0 : the mean of multi-representation ability of RME class is less than the average of conventional class. Ha : the mean of multi-representation ability of RME class is better than the average of conventional class Students are said to master learning if they get multi-representation ability at the value of 75, and mastery learning is classically met if at least 85% of all students complete the study. 75 is the minimum criteria of mastery learning (MCML) established by the school (Hernawan, 2008). To calculate the improvement of students’ multi-representation skills before and after learning, it is calculated by the normalized gain formula (Meltzer, 2002), namely: scoretestprescoreidealmaksimum scoretestprescoretestpost )g(GainN    The result of N-Gain calculation then interpreted on Table 3. Table 3. N-Gain Representation (g) Amount of N-Gain (g) Interpretation g ≥ 0,7 High 0,3 ≤ g < 0,7 Medium g < 0,3 Low (Meltzer, 2002) After the questionnaire is completed by the students, then it is analyzed and counted in percent. To be able to provide meaning and decision making, the researcher uses the provision as an indicator of student responses presented in Table 4. Muhtarom, Nizaruddin, Nursyahidah, & Happy, The effectiveness of realistic mathematics … 26 Table 4. Percentage Range and Student Response Criteria Interval Criteria 81% - 100% Very enthusiastic and interested 61% - 80% Enthusiastic and interested 41% - 60% Quite enthusiastic and interested 21% - 40% Less enthusiastic and interested < 21% Not enthusiastic and interested (Arikunto, 2010) 3. RESULTS AND DISCUSSION 3.1. Results Table 5. Normality Test Result Learning strategy n Lobs Ltable Hypothesis Remark RME 32 0.149 0.157 H0 accept Conventional 32 0.148 0.157 H0 accept Table 5 presents that Lobs < Ltable, with α = 0.05 and n = 32. This means that sample from a class that uses conventional learning and a class that uses RME come from a normally distributed population. Table 6. Homogenity Test Result Learning strategy N varians Fobs Ftable Hypothesis Remark RME 32 80.32 0.883 1.822 H0 accept Conventional 32 71.35 Table 6 shows that Fobs = 0.883, and Ftable = 1.822, therefore H0 is accepted. It can be concluded that both goup varians are homogen. Table 7. The Results from the T-Test of The Post-Test Scores Learning strategy N mean tobs ttable Hypothesis Remark RME 32 80.78 3.296 1.99 9 H0 reject Conventional 32 73.59 Table 7 presents the result of t-test with the dependent variable is the students’ multi-representation ability. It is clear that there is a significant difference between the multi-representation ability of the students, where sp = 8.723, tobs = 3.296, with the value of v = 32 + 32 - 2 = 62 and α = 0.05, obtained t(0.05, 62) = 1.999; thus H0 is rejected. It means that the multi-representation ability of students who get RME learning is better than the multi-representation ability of students who get conventional learning. Student learning mastery is seen from the pre-test score taken before the students are given RME study, while post-test value is taken after students are given RME learning. Table 8 clearly shows the value of pre-test and post-test taken from both research classes. It is clear that the average post-test score is higher than the average pre-test. Related to the achievement of student learning, in the class with RME the percentage of students who achieve mastery of 87.25% which means that almost all students complete the KKM. While in the conventional learning class percentage of students who achieve completeness only amounted to 53.125%. Volume 8, No 1, February 2019, pp. 21-30 27 Table 8. Mean of Pre-Test, Post-Test, and Mastery Learning Percentage Learning strategy Mean Mastery learning Percentage Pre-test Post-test RME 45.47 80.78 87.25% Conventional 19.69 63.59 53.125% After getting the value of pre-test and post-test, then in each class is tested with N- Gain test which aims to see improvement of multi-representation ability of students. Table 9 provides an overview of the multi-representation skills of students on RME learning. Consider that the image representation increases by 0.74, the increase in verbal representation by 0.79 and the increase in symbol representation by 0.95 or the increase in the high category. Table 9. Improved Students’ Multi Representation Skill in RME Class Representation N-Gain Interpretation Visual 0.74 High Verbal 0.79 High Symbol 0.95 High Table 10. Improved Students’ Multi-Representation in the Conventional Class Representation N-Gain Interpretation Visual 0.50 Medium Verbal 0.25 Low Symbol 0.89 High Table 10 gives the depiction of students’ multi-representation skill improvement in conventional learning. It is seen that the picture representation improvement amounted 0.50 or categorized as medium improvement, verbal representation improvement amounted 0.25 and symbol representation improvement as much as 0.89. While the comparison of multi-representation capability improvement of each class is presented in Table 11. It shows that almost all students who get RME learning have improved their multi- representation ability. Table 11. Improved Students’ Multi-Representation Learning strategy N-Gain Interpretation RME 0.80 High Conventional 0.40 Medium The RME learning implemented in the experimental class is equipped with RME- based tools. As already described that this device has been validated and feasible to use. The results of the