Students Mathematical Representation Ability in Learning Algebraic Expression using Realistic Mathematics Education

Yuhasriati Yuhasriati, Rahmah Johar, Cut Khairunnisak, Ulya Rohaizati, Al Jupri, Tuti Zubaidah


Mathematical representation ability (MRA) is crucial in solving mathematical problems, particularly in the topic of algebraic expressions. However, some students struggle to grasp algebraic forms in real-world circumstances. Learning through realistic mathematics education (RME) using context is one of the learning approaches that could help improve students' MRA. The objective of this study was to assess students' MRA in learning algebraic expressions through realistic mathematics education. This research employed mixed-method research with a sequential explanatory design. The subjects of this study were 27 seventh-grade students from a junior high school in Banda Aceh, Indonesia. Data on students' MRA were gathered through written test and task-based interviews. The descriptive analysis of written test data revealed that students' average score is 3.6, which is considered low compared to the maximum score of 8. The majority of students (n=24) satisfied the visual indicators of MRA as they successfully drew the composite shape. Whereas the most challenging MRA aspect for students to master was symbolic representation, only a few students (n=6) could solve the problem related to the multiplication of algebraic expressions. Students’ learning loss in the prerequisites due to online learning during the Covid-19 outbreak was one cause of the students' low performance on MRA.


mathematical representation, algebraic expressions, realistic mathematics education

Full Text:



Aziz, T. A., Pramudiani, P., & Purnomo, Y. W. (2017). How do college students solve logarithm questions? International Journal on Emerging Mathematics Education, 1(1), 25.

Bal, A. P. (2015). Skills of using and transform multiple representations of the prospective teachers. Procedia - Social and Behavioral Sciences, 197(February), 582–588.

Baroudi, Z. (2006). Easing students’ transition to algebra. Australian Mathematics Teacher, The, 62(2), 28–33.

Brandell, G., Hemmi, K., & Thunberg, H. (2008). The widening gap—A Swedish perspective. Mathematics Education Research Journal, 20(2), 38–56.

Cai, J., & Lester Jr, F. K. (2005). Solution representations and pedagogical representations in Chinese and US classrooms. The Journal of Mathematical Behavior, 24(3–4), 221–237.

Chow, T.-C. F., & Treagust, D. F. (2013). An intervention study using cognitive conflict to foster conceptual change. Journal of Science and Mathematics, 36(1), 44–64.

Creswell, W. J., & Creswell, J. D. (2018). Research design: qualitative, quantitative and mixed methods approaches. Sage Publications, Inc.

Davidenko, S. (1997). Building the concept of function from students’ everyday activities. The Mathematics Teacher, 90(2), 144–149.

Egodawatte, G. (2011). Secondary school students’ misconceptions in algebra. University of Toronto, Toronto.

Fauzan, A., Musdi, E., & Yani, R. (2018). The influence of realistic mathematics education (RME) approach on students’ mathematical representation ability. 1st International Conference on Education Innovation (ICEI 2017), 173, 9–12. Atlantis Press.

Fitrianna, A. Y., Dinia, S., Mayasari, M., & Nurhafifah, A. Y. (2018). Mathematical representation ability of senior high school students: an evaluation from students’ mathematical disposition. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 3(1), 46–56.

Freudenthal, H. (1991). Revisiting mathematics education. China Lectures. Dordrecht, The Netherlands: Kluwer. In Springer. Dordrecht: Kluwer.

Goldin, G. A. (2020). Mathematical representations. In Encyclopedia of mathematics education (pp. 566–572). Springer.

Gravemeijer, K. P. E. (1994). Developing realistic mathematics education.

Greenes, C. E., & Rubenstein, R. (2008). Algebra and algebraic thinking in school mathematics, 70th yearbook. NCTM.

Hiebert, J., Stigler, J. W., Jacobs, J. K., Givvin, K. B., Garnier, H., Smith, M., … Gallimore, R. (2005). Mathematics teaching in the United States today (and tomorrow): Results from the TIMSS 1999 Video Study. Educational Evaluation and Policy Analysis, 27(2), 111–132.

Johar, R., Zubainur, C. M., & Khairunnisak, C. (2017). Pre-service teachers’ perception of democratic classroom in teaching multiplication through video. Applied Science and Technology, 1(1), 273–278.

Jupri, A., Drijvers, P., & van den Heuvel-Panhuizen, M. (2014). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal, 26(4), 683–710.

Kemendikbud. (2021). Dampak negatif satu tahun pjj, dorongan pembelajaran tatap muka menguat.

Khairunnisak, C., Johar, R., Zubainur, C. M., & Sasalia, P. (2021). Learning trajectory of algebraic expression: supporting students ’ mathematical representation ability. 13(4), 27–41.

