El rol de las tareas realistas en la interpretación del residuo de la división aritmética

Lucía  Zapata-Cardona

doi:10.17533/udea.unipluri.20.2.04

Authors

Lucía Zapata-Cardona University of Antioquia https://orcid.org/0000-0003-4266-5273

DOI:

https://doi.org/10.17533/udea.unipluri.20.2.04

Keywords:

realistic mathematics, school arithmetic, childhood, division

Abstract

This paper reports an experience that studied the contribution of realistic tasks inspired by the Realistic Mathematics Education to the interpretation of the remainder in the arithmetic division in young children. The participants were three primary school students (6 to 10 years old) who solved a division task with remainder in a realistic context. The participants were interviewed in a space outside the school environment and they were provided with manipulatives to support the solution and as a tool to make visible the strategies used in the modeling. The main findings reveal that realistic mathematical tasks have the potential to promote exploration, construction, and implementation of spontaneous algorithms in students; seem to solve the problem of interpreting the remainder in arithmetic division; and promote modeling and mathematization by giving access to much more formal mathematics.

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References

Alsina, A. (2009). El aprendizaje realista: una contribución de la investigación en Educación Matemática a la formación del profesorado. En M. J. González, M. T. González & J. Murillo (Eds.), Investigación en Educación Matemática XIII (pp. 119–127). Santander: SEIEM.

Bakker, A., & Derry, J. (2011). Lessons from Inferentialism for Statistics Education [Lecciones del inferencialismo para la educación estadística]. Mathematical Thinking and Learning, 13(1-2), 5–26. doi: 10.1080/10986065.2011.538293

Beswick, K. (2011). Putting context in context: an examination of the evidence for the benefits of ‘contextualised’ tasks. International Journal of Science and Mathematics Education 9, 367–390.

Carpenter, T. P., Lindquist, M. M., Matthews, W., & Silver, E. A. (1983). Results of the third NAEP mathematics assessment: Secondary school. Mathematics Teacher, 76, 652–659.

Cisternas Rojas, Y., Gil Llario, M. D., Ceccato, R., y Marí-Sanmillán. (2019). Analysis of the psychometric properties of a multiplication and division processes assessment scale. International Journal of Developmental and Educational Psychology, 1 Monográfico 2, 159–166.

Creswell, J. W. (2013). Research design qualitative, quantitative, and mixed methods approaches. Los Angeles: Sage.

Defranco, T. C., & Curcio, F. R. (1997). A division problem with a remainder embedded across two contexts: Children’s solutions in restrictive versus real-world settings. Focus on Learning Problems in Mathematics, 19 (2), 58–72.

De Lange, J. (1996). Using and applying mathematics in education. En A.J. Bishop (Ed). International Handbook of Mathematics Education, Part I (pp. 49–97). Utrecht: Kluwer Academia Press.

Denzin, N. K., & Lincoln, Y. (2012). La investigación cualitativa como disciplina y como práctica. En N. K.

Denzin, & Y. Lincoln (Edits.), Manual de investigación cualitativa, vol. 1: El campo de la investigación cualitativa (pp. 43–102). Barcelona: Gedisa.

Freudenthal, H. (1991). Revisiting mathematics education. Dordrectht: Kluwer Academic Publishers.

Gravemeijer, K (1994). Developing realistic mathematics education. Utrecht: Freudenthal Institute.

Gravemeijer, K. (2020). A socio-constructivist elaboration of Realistic Mathematics Education. En M. Van den Heuvel-Panhuizen (ed.), National Reflections on the Netherlands Didactics of Mathematics, ICME-13 Monographs, (pp. 217–233). Springer https://doi.org/10.1007/978-3-03033824-4_12

Hernández, R. (2014). Qualitative research through interviews: Its analysis by Grounded Theory. Cuestiones Pedagógicas, 23, 187–210.

Itzcovich, H., Resia de Moreno, B., Novembre, A., & Becerril, M. M. (2009). La matemática escolar: las prácticas de enseñanza en el aula. Buenos Aires: AIQUE.

