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Habilitation à diriger des recherches

Recherches sur l'articulation entre la logique et le raisonnement mathématique dans une perspective didactique. Un cas exemplaire de l'interaction entre analyses épistémologique et didactique. Apports de la théorie élémentaire des modèles pour une analyse didactique du raisonnement mathématique

Abstract : This text consists in a synthesis of the research in which I have been engaged for about fifteen years concerning the relationship between logic and mathematical reasoning, through the enlightening perspective offered by the model theoretic point of view due to Tarski.
In a first part, I present the specific aspects of Model theory that I use in the didactic studies and I give an example of the relevance of this theoretical frame in order to deal with truth, validity, necessity and certainty. In the following parts, the analysis are developed according with three axis: the consideration of logical connectors beyond truth-value tables; some questions about the way mathematics teachers deal with quantification matters; the interpretation of mathematical statements under syntactic, semantic and pragmatic points of view. This leads to reinterpret some classical logical errors; to minor the distance between common sense logic and mathematical logic and to question some teaching choices concerning the learning of rigor.
The results I have obtained in this general theoretical framework allow developing research programs according to two main perspectives. The first one concerns the role played by logical formalism in the development of mathematical knowledge at tertiary level. The second one concerns crossed studies between didactic and linguistic analysis of mathematical discourse, using the resources offered by logical semantics.
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Habilitation à diriger des recherches
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https://tel.archives-ouvertes.fr/tel-00201626
Contributor : Viviane Durand-Guerrier <>
Submitted on : Tuesday, January 1, 2008 - 8:40:50 PM
Last modification on : Friday, October 23, 2020 - 4:38:13 PM
Long-term archiving on: : Tuesday, April 13, 2010 - 4:00:48 PM

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Viviane Durand-Guerrier. Recherches sur l'articulation entre la logique et le raisonnement mathématique dans une perspective didactique. Un cas exemplaire de l'interaction entre analyses épistémologique et didactique. Apports de la théorie élémentaire des modèles pour une analyse didactique du raisonnement mathématique. Mathématiques [math]. Université Claude Bernard - Lyon I, 2005. ⟨tel-00201626⟩

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