Generating the raison d’être of logical concepts in mathematical activity at secondary school: Focusing on necessary/sufficient conditions<br>Générer la raison d’être des concepts logiques dans l’activité mathématique à l’école secondaire: se concentrer sur les conditions nécessaires / suffisantes
DOI:
https://doi.org/10.23925/1983-3156.2020v22i4p438-453Palabras clave:
Logical concepts, anthropological theory of the didactic, necessary/sufficient conditionsResumen
Abstract
In this paper, we focus on the absence of the raison d’être for logical concepts, especially regarding necessary conditions and sufficient conditions, in mathematics at secondary schools. We investigated the fundamental role of these concepts in the mathematical organisation of mathematicians, which is related to their protomathematical and paramathematical values. Then we designed, implemented, and analysed a study and research activity with the aim to activate their functionality.
Keywords: Logical concepts, Anthropological theory of the didactic, Necessary/sufficient conditions.
Résumé
Cet article porte sur l’absence de la raison d’être des concepts logiques, en particulier des conditions nécessaires et des conditions suffisantes, dans les mathématiques secondaires au Japon. Nous étudions le rôle fondamental de ces concepts dans l’organisation mathématique de mathématiciens, qui est lié à leurs valeurs protomathématiques et paramathématiques. Ensuite, nous concevons, mettons en place et analysons une activité d’étude et de recherche ayant pour but d'activer leur fonctionnalité.
Mots-clés: Concepts logiques, Théorie anthropologique de la didactique, Conditions nécessaires / suffisantes.
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