Promote proportional reasoning through digital technology

Authors

DOI:

https://doi.org/10.32870/Ap.v15n1.2344

Keywords:

Razonamiento proporcional, matemáticas, tecnología digital, educación secundaria, didáctica

Abstract

This article explores alternative teaching methods that promote proportional reasoning in Mexican students aged fourteen to fifteen using digital technology. To this end, a sequence of didactic activities has been designed to give meaning to the concepts of ratio and proportion in their different representations from the approach of linear functions. For the design of the tasks, elements of the theory of Realistic Mathematics Education and the Didactics of Cuevas-Pluvinage were used, coinciding with several didactic points. The proposed learning objectives and activities have been organized through a hypothetical learning trajectory. The analysis and detailed evaluation of the responses allowed us to identify: the didactic advantages of the design, the learning difficulties, and the vital role played by technology in the learning process.

Author Biographies

  • Armando Cuevas-Vallejo, Departamento de Matemática Educativa, Cinvestav-IPN

    Doctor en Ciencias con especialidad en Matemática Educativa por el Centro de Investigación y de Estudios Avanzados del IPN, México. Investigador titular del Departamento de Matemática Educativa del Cinvestav, IPN.

  • Erasmo Islas-Ortiz, Departamento de Matemática Educativa, Cinvestav-IPN
    Maestro en Ciencias con especialidad en Matemática Educativa por el Centro de Investigación y de Estudios Avanzados del IPN, México. Estudiante de Doctorado del Departamento de Matemática Educativa del Cinvestav, IPN.
  • José Orozco-Santiago, Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla
    Doctor en Ciencias con especialidad en Matemática Educativa por el Centro de Investigación y de Estudios Avanzados del IPN, México. Investigador titular en la Facultad de Ciencias Físico Matemáticas de la Benemérita Universidad Autónoma de Puebla.

References

Bakker, A. (2018). Design research in education: a practical guide for early career researchers. Routledge. https://doi.org/10.4324/9780203701010

Balderas, R.; Block D. y Guerra, M. T. (2014). Fortalezas y debilidades de los saberes sobre la proporcionalidad de maestro de secundaria. Educación Matemática, 26(2), 7-32. https://www.revistaeducacion-matematica.org.mx/revista/2016/05/15/vol26-2-1/

Cobb, P.; Yackel, E. & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Math Education, 23(1), 2-33. https://doi.org/10.2307/749161

Cuevas, A. & Pluvinage, F. (2003). Les projets d’action practique, elements d’une ingeniere d’ensigment des mathematiques. Annales de Didactique et Sciences Cognitives, 8, 273-292. https://mathinfo.unistra.fr/websites/math-info/irem/Publications/Annales_didactique/vol_08/adsc8-2003_014.pdf

Cuevas, A.; Villamizar, F. y Martínez, A. (2017). Actividades didácticas para el tono como cualidad del sonido, en cursos de física del nivel básico, mediadas por la tecnología digital. Enseñanza de las Ciencias, 35(3), 129-150. https://doi.org/10.5565/rev/ensciencias.2091

Confrey, J. & Carrejo, D. (2005). Ratio and fraction: The difference between epistemological complementarity and conflict. Journal for Research in Mathematics Education. Monograph, 13. http://www.jstor.org/stable/30037732

De Bock, D.; Van Dooren, W.; Janssens, D. & Verschaffel, L. (2007). The illusion of linearity. Springer Publishing. https://doi.org/10.1007/978-0-387-71164-5

Duijzer, C.; Shayan, S.; Bakker, A.; Van der Schaaf, M. F. & Abrahamson, D. (2017). Touchscreen tablets: Coordinating action and perception for mathematical cognition. Frontiers in Psychology, 8. https://doi.org/10.3389/fpsyg.2017.00144

Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Kluwer Academic Publishers. http://doi.org/10.1007/0-306-47202-3