assessment of 32 students who received learning with RME-based tools showed that 87.5% or 28 students stated very enthusiastic and interested, and 4 students stated quite enthusiastic and interested in learning with tools based on RME, thus increasing the learning spirit in the learning process. Muhtarom, Nizaruddin, Nursyahidah, & Happy, The effectiveness of realistic mathematics … 28 3.2. Discussion Our preliminary analysis indicates that many students only mastered the representation of symbols in a math problem. Thus, teaching materials are needed that triggers the multi-representation abilities of students. This teaching material contains several representations (verbal, pictures and symbols) so that it is expected to be able to improve students’ multi-representation ability. The development of RME based learning tools that include lesson plans, modules based multi-representation, media, test description and student response questionnaires. The RME tools developed have been validated and declared feasible to be implemented in the learning process. The results showed that multi-representation ability in students who got RME better than the ability of multi-representation in students who received conventional learning. This indicates that the RME tools developed have been able to foster students' beliefs and confidence in the use of multiple representations to solve mathematical problems (Nizaruddin et al., 2017). Supporting the description is shown that 87.25% or almost all students who get RME learning with the developed device have completed the KKM as determined by the school that is the value of 75; this is inversely proportional mastery of students with conventional learning is only equal to 53.125%. Further data show that many students are very enthusiastic and interested in RME based learning, thus increasing their learning spirit in learning process. Furthermore, the implementation of RME has been able to improve the multi-representation ability of students, which is obtained by an increase of 0.8 with high category in the application of RME and only an increase of 0.4 in the moderate category on conventional learning. The number of representations students use to solve math problems is a reflection of their understanding of mathematical concepts and procedures (Brenner et al., 1997). The learning process begins using symbol representation, then using verbal and visual representations that help students in translating their representations. This is in line with the opinion of Keller & Hirsch (1998); Bransford & Schwartz (1999); Ainsworth (2006); and Hwang et al., (2007) saying that the use of more than one representation can avoid the limitations of one type of representation so as to build student understanding. During the student learning process in groups, students actively solve math problems, feel enthusiastic and more challenged to do using some kind of representation. Students actively develop an understanding of the concepts and their relationships so that they have multiple representational skills, and the multi-representation capabilities themselves can anticipate mistakes in understanding mathematical concepts (Hwang et al., 2007). This is shown when one group presents the results of the discussion, the others actively respond to what has been described; so that the mutual process of cooperative knowledge formation can be realized. While the conventional learning process shows students passively receive the knowledge described by teachers and students do not do the construction of knowledge (Muhtarom, Juniati & Siswono, 2017). Thus, students have been able to make different representations because they possess good mathematical knowledge and have knowledge of the kinds of representations as well as the nature of the relationships between their chosen representations (Janvier, 1987; Nizaruddin et al., 2017; Supandi et al., 2018), as was done during the process learning RME. 4. CONCLUSION Multi-representation-based RME is one of the main factors in improving students' ability in learning mathematics. This research shows the fundamental differences in the multi-representation skills of students who get RME lessons and students who get Volume 8, No 1, February 2019, pp. 21-30 29 conventional learning. Furthermore, RME learning by incorporating multi-representation is expected to be applied continuously by the teacher as an alternative in improving the quality of mathematics learning at school. Teachers need to be encouraged to always trill the ability of the representation, so that students are challenged to elicit multi- representation skills, especially in solving math problems. ACKNOWLEDGEMENTS We would like to thank the Rector of Universitas PGRI Semarang (UPGRIS) and the Dean of the Faculty of Mathematics Education, Natural Science, UPGRIS. REFERENCES Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and instruction, 16(3), 183-198. Almomen, R. K., Kaufman, D., Alotaibi, H., Al-Rowais, N. A., Albeik, M., & Albattal, S. M. (2016). Applying the ADDIE—analysis, design, development, implementation and evaluation—instructional design model to continuing professional development for primary care physicians in Saudi Arabia. Int J Clin Med, 7(08), 538-546. Arikunto, S. (2010). Prosedur Penelitian Suatu Pendekatan Praktek. Jakarta: Rineka Cipta. Bransford, J. D., & Schwartz, D. L. (1999). 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