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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