Strategies used in solving proportion problems among seventh-grade students
Authors
View
Keywords
License
Copyright (c) 2025 Gábor Torma, József Kosztolányi

This work is licensed under a Creative Commons Attribution 4.0 International License.
How To Cite
Abstract
In the 2023/2024 school year, 146 seventh-grade Hungarian students (aged 12-13) participated in our classroom experiment on solving proportion problems. At the beginning and the end of the teaching phase, both the experimental and the control groups solved a test. Regarding the answers of the students, in the pre- and post-test mostly consisting of word problems, we examined the success of solving the problems, as well as the solution strategies. For this, we used the strategies of proportional thinking that already exist in the literature of mathematical didactics. We intended to answer the following questions: To what extent and in which ways do the different types of problems and texts influence the solution strategies chosen by the students? How successfully do seventh-grade students solve proportion problems?
Subject Classification: 97D50, 97F80
References
- Arican, M. (2019). Facilitating pre-service mathematics teachers’ understanding of directly and inversely proportional relationships using hands-on and realworld problems. International Journal of Research in Education and Science (IJRES), 5 (1), 102–117.
- Avcu, R., & Avcu, S. (2010). 6th grade students’ use of different strategies in solving ratio and proportion problems. Procedia - Social and Behavioral Sciences, 9, 1277–1281. https://doi.org/10.1016/j.sbspro.2010.12.320
- Ben-Chaim, D., Fey, J. T., Fitzgerald, W. M., Benedetto, C., & Miller, J. (1998). Proportional reasoning among 7th grade students with different curricular experiences. Educational Studies in Mathematics, 36 (3), 247–273. https://www.jstor.org/stable/3482707
- Bereczki, I. (2023). Az arányossági gondolkodás vizsgálata felső tagozatos tanulók körében. In Zs. Molnár-Kovács, H. Andl, & J. Steklács (Eds.), 21. századi képességek, írásbeliség, esélyegyenlőség (pp. 81–92). MTA Pedagógiai Tudományos Bizottság, Pécsi Tudományegyetem Bölcsészet- és Társadalomtudom ányi Kar, Neveléstudományi Intézet.
- De Bock, D., Van Dooren, W., & Verschaffel, L. (2015). Students’ understanding of proportional, inverse proportional, and affine functions: Two studies on the role of external representations. International Journal of Science and Mathematics Education, 13 (Suppl 1), 47–69. https://doi.org/10.1007/s10763-013-9475-z
- De Bock, D., Van Dooren, W., Janssens, D., & Verschaffel, L. (2002). Improper use of linear reasoning: An in-depth study of the nature and the irresistibility of secondary school students’ errors. Educational Studies in Mathematics, 50, 311–334. https://doi.org/10.1023/a:1021205413749
- Education Office (n.d.). Kerettanterv az általános iskola 5-8. évfolyama számára. Retrieved May 1, 2024. https://www.oktatas.hu/kozneveles/kerettantervek/2020_nat/kerettanterv_alt_isk_5_8
- Fernández, C., Llinares, S., & Valls, J. (2008). Implicative analysis of strategies in solving proportional and nonproportional problems. In O. Figueras, & A. Sepúlveda (Eds.), Proceedings of the Joint Meeting of the 32nd Conference of the International Group for the Psychology of Mathematics Education, and the XX North American Chapter, Morelia, Michoacán, México (Vol. 3, pp. 1–8). PME.
- Fisher, L. C. (1988). Strategies used by secondary mathematics teachers to solve proportion problems. Journal for Research in Mathematics Education, 19 (2), 157–168. https://doi.org/10.5951/jresematheduc.19.2.0157
- 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
- Molnár, Gy., & Csapó, B. (2003). A képességek fejlődésének logisztikus modellje. Iskolakultúra, 13 (2), 57–69. https://www.iskolakultura.hu/index.php/iskolakultura/article/view/19797
- Nagy, L., Korom, E., Pásztor, A., Veres, G., & B. Németh, M. (2015). A természettudományos gondolkodás online diagnosztikus értékelése. In B. Csapó, E. Korom, & Gy. Molnár (Eds.), A természettudományi tudás online diagnosztikus értékelésének tartalmi keretei (pp. 35–116). Oktatáskutató és Fejlesztő Intézet (OFI).
- Nurhayati, N., & Kusumah, Y. S. (2020). Students’ proportional reasoning ability in junior high school using collaborative problem solving. Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 2019. European Alliance for Innovation (EAI). https://doi.org/10.4108/eai.12-10-2019.2296522
- Saleem, T., Mukhtar, S., & Aziz, S. (2021). Teaching direct and inverse proportion to 5th grade students through pictures and real-life problems, leading towards autonomous learning. Journal of Science Education, 3 (1), 63–80.
- Varga, J., Józsa, K., & Pap-Szigeti, R. (2007). Az arányosságszámítási készség kritériumorientált fejlesztése 7. osztályban. Magyar Pedagógia, 107 (1), 5–27. https://magyarpedagogia.bibl.u-szeged.hu/index.php/magyarpedagogia/article/view/447
https://doi.org/10.5485/TMCS.2025.14608