Résumé
L’intégration par l’élève de connaissances nouvelles est abordée dans le domaine de l’algèbre élémentaire, qui s’appuie sur l’arithmétique, mais s’en différencie.
La tâche proposée à des sujets de 11 à 16 ans consiste à juger de l’équivalence d’expressions isomorphes numériques ou littérales. Les résultats montrent le rôle déterminant du contexte dans le choix d’une stratégie de comparaison. Pour comparer les expressions littérales, des règles formelles sont utilisées. Les erreurs observées proviennent d’une sur-généralisation des conditions d’application de règles prototypiques. Quand les expressions à comparer sont numériques, les stratégies dominantes sont des stratégies de ré-écriture pouvant conduire à une évaluation quantifiée ou non des expressions. On observe dans ce cas moins d’erreurs, mais l’analyse montre que la sémantique des procédures n’est pas toujours assimilée.
Les élèves disposent donc de nombreuses connaissances, de différents types, mais celles-ci sont peu reliées les unes aux autres: la base de connaissances est ainsi peu stable et facilement déformable.
Abstract
This study analyses students integration of new knowledge in the domain of elementary algebra, which is based on arithmetics, but differs from it in a number of ways.
Subjects aged between 11 and 16 years were presented with a task which consisted in evaluating equivalence of either numerical or algebraic isomorphic expressions. The results indicate that the context plays an important role in determining the choice of a strategy of comparison. In evaluating algebric expressions, students use formal rules. The observed errors derive from over-generalisation of prototypical rules and their conditions of application. In the case of numerical expressions, the dominant strategies are re-writing procedures: these may or may not be followed by quantitative evaluations of the resulting expressions. Errors are less frequent, but our analyses show that the semantics of the procedures are not always well understood.
In sum, students posses a fair amount of knowledge of various kinds, but this knowledge is not well integrated or interrelated. Hence their knowledge base is not very stable and can easily become deformed.
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Cauzinille-Marmèche, E., Mathieu, J. & Resnick, L. L’Intégration de Nouvelles Connaissances: Entre Arithmétique et Algèbre. Eur J Psychol Educ 2, 41–56 (1987). https://doi.org/10.1007/BF03172705
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DOI: https://doi.org/10.1007/BF03172705