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Etude didactique et cognitive des rapports entre argumentation et démonstration dans l'apprentissage des mathématiques

Abstract : The purpose of this research is to analyze some aspects of the relationships between argumentation and proof. Our assumption is that a didactical research on the learning of proof needs to understand the nature and the complexity of the notions of argumentation and proof in the referential of the student rational activity: how he decides, he chooses and he proves. At the beginning, we characterize argumentation and proof in mathematics. On the base of the contemporary linguistics theory, we put forward the hypothesis that proof is a particular mathematical argumentation and we propose Toulmin's model as a methodological tool to compare them. Argumentation and proof can be compared from two points of view: structure and referential system. First, besides clear cases of continuity, our structural analysis highlights the distance distances between the argumentation supporting the conjecture and its proof (from an abductive argumentation to a deductive proof, from a inductive argumentation to a deductive proof and so on). Then it is possible, by means of Toulmin's model, to compare the statements mobilized by student during the argumentation with the theorems used in the proof. This comparison constitutes the basis of the analysis concerning the continuity or the distance between conceptions and theory in the referential system. An experimental design was carried out. We proposed three geometric problems requiring the production of conjectures and the related proofs. The students' productions were analysed according to Toulmin's model in order to highlight and to understand the cognitive relation between argumentation and proof. Our results show the potentialities of our cognitive analysis in order to interpret and foresee students' difficulties related to the passage from argumentation to proof.
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Submitted on : Saturday, February 7, 2004 - 10:37:51 PM
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  • HAL Id : tel-00004579, version 1




Bettina Pedemonte. Etude didactique et cognitive des rapports entre argumentation et démonstration dans l'apprentissage des mathématiques. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2002. Français. ⟨tel-00004579⟩



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