Thought and language: a discussion in the field of psychology of mathematics education / Pensamento e linguagem: uma discussão no campo da psicologia da educação matemática

Abstract

This paper brings back the theoretical debate concerning the relationship between thought and language in the process of mathematical conceptualization. Empirical data issued from other studies are offered for discussing and refusing the idea of assigning a central role to language in concept development and learning in mathematics. These data referred to a didactic research aimed at helping in the understanding of the principle of equivalence between equations, in introductory algebra. Two different didactic contexts were compared: a group working with non-verbal competencies-in-action connected with the principle of equivalence, and another group working on making verbally explicit the meaning of the equality between equations. Results showed no difference in terms of algebraic procedures in problem solving between the two groups. Instead, both methods seem to be complementary. These data confirm the interest of symbolic representation in the process of mathematical conceptualization, neither excluding nor assigning a secondary role to action and corporeality.

Keywords

• Thought and language
• competences-in-action
• algebraic and mathematical knowledge