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Vol. 6 No 3 (2003): Noviembre

MODELES ET TEORIES SUR L’ ENTENDEMENT MATHEMATIQUE: COMPARAISON ENTRE LES MODELES DE PIRIE ET KIEREN DU PROGRES DE L´ENTENDEMENT MATHEMATIQUE ET LA TEORIE APOS

Soumis
décembre 23, 2024
Publiée
novembre 30, 2003

Résumé

La recherche d’ une éloquente description cognitive sur l’ entendement s’ y a ensuivit depuis la dernière moitié du siècle. Pendant les trois dernières décades, nouvelles et intégratives perspectives montrent , selon Richard Skemp, des différences entre l’ entendement intrumentale et relationnel. Le dévéloppement de ces perspectives, depuis 1987, a été documenté par Tom Schroeder dans sa synthèse prensentée au PME du travail sur l’ entendement resulté des contrastes entre l’ entendement instrumental et relationnel de Richard Skemp. Depuis 1987, le travail sur l’ entendement a progressé et cet article examine les plus récentes et nouveaux cadres téoriques qui ont surgit de ces origines. Cet ariticle se concentre en deux cadres téoriques , le modèle de Pirie et Kieren du progrès de l’ entendement mathématique et la téorie APOS de Dubinsky. Il discute aussi autres cadres téoriques contémporaines telles que le travail de Cornu et Sierpinska sur les obstacles épistémologiques et cognitifs ; ainsi les recherches sur les concepts de définition et image par Vinner et Tall ; les explorations de Kaput sur multiples représentations et finalement les différences entre les conceptions operationnel et structurel de Sfard. En plus des définitions explicatives sur l´entendement proposés par ces deux encadrements, la discussion adresse ses éléments et construit en plus ses liens dans les caractérisations historiques recéntes de l’ entendement. L’ article argumente pourquoi le modèle de Pirie et Kieren et la téorie APOS satisfassent le critère Schoenfeld (2000) de la clasification donnée de téorie et finalement conclue avec les discussions d’ une varieté d’ interconections entre ces deux téories ainsi qu’ élements qui sont différents un de l´autre tels que ses origines, organizations, rélations et autres encadrements ; et implications des deux téories pour practiques d´évaluation et pédagogiques.

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