Interdisciplinarity Between Mathematics and Physics: Solving Strategies for Simple Proportionality Problems

Authors

  • Juan Carlos Tinoco Universitat Autònoma de Barcelona
  • Lluís Albarracín Universitat Autònoma de Barcelona
  • Jordi Deulofeu Universitat Autònoma de Barcelona https://orcid.org/0000-0002-5834-0863

DOI:

https://doi.org/10.35763/aiem27.5398

Keywords:

Simple proportionality, Strategy analysis, Interdisciplinarity, Secondary education

Abstract

This article analyses the strategies used by 3rd year ESO and 1st year Bachelor students to solve simple proportionality problems in mathematics and physics classes, with the aim of understanding how the teaching traditions of each discipline influence students’ responses. The results show that students in the 3rd year of ESO use a greater variety of strategies, while those in the 1st year of Bachelor have a higher success rate. It is also observed that the strategies used in Physics are different from those used in Mathematics, regardless of the year. These findings highlight the importance of interdisciplinary teaching that promotes a deeper understanding of simple proportionality, adapting teaching strategies to the characteristics and needs of students at each educational level.

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References

Alvargonzález, D. (2011). Multidisciplinarity, interdisciplinarity, transdisciplinari-ty, and the sciences. International Studies in the Philosophy of Science, 25(4), 387–403. https://doi.org/10.1080/02698595.2011.623366

Berg, B. L. (2007). Qualitative research methods for the social sciences. Allyn and Bacon.

Chapman, O. (2006). Classroom practices for context of mathematics word prob-lems. Educational Studies in Mathematics, 62(2), 211–230. https://doi.org/10.1007/s10649-006-7834-1

Choi, B. C. K., & Pak, A. W. P. (2006). Multidisciplinarity, interdisciplinarity and transdisciplinarity in health research, services, education and policy: 1. Defi-nitions, objectives, and evidence of effectiveness. Clinical and Investigative Medicine, 29(6), 351–364.

Cramer, K., Post, T., & Graeber, A. O. (1993). Connecting research to teaching: Pro-portional reasoning. Mathematics Teacher, 86(5), 404–407. https://doi.org/10.5951/MT.86.5.0404

Freudenthal, H. (1978). Didactical phenomenology of mathematical structures. Reidel.

Gabel, D., Sherwood, R., & Enochs, L. (1984). Problem-solving skills of high school chemistry students. Journal of Research in Science Teaching, 21(2), 221–233. https://doi.org/10.1002/tea.3660210212

Jurdak, M. E. (2006). Contrasting perspectives and performance of high school stu-dents on problem solving in real world, situated, and school contexts. Educa-tional Studies in Mathematics, 63(3), 283–301. https://doi.org/10.1007/s10649-005-9008-y

Lamon, S. J. (1993). Ratio and proportion: Connecting content and children’s think-ing. Journal for Research in Mathematical Education, 24(1), 41–61. https://doi.org/10.5951/jresematheduc.24.1.0041

Lau, P. N.-K., Singh, P., & Hwa, T.-Y. (2009). Constructing mathematics in an in-teractive classroom context. Educational Studies in Mathematics, 72(3), 307–324. https://doi.org/10.1007/s10649-009-9196-y

Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In M. Behr & J. Hiebert (Eds.), Number concepts and operations in the middle grades (Vol. 2, pp. 93–118). National Council of Teachers of Mathematics; Lawrence Erlbaum Associates.

Martínez-Juste, S., Muñoz-Escolano, J. M., & Oller-Marcén, A. (2015). Estrategias utilizadas por estudiantes de distintos niveles educativos ante problemas de proporcionalidad compuesta. En C. Fernández, M. Molina, & N. Planas (Eds.), Investigación en educación matemática XIX (pp. 351–359). SEIEM.

Martínez-Juste, S., Muñoz-Escolano, J. M., Oller-Marcén, A., & Rincón, T. (2017). Análisis de problemas de proporcionalidad compuesta en libros de texto de 2º de ESO. Revista Latinoamericana de Investigación en Matemática Educativa, 20(1), 95–122. https://doi.org/10.12802/relime.17.2014

Mejía, J. (2000). El muestreo en la investigación cualitativa. Investigaciones Sociales, 4(5), 165–180. https://doi.org/10.15381/is.v4i5.6851

Michelsen, C. (1998). Expanding context and domain: A cross-curricular activity in mathematics and physics. ZDM—Mathematics Education, 30(4), 100–106. https://doi.org/10.1007/BF02653149

Nunes, T., Desli, D., & Bell, D. (2003). The development of children’s understanding of intensive quantities. International Journal of Educational Research, 39(7), 651–675. https://doi.org/10.1016/j.ijer.2004.10.002

Park, J., Park, H., & Kwon, O. (2010). Characterizing proportional reasoning of mid-dle school students. The SNU Journal of Education Research, 19, 119–144.

Planinic, M., Milin-Sipus, Z., Katic, H., Susac, A., & Ivanjek, L. (2012). Comparison of student understanding of line graph slope in physics and mathematics. In-ternational Journal of Science and Mathematics Education, 10(6), 1393–1414. https://doi.org/10.1007/s10763-012-9344-1

Planinic, M., Ivanjek, L., Susac, A., & Milin-Sipus, Z. (2013). Comparison of univer-sity students’ understanding of graphs in different contexts. Physical Review Special Topics—Physics Education Research, 9(2), 020103. https://doi.org/10.1103/PhysRevSTPER.9.020103

Raviolo, A., Carabelli, P., & Ekkert, T. (2022). Aprendizaje del concepto de densidad: La comprensión de las relaciones entre las variables. Latin-American Journal of Physics Education, 16(2), 2310–2319.

Riehl, S. M., & Steinthorsdottir, O. B. (2019). Missing‐value proportion problems: The effects of number structure characteristics. Investigations in Mathematics Learning, 11(1), 56–68. https://doi.org/10.1080/19477503.2017.1375361

Steinthorsdottir, O. B. (2006). Proportional reasoning: Variable influencing of the problem’s difficulty level and one’s use of problem solving strategies. In J. Novotná, H. Moraová, K. M., & N. Stehliková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 169–176). PME.

Tinoco, J. C., Albarracín, L., & Deulofeu, J. (2021). Estrategias de proporcionalidad simple en las aulas de matemáticas y de física. In In P. D. Diago, D. F. Yáñez, M. T. González-Astudillo, & D. Carrillo (Eds.), Investigación en educación ma-temática XXIV (pp. 587–594). SEIEM.

Tinoco, J. C., Albarracín, L., & Deulofeu, J. (2022). Interdisciplinariedad: Haciendo crecer el concepto de proporcionalidad. Uno: Revista de Didáctica de las Mate-máticas, 96, 68–74.

Van Dooren, W., De Bock, D., Evers, M., & Verschaffel, L. (2009). Students’ overuse of proportionality on missing‐value problems: How numbers may change so-lutions. Journal for Research in Mathematics Education, 40(2), 187–211. https://doi.org/10.2307/40539331

Published

2025-05-02

How to Cite

Tinoco, J. C., Albarracín, L., & Deulofeu, J. (2025). Interdisciplinarity Between Mathematics and Physics: Solving Strategies for Simple Proportionality Problems. Advances of Research in Mathematics Education, (27), 1–20. https://doi.org/10.35763/aiem27.5398

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Artículos