La logique : d'un outil pour le langage et le raisonnement mathématique vers un objet d'enseignement

Abstract : The thesis focuses on the teaching of concepts of logic in high school. The current official instructions state that the aim is not to give a course of mathematical logic, but to develop its use as a tool for the formulation of considered logic. To take this constraint into account in the study of the process of didactic transposition, I introduce, between the scholar knowledge and the knowledge to teach, a knowledge of reference for logic, which has never been established by the mathematics teaching community. To provide such a reference, I lead an epistemological and didactic study, in which I highlight the relationship between logic and language, often less present in the minds of teachers than the links between logic and reasoning. This reference takes into account theoretical and pragmatic aspects of the concepts of logic towards the study of language utilised by mathematicians and didactical elements in existing works. A more detailed study of the knowledge to teach, in which the current choices are situated in a historical perspective, reveals the complexity of the requirements and constraints on the teaching of these concepts. Nevertheless, teacher training on these issues is virtually nonexistent. The analysis of a three-day training on logic for active teachers, in which the concepts of logic are addressed from a naive study of mathematical language, shows the relevance of this approach : many trainees seem to become aware of the ambiguities implicit in our linguistic practices, and express their intention consequently to change their methods.
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  • HAL Id : tel-01114281, version 3

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Zoé Mesnil. La logique : d'un outil pour le langage et le raisonnement mathématique vers un objet d'enseignement. Histoire et perspectives sur les mathématiques [math.HO]. Université Paris Diderot, 2014. Français. ⟨tel-01114281v3⟩

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