Des conditions de conception d'une ingénierie didactique relative à la définition de la notion de limite : élaboration d'un cadre basé sur un modèle de rationalités pour l'accès aux objets mathématiques complexes

Abstract : The aim of this work is to study the means necessary to allow students to accede to the raison d'être of the knowledge involved in the building of notions of Calculus and Analysis. The thesis deals with this question and develops a theoretical frame for the conception of engineering which aims this sense and this necessity. This theoretical frame, designed in TDS theory, stands on a model of rationalities and some adaptations of TDS mainly on heuristic levels. We deploy the scientific debate construct to design lessons based on this frame. A didactic engineering aiming at the notion of limit and its formal definition is developed and experimented. Productions resulting from this work suggest a best appropriation of the definition of a limit, as well as a better link between the mathematical objects handled in situations (sequences, functions…) and the formal definition.
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Thomas Lecorre. Des conditions de conception d'une ingénierie didactique relative à la définition de la notion de limite : élaboration d'un cadre basé sur un modèle de rationalités pour l'accès aux objets mathématiques complexes. Education. Université Grenoble Alpes, 2016. Français. ⟨NNT : 2016GREAM049⟩. ⟨tel-01679994⟩

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