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Covariation between variables in a modelling process: The ACODESA (collaborative learning, scientific debate and self-reflection) method

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Abstract

Semiotic representations have been an important topic of study in mathematics education. Previous research implicitly placed more importance on the development of institutional representations of mathematical concepts in students rather than other types of representations. In the context of an extensive research project, in progress since 2005, related to modelling mathematical situations in Québec secondary schools (grades 8 and 9), we have addressed the problem of constructing a specific mathematical concept: covariation between variables as a prerequisite for the concept of function and its graphical representation. However, our research differs from previous studies as we attempt to take into consideration, in a cultural semiotic perspective, the spontaneous non-institutional representations that students produce when solving a problem situation in mathematics. We report our results with a group of students in grade 9, discussing the evolution of the representations the students produced to solve a problem situation, and the key role that the concept of covariation seems to play in helping students grasp the graphical representation of functions. We also discuss the different stages of the teaching method used, based upon collaborative learning, scientific debate and self-reflection (the ACODESA method of teaching) which aims to help the students acquire a cultural semiotic system.

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Notes

  1. Some of these activities were inspired by preliminary versions constructed in an undergraduate course by C. Janvier, B. Janvier and L. Charbonneau: Didactique de la variable et des fonctions, at Université du Québec à Montréal. Passaro added some modifications in her Masters’ study of the activity The hiker (see Passaro, 2009).

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Acknowledgments

We thank the Conseil de Recherche en Sciences Humaines du Canada (No. 410-2008-1836, CID 130 252). We also express our gratitude to the students and to the teacher Christian Morasse who participated in our research.

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Authors and Affiliations

  1. Université du Québec à Montréal—Université de Montréal, Montreal, QC, Canada

    Fernando Hitt & Alejandro S. González-Martín

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  1. Fernando Hitt
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  2. Alejandro S. González-Martín
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Correspondence to Fernando Hitt.

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This work has been funded by Conseil de Recherche en Sciences Humaines du Canada (No. 410-2008-1836, CID 130 252).

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Hitt, F., González-Martín, A.S. Covariation between variables in a modelling process: The ACODESA (collaborative learning, scientific debate and self-reflection) method. Educ Stud Math 88, 201–219 (2015). https://doi.org/10.1007/s10649-014-9578-7

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