Enseigner l'algorithme pour quoi ? Quelles nouvelles questions pour les mathématiques ? Quels apports pour l'apprentissage de la preuve ?

Abstract : Recently, the notion of algorithm has gained in importance in secondary school curricula, in France and abroad. Algorithm is strongly linked with computer science, mathematics and proof and its teaching raises many didactical questions. In this thesis, we propose an epistemological analysis of the algorithm in order to study its transposition and to build didactical situations. To begin with, we introduce a detailed epistemological analysis of the concept, highlighting its fundamental aspects. It leads us to construct a model of conceptions for algorithm regarding the academical knowledge (in mathematics and computer science) and taking into account the different forms an algorithm can take. Those results have been experimentally validated by the analysis of interviews of researchers. This allows us to study the didactical transposition involved in the French high school. Through the study of the official curricula, selected textbooks and online resources, we emphasize a partial transposition of the concept, mainly tool-oriented and based on programming. In the last part, we propose a characterization of fundamental problems for algorithm and perspectives for the design and the study of didactical situations in algorithmics.
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Simon Modeste. Enseigner l'algorithme pour quoi ? Quelles nouvelles questions pour les mathématiques ? Quels apports pour l'apprentissage de la preuve ?. Histoire et perspectives sur les mathématiques [math.HO]. Université de Grenoble, 2012. Français. ⟨tel-00783294⟩

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