Kaasila, R., Pehkonen, E. & Hellinen, A. (2010). Finnish pre-service teachers’ and upper secondary students’ understanding of division and reasoning strategies used. Educational Studies in Mathematics, 73 (3) 247–261.

Kool, M. (2020). Sixteenth century reckoners versus twenty-first century problem solvers. En M. Van den Heuvel-Panhuizen (ed.), National Reflections on the Netherlands Didactics of Mathematics, ICME-13 Monographs, (pp.105–120). Springer https://doi.org/10.1007/978-3-030-33824-4_7

Lerman, S. (2001). Cultural, discursive psychology: a sociocultural approach to studying the teaching and learning of mathematics. Educational Studies in Mathematics, 46, 87–113.

Ministerio de Educación Nacional. (2006). Estándares Básicos de Competencias en Lenguaje, Matemáticas, Ciencias y Ciudadanas. Bogotá: Revolución Educativa Colombia Aprende MEN.

National Governors Association & Council of Chief State School Officers. (2010). Common Core State Standards Initiative. Washington, DC: NGA and CCSSO.

Sánchez-Barbero, B; Calatayud, M., y Chamoso, J. M. (2019). Análisis de la interacción de maestros cuando resuelven problemas realistas conjuntamente con sus alumnos en aulas de primaria, teniendo en cuenta su experiencia docente. Uni-pluriversidad, 19(2), 40-59. doi: 10.17533/udea.unipluri.19.2.03

Silver, E., Shapiro, L., & Deutsch, A. (1993). Sense making and the solution of division problems involving remainders: An examination of middle school students’ solution processes and their interpretations of solutions. Journal for Research in Mathematics Education, 24(2), 117–135.

Van den Heuvel-Panhuizen, M. (2002). Realistic Mathematics Education as work in progress. En Fou-Lai Lin (Eds.). Common sense in mathematics education. Proceedings of 2001 The Netherlands and Taiwan Conference on Mathematics Education (pp. 1–43). Taiwan: National Taiwan Normal University.

Van den Heuvel-Panhuizen (2020). A spotlight on Mathematics Education in the Netherlands and the central role of Realistic Mathematics Education. En M. Van den Heuvel-Panhuizen (ed.), National Reflections on the Netherlands Didactics of Mathematics, ICME-13 Monographs, (pp. 1–14) https://doi.org/10.1007/978-3-030-33824-4_1

Van den Heuvel-Panhuizen, M., & van den Boogaard, S. (2008). Picture Books as an Impetus for Kindergartners’ Mathematical Thinking. Mathematical Thinking and Learning, 10(4) 341–373, DOI: 10.1080/10986060802425539

Vicente, S., van Dooren, W., & Verschaffel (2014). Utilizar las matemáticas para resolver problemas reales. Cultura y Educación, 20 (4) 391–406, DOI:10.1174/113564008786542235

Voigt, M., Fredriksen, H., Rasmussen, C. (2020). Leveraging the design heuristics of realistic mathematics education and culturally responsive pedagogy to create a richer flipped classroom calculus curriculum. ZDM.https://doi.org/10.1007/s11858-019-01124-x

Vos, P. (2020). Task contexts in Dutch Mathematics Education. En M. Van den Heuvel-Panhuizen (ed.), National Reflections on the Netherlands Didactics of Mathematics, ICME-13 Monographs, (pp. 31–53). Springer https://doi.org/10.1007/978-3-030-33824-4_3

Vygotsky, L. (1983). Pensamiento y lenguaje: Teoría del desarrollo cultural y las funciones psíquicas. Buenos Aires: La Pleyade.

Zapata-Cardona, L. (2018). Enseñanza de la estadística desde una perspectiva crítica. Yupana, 10, 30–41.

Zapata-Cardona, L. & Marrugo, L. (2019). Critical citizenship in Colombian statistics textbooks. En G. Burrill, & D. Ben-Zvi (Eds.), Topics and Trends in Current Statistics Education Research. International Perspectives (pp. 373–389). Switzerland: Springer.