L'argumentation en mathématiques et sa relation avec la démonstration

Abstract

 In mathematics education there is no shared definition for argumentation, even if this is one of the most recurrent activities in the class. But, what can be considered as argumentation? What is argumentation in mathematics? And what is its relation with mathematical proof? The aim of this paper is to provide an answer to these questions. Because current research in mathematics education does not offer much insight on these matters, historical and contemporary linguistic and philosophical theories have been considered to suggest a possible characterisation of argumentation in mathematics. More specifically, functional and structural characteristics of argumentation in mathematics are provided. Functional characteristics establish the finality of argumentation, its utility, its role within a discourse. Structural characteristics provide a structural model, the Toulmin’s model, for argumentation. This characterisation shows that proof can be considered as a special case of argumentation in mathematics.