Knuth, E. J., Alibali, M. W., McNeil, N. M., Weinberg, A., & Stephens, A. C. (2005). Middle school students’ understanding of core algebraic concepts: Equivalence & Variable. Zentralblatt Für Didaktik Der Mathematik, 37(1), 68–76. Retrieved from

Laurens, T., Batlolona, F. A., Batlolona, J. R., & Leasa, M. (2017). How does realistic mathematics education (RME) improve students’ mathematics cognitive achievement? Eurasia Journal of Mathematics, Science and Technology Education, 14(2), 569–578.

Mainali, B. (2021). Representation in teaching and learning mathematics. International Journal of Education in Mathematics, Science and Technology, 9(1), 0–21. Retrieved from

Marpa, E. P. (2019). Common errors in algebraic expressions: a quantitative-qualitative analysis. International Journal on Social and Education Sciences, 1(2), 63–72.

Minarni, A., Napitupulu, E., & Husein, R. (2016). Mathematical understanding and representation ability of public junior high school in North Sumatra. Journal on Mathematics Education, 7(1), 43–56.

NCTM. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.

Norton, S., & Irvin, J. (2007). A concrete approach to teaching symbolic algebra. Proceedings of the 30th Annual Conference of the Mathematics Education Research Group of Australasia, 2, 551–560.

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 Journal, 9(2), 173–182.

Panasuk, R. M., & Beyranevand, M. L. (2011). Preferred representations of middle school algebra students when solving problems.

Pape, S. J., & Tchoshanov, M. A. (2001). The role of representation (s) in developing mathematical understanding. Theory into Practice, 40(2), 118–127.

Putra, I. P. (2021). Pandemi, Kemendikbud akui terjadi learning loss di sekolah. Retrieved from

Rasmussen, C. L., & King, K. D. (2000). Locating starting points in differential equations: A realistic mathematics education approach. International Journal of Mathematical Education in Science and Technology, 31(2), 161–172.

Roubíček, F. (2006). Variety of representational environments in early geometry. Proceedings of the 30th Conference of International Group for the Psychology of Mathematics Education, 321. Czech Republic: ERIC.

Rudyanto, H., Marsigit, M., Wangid, M., & Gembong, S. (2019). The use of bring your own device-based learning to measure student algebraic thinking ability. International Journal of Emerging Technologies in Learning (IJET), 14(23), 233–241.

Sari, D. P., Darhim, & Rosjanuardi, R. (2018). Errors of students learning with react strategy in solving the problems of mathematical representation ability. Journal on Mathematics Education, 9(1), 121–128.

Sarimanoğlu, N. U. (2019). The investigation of middle school students’ misconceptions about Algebra. Studies in Educational Research and Development, 3(1), 1–22.

Stacey, K., & Chick, H. (2004). Solving the problem with algebra. In The Future of the Teaching and Learning of Algebra. The 12th ICMI Study (pp. 1–20). Springer.

Stacey, K., & MacGregor, M. (1994). Algebraic sums and products: Students’ concepts and symbolism. Proceedings of the 18th International Conference for the Psychology of Mathematics Education, 43, 289–296.

Supandi, S., Waluya, S. B., Rochmad, R., Suyitno, H., & Dewi, K. (2018). Think-Talk-Write model for improving students’ abilities in mathematical representation. International Journal of Instruction, 11(3), 77–90.

Thompson, D. R., & Chappell, M. F. (2007). Communication and representation as elements in mathematical literacy. Reading and Writing Quarterly, 23(2), 179–196.

Treffers, A. (1987). Three dimensions: A model of goal and theory description in mathematics instruction—The Wiskobas Project (Vol. 3). Reidel Publishing Company.

Usiskin, Z. (1995). Why is algebra important to learn. American Educator, 19(1), 30–37.

Witzel, B. S., Mercer, C. D., & Miller, M. D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research & Practice, 18(2), 121–131.

Yasseen, A.-R., Yew, W. T., & Meng, C. C. (2020). Misconceptions in school algebra. International Journal of Academic Research in Business and Social Sciences, 10(5), 803–812.



  • There are currently no refbacks.

Copyright (c) 2022 Rahmah Johar, Yuhasriati Yuhasriati, Cut Khairunnisak, Tuti Zubaidah, Ulya Rohaizati

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Jurnal Didaktik Matematika

ISSN 2355 – 4185 (print) | 2548 – 8546 (online)

Published by:

Master Program of Mathematics Education incorporated with Himpunan Matematika Indonesia (Indonesian Mathematical Society/IndoMs)

Faculty of Teacher Training and Education

Universitas Syiah Kuala

Darussalam, Banda Aceh, Indonesia - 23111

Website : 
Email     : 

Creative Commons License

Jurnal Didaktik Matematika by Program Studi Magister Pendidikan Matematika FKIP Universitas Syiah Kuala is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at