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Artículos

Vol. 11 No 1 (2008): Marzo

A SEARCH FOR A CONSTRUCTIVIST APPROACH FOR UNDERSTANDING THE UNCOUNTABLE SET P(N)

Soumis
mai 22, 2024
Publiée
2008-01-24

Résumé

Dans cette étude nous nous demandons si les individus construisent des structures mentales spécifiques pour l' ensemble P(N) («ensemble des sous-ensembles de N»). Nous décrivons ici deux des principaux apports de notre recherche en relation à cette question. Nous identifions tout d' abord les perspectives constructivistes utilisées ou potentiellement utilisables pour décrire les mécanismes de la pensée à propos des ensembles infinis, et en particulier l' ensemble des entiers naturels. Ensuite, pour déterminer si ces mécanismes de pensée des individus sur l' ensemble P(N) peuvent être interprétés en termes d' une ou plusieurs des perspectives considérées, nous analysons la forme de penser de huit mathématiciens. Au-delà des conceptions négatives, c'est-à-dire les approches de P(N) essentiellement par ce qu' il n' est pas, les résultats de notre analyse laissent à penser que la compréhension des individus de l' ensemble P(N) n' est va pas au delà de la définition formelle. Nous exposons enfin les possibles implications de nos résultats et nous soulignons de futurs sujets de recherche que cette étude peut dégager.

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