Évolution et interinfluence des modes d’agir, parler et penser les fractions dans deux problèmes multiplicatifs

Abstract

Based on studies focusing on the roles of language in the teaching and the learning of mathematics, three dimensions are distinguished - acting, talking and thinking - interrelated. In order to explore the interactions and progressive transformations of these dimensions during the teaching and the learning of fractions, a teaching sequence was experimented in a specialized class. The sequence is composed of a network of problem focusing on multiplicative relationships inherent in the concept of fraction. In this article, we present the a priori and a posteriori analyses of two of these problems. These analyses are carried out in a didactic framework enriched with a specific perspective on the modes of acting, speaking and thinking the multiplicative relationships in question.