Jurnal Riset Pendidikan Matematika


Proportional reasoning, proportion problem, direct proportion, inverse proportion, mathematics learning

Document Type



This study aims to describe proportional reasoning skills and students' difficul­ties in solving proportional reasoning problems. The population of this research was 3480 seventh-grade students of state junior high schools in the Yogyakarta region. The samples were 158 students chosen using proportionate stratified random sampling that represent four categories of school (very high, high, me­dium, low) based on the average scores of the national examination in mathe­matics in 2016. Data were collected through essay tests and interviews. Data were analyzed quantitatively and qualitatively. The result showed that the stu­dents in very high and high category schools had moderate proportional rea­soning ability. Students in medium and low category schools had low propor­tional reasoning ability. Students' difficulties in solving proportional reasoning problems vary based on the type of the problem, such as the difficulty in finding the multiplicative relationship contained in the problem, the difficulty in under­standing the value of inverse proportion, and the difficulty in explaining the obtained solution of the problems.

Page Range

22 - 32





Digital Object Identifier (DOI)





Aryvaty, A., & Saputra, C. (2013). Pengaruh model pembelajaran berbasis masalah (PBM) terhadap kemampuan penalaran proporsional siswa sekolah menengah pertama [The effect of problem-based learning model on the proportional reasoning ability of junior high school students]. Jurnal Pendidikan Matematika, 4(1), 61-72. https://doi.org/http://dx.doi.org/10.36709/jpm.v4i1.2002

Azwar, S. (2015). Tes prestasi, fungsi dan pengembangan pengukuran prestasi belajar [Achievement test, function and development of learning achievement measurement]. Pustaka Pelajar.

Ben-Chaim, D., Keret, Y., & Ilany, B. S. (2012). Ratio and proportion. Sense Publishers.

Carney, M. B., Hughes, G., Brendefur, J. L., Crawford, A., Totorica, T., & Smith, E. (2015). Analysis of students' proportional reasoning strategies. The 37th Annual Conference of the North American Chapter of International Group for the Psychology of Mathematics Education, March 2016. https://scholarworks.boisestate.edu/cifs_facpubs/156/

Creswell, J. W., & Plano-Clark, V. L. (2011). Choosing a mixed methods design. Designing and Conducting Mixed Method Research, 2, 53-106. https://www.sagepub.com/sites/default/files/upm-binaries/10982_Chapter_4.pdf

Dooley, K. B. (2006). An investigation of proportional thinking among high school students [Doctoral dissertation, Clemson University]. https://tigerprints.clemson.edu/all_dissertations/17/

Hilton, A., Hilton, G., Dole, S., & Goos, M. (2016). Promoting middle school students' proportional reasoning skills through an ongoing professional development programme for teachers. Educational Studies in Mathematics, 92(2), 193-219. https://doi.org/10.1007/s10649-016-9694-7

Howe, C., Nunes, T., & Bryant, P. (2011). Rational number and proportional reasoning: Using intensive quantities to promote achievement in mathematics and science. International Journal of Science and Mathematics Education. 9(2), 391-417. https://doi.org/10.1007/s10763-010-9249-9

Hurst, C., & Hurrell, D. (2016). Investigating children's multiplicative thinking: Implications for teaching. European Journal of STEM Education, 1(3), 1-11. https://doi.org/10.20897/lectito.201656

Lamon, S. (2012). Teaching fractions and ratios for understanding: Ratio and proportion (3rd ed.). Routledge.

Lamon, S. J. (1993). Ratio and proportion: Connecting content and children's thinking. Journal for Research in Mathematics Education, 24(1), 41-61. https://doi.org/10.2307/749385

Langrall, C. W., & Swafford, J. (2000). Three balloons for two dollars: Developing proportional reasoning. Mathematics Teaching in The Middle School, 6(4), 254-261. https://doi.org/10.5951/MTMS.6.4.0254

Lobato, J., & Ellis, A. B. (2010). Developing essential understandings of ratios, proportions, and proportional reasoning for teaching mathematics: Grades 6-8. National Council of Teachers of Mathematics.

Mcintosh, M. B. (2013). Developing proportional reasoning in middle school students [Master's thesis, The University of Utah]. https://csme.utah.edu/wp-content/uploads/2013/06/Marcie-McIntosh.pdf

Modestou, M., & Gagatsis, A. (2010). Cognitive and metacognitive aspects of proportional reasoning. Mathematical Thinking and Learning, 12(1),36-53. https://doi.org/10.1080/10986060903465822

NCTM. (2000). Principles and standards for school mathematics. Author.

Nugraha, Y., Sujadi, I., & Pangadi, P. (2016). Penalaran proporsional siswa kelas VII [Grade VII students' proportional reasoning]. Beta: Jurnal Tadris Matematika, 9(1), 34-47. https://doi.org/10.20414/betajtm.v9i1.2

Prayitno, A., Rossa, A., & Widayanti, F. D. (2019). Level penalaran proporsional siswa dalam meme¬cahkan missing value problem [The level of students' proportional reasoning in solving the missing value problem]. Jurnal Riset Pendidikan Matematika, 6(2), 177-187. https://doi.org/10.21831/jrpm.v6i2.19728

Raharjanti, M., Nusantara, T., & Mulyati, S. (2016). Kesalahan siswa dalam menyelesaikan permasalahan perbandingan senilai dan berbalik nilai [Student errors in solving the problem of direct and inverse proportion]. Konferensi Nasional Penelitian Matematika dan Pembelajarannya (KNPMP I). https://publikasiilmiah.ums.ac.id/handle/11617/6971

Silvestre, A. I., & da Ponte, J. P. (2012). Missing value and comparison problems: What pupils know before the teaching of proportion. PNA, 6(3), 73-83. https://doi.org/10.30827/pna.v6i3.6142

Steinthorsdottir, O. B. (2005). Girls journey towards proportional reasoning. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 4, 225-232. https://www.emis.de/proceedings/PME29/PME29RRPapers/PME29Vol4Steinthorsdottir.pdf

Sumarto, S. N. (2013). Design research on mathematics education: Ratio table in developing the students' proportional reasoning [Masters' thesis, Universitas Sriwijaya, and Utrecht University]. http://www.fisme.science.uu.nl/en/impome/theses_group_2012/thesis_Sylvana.pdf

Tjoe, H., & Torre, J. De. (2013). Designing cognitively-based proportional reasoning problems as an application of modern psychological measurement models. Journal of Mathematics Education, 6(2), 17-26. http://personal.psu.edu/hht1/Tjoe_2013_JME.pdf

Van De Walle, J. A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). Pearson Education.

Vig, R., Star, J. R., Dupuis, D. N., Lein, A. E., & Jitendra, A. K. (2015). Exploring the impact of knowledge of multiple strategies on students' learning about proportions. In J. Middleton, J. Cai, S. Hwang (Eds.), Large-scale studies in mathematics education (pp. 61-73). Springer. https://doi.org/10.1007/978-3-319-07716-1_4