Rôle de la visualisation dans la conceptualisation des objets de l'Analyse en classes préparatoires -Cas d'approximation polynômiale locale d'une fonction - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2024

Rôle de la visualisation dans la conceptualisation des objets de l'Analyse en classes préparatoires -Cas d'approximation polynômiale locale d'une fonction

Résumé

The concept of local polynomial approximation of a function plays a decisive role in solving problems related to intra-and extra-mathematical domains at the beginning of the preparatory classes for engineering studies. This article presents the development and implementation of a situation, in the context of collaborative work with the teacher of the first-year Physics-Chemistry (PC) class, enabling the visualization of graphical representations with a view to helping students appropriate the concepts of limited developments and the best approximation of a function in the vicinity of a point. The methodology used to analyze the students' work was based, within the framework of the theory of didactic situations, on the model of reasoning analysis, with a view to identifying and characterizing the difficulties experienced by the students in conceptualizing these mathematical objects. Experimentation demonstrated the value of graphs as a model for polynomial approximation of a function in the vicinity of a real. Indeed, visualizing graphical representations helped students distinguish the formulas used to determine a polynomial approximation of a function in the vicinity of a real: the Taylor-Young formula and the generalized definition of limited development.
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Dates et versions

hal-04411114 , version 1 (23-01-2024)

Identifiants

  • HAL Id : hal-04411114 , version 1

Citer

Fatma Belhaj Amor. Rôle de la visualisation dans la conceptualisation des objets de l'Analyse en classes préparatoires -Cas d'approximation polynômiale locale d'une fonction. 2024. ⟨hal-04411114⟩
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