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Spécificités et potentialités de l'arithmétique élémentaire pour l'apprentissage du raisonnement mathématique.

Abstract : In this doctorate thesis, combining epistemological and didactic approaches, we study the potential of elementary number theory for the learning of mathematical reasoning, and the ecology of this potential in the French grade 12 curriculum where number theory has been reintroduced for scientific students in 1998. The epistemological analysis relies on the distinction between two complementary dimensions of reasoning called respectively the organizing dimension and the operative dimension. By analysing historical and modern proofs in this field, we identify the specific characteristics these two dimensions present in number theory and the potential for the learning of mathematical reasoning that result from these characteristics. The didactic analysis uses different sources: exercises proposed at the baccalauréat examination, didactic material published for teachers, students' production at a training test for the baccalauréat, transcripts of a research session in a grade 12 classroom. The institutional analysis developed on baccalauréat exercises and teacher resources shows that the potential a priori identified is only partially exploited in the French curriculum, and gives some rationale for that. The analysis of students' productions shows an evident creativity of these in terms of reasoning modes, but also some serious difficulties which it helps understand. Moreover, the didactic analysis leads us to better understand both the interest and limits of the epistemological approach.
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https://tel.archives-ouvertes.fr/tel-00141080
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Submitted on : Wednesday, April 11, 2007 - 1:11:26 PM
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Véronique Battie. Spécificités et potentialités de l'arithmétique élémentaire pour l'apprentissage du raisonnement mathématique.. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2003. Français. ⟨tel-00141080⟩

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