Abstract

HITT, Fernando; QUIROZ, Samantha; SABOYA, Mireille  and  LUPIANEZ, José Luis. Construction of arithmetic-algebraic generalization processes in a sociocultural approach skills-based approach in Quebec and Mexican schools. Educ. mat. [online]. 2023, vol.35, n.3, pp.112-150.  Epub Mar 19, 2024. ISSN 2448-8089.  https://doi.org/10.24844/em3503.04.

Abstract: The world of education was marked at the beginning of this century by the notion of competence, particularly in Quebec and Mexican schools, and more particularly in mathematics. In this new vision of teaching and learning, mathematical modeling is ubiquitous and linked to divergent thinking. Our project focuses on the development of this thinking in pupils during algebraic generalization to negotiate the transition from arithmetic to algebra in the primary-secondary transition. Through the proposal of teaching and learning conditions based on collaborative work and the use of technological resources, we report the development in Quebec and Mexican pupils of what we have called the arithmetic-algebraic thinking solicited during the generalization of figurative sequences. In this experiment, the pupils of the two countries mobilized an arithmetic-algebraic cognitive structure which was operationalized through prediction procedures, conjectures, the process of generalization from a non-institutional algebraic point of view and from a numerical validation using applets made available to pupils. In addition, the results from the Mexican side open the way to the consideration of functional-spontaneous representations from primary school in a perspective of primary-secondary transition linked to arithmetic-algebraic thinking.

Keywords : arithmetic-algebraic thinking; generalization; spontaneous-function-al representations; ACODESA.

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