Gueudet, G. (2007). Learning mathematics with e-exercises: A case study about proportional reasoning. International Journal of Technology in Mathematics Education, 14(4), 169-182. https://cloud.3dissue.com/170388/199108/233436/IJTMEVol14-4-2007/index.html

Gravemeijer, K. (2020). Emergent modeling: an RME design heuristic elaborated in a series of examples. Journal of the International Society for Design and Development in Education, 4(13), 1-31. http://www.educationaldesigner.org/ed/volume4/issue13/article50/

Hemmi, K.; Bråting, K. & Lepik, M. (2021). Curricular approaches to algebra in Estonia, Finland and Sweden - a comparative study. Mathematical Thinking and Learning, 23(1), 49-71. https://doi.org/10.1080/10986065.2020.1740857

Lamon, S. J. (2007). Rational numbers and proportional reasoning: towards a theoretical framework for research, en F. K. Lester (ed.), Second Handbook of Research on Mathematics Teaching and Learning (629-667). Information Age Publishing.

Lamon, S. J. (2020). Teaching fractions and ratios for understanding: essential content and instructional strategies for teachers. Routledge.

Lesh, R.; Post, T. & Behr, M. (1988). Proportional reasoning, en J. Hiebert & M. Behr (eds.), Number concepts and operations inthe middle grades (93-118). NCTM.

Lobato, J. & Thanheiser, E. (2002). Developing understanding of ratio-as-measure as a foundation for slope, en B. Litwiller (ed.), Making sense of fractions, ratios, and proportions, 2002 Yearbook of the National Council of Teachers of Mathematics. NCTM.

Lobato, J. E.; Ellis, A. B. & Charles, R. I. (2010). Developing essential understanding of ratios, proportions, and proportional reasoning for teaching mathematics in grades 6-8. NCTM.

Miyakawa, T. & Winsløw, C. (2009). Didactical designs for students’ proportional reasoning: An “open approach” lesson and a “fundamental situation”. Educational Studies in Mathematics, 72(2), 199-218. https://doi.org/10.1007/s10649-009-9188-y

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

Moyer-Packenham, P. & Bolyard, J. (2016). Revisiting the definition of a virtual manipulative, en P. Moyer-Packenham (ed.), International perspectives on teaching and learning mathematics with virtual manipulatives (3-23). Springer. https://doi.org/10.1007/978-3-319-32718-1_1

Muttaqin, H.; Putri, R. I. & Somakim, S. (2017). Design research on ratio and proportion learning by using ratio table and graph with Oku Timur context at the 7th grade. Journal on Mathematics Education, 8(2), 211-222. http://dx.doi.org/10.22342/jme.8.2.3969.211-222

National Council of Teacher Mathematics (NCTM). (2000). Principles Standards and for School Mathematics. NCTM.

Padilla-Partida, S. (2018). Usos y actitudes de los formadores de docentes ante las TIC. Entre lo recomendable y la realidad de las aulas. Apertura, 10(1), 132-148. https://doi.org/10.32870/Ap.v10n1.1107

Secretaría de Educación Pública (SEP). (2017). Aprendizajes clave para la educación integral: Matemáticas. SEP.

Sierpinska, A. (2004). Research in mathematics education through a keyhole: task problematization. For the Learning of Mathematics, 24(2), 7-15. https://flm-journal.org/Articles/51AB9D0E4247C5E9883E32091E242.pdf

Simon, M. A. (2020). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 25(4), 887-896. https://doi.org/10.5951/jresematheduc.26.2.0114

Van den Heuvel-Panhuizen, M. & Drijvers, P. (2020). Realistic mathematics education, en S. Lerman (ed.), Encyclopedia of Mathematics Education. Springer. https://doi.org/10.1007/978-3-030-15789-0_170

Weiland, T.; Orrill, C. H.; Nagar, G. G.; Brown, R. & Burke, J. (2021). Framing a robust understanding of proportional reasoning for teachers. Journal of Mathematics Teacher Education, 24, 179-202. https://doi.org/10.1007/s10857-019-09453-0

Published

2023-03-29