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.
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