Actividad matemática creativa y desarrollo del talento matemático a través del modelo praxeológico

Zeidy Margarita Barraza-García; Avenilde Romo Vázquez; Solange Roa-Fuentes

doi:10.24320/redie.2022.24.e01.4167

Authors

Zeidy Margarita Barraza-García Instituto Politécnico Nacional, México https://orcid.org/0000-0002-2900-481X
Avenilde Romo Vázquez Cinvestav, Instituto Politécnico Nacional, México https://orcid.org/0000-0002-1364-5997
Solange Roa-Fuentes Universidad Industrial de Santander, España https://orcid.org/0000-0001-8580-2763

DOI:

https://doi.org/10.24320/redie.2022.24.e01.4167

Keywords:

creativity, talent, generalization, mathematics

Abstract

This paper presents a theoretical model for the study of mathematical talent, grounded in the Anthropological Theory of Didactics (ATD) and the notion of creativity. This model proposes two components of creative mathematical activity: the mathematical component, which supports mathematical techniques; and the creative component, defined by four functions: producing new techniques, optimizing techniques, considering tasks from different angles, and adapting a technique. Based on the theoretical model and a reference epistemological model on infinite sequences, a learning design comprising six problem situations was developed and then implemented in an institution established to foster mathematical talent. The analysis of two tasks performed by a pair of children offers a case study that illustrates how tackling challenging tasks of the same kind, in a favorable institutional setting, makes it possible to develop mathematical talent.

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