Enseignement du début de l'analyse réelle à l'entrée à l'université : Articuler contrôles pragmatique et formel dans des situations à dimension a-didactique.

Abstract : This study of secondary-tertiary transition on real Analysis allows us to identify a model of macro-didactic variables (VMD) related to levels of familiarity with mathematical knowledge. From upper secondary school to University, the values of each variable undergo from very plain calculation to conceptual knowledge, which led us to identify potential students' difficulties. This research focuses on the means that could be undertaken in tertiary education in order to manage such variations and to allow students build more relevant Analysis knowledge.
Assuming the frame of the theory of didactical situations, we build and experiment two situations with an a-didactic dimension at a level (first year at University) where only a formal existence of mathematical objects has been taught to students. Our situations focus on approximation methods, such as to allow either geometrical or numerical 'pragmatic proofs' or the use of theorems. These situations allow then to consider the semantic / syntactic dialectic in a process of proof, and so permit an effective return to the aimed knowledge. More precisely, the entrance to a mixed process of proofs – formal vs. pragmatic – was unavoidable in the students' work through the emergence of issues related to the existence and accessibility of specific objects: irrational numbers, sequences, limits.
As a conclusion, we suggest to study more in depth the efficiency of the kind of theoretical milieu we built, for instance by introducing other experimental situations and by evaluating knowledge that have been built by students in this new didactical contract.
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Education. Université de Tunis; Université Victor Segalen - Bordeaux II, 2008. Français
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Imène Ghedamsi. Enseignement du début de l'analyse réelle à l'entrée à l'université : Articuler contrôles pragmatique et formel dans des situations à dimension a-didactique.. Education. Université de Tunis; Université Victor Segalen - Bordeaux II, 2008. Français. 〈tel-00361848〉

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