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A propos de l'apprentissage des limites de fonctions dans un "environnement calculatrice" : étude des rapports entre processus d'instrumentation et processus de conceptualisation

Abstract : The epistemological study reveals three points of view on the limits of functions: kinematic, operative and "approximation". It is this last point of view which allowed the stabilization of the concept. After many oscillations, the teaching programs in France gave up giving a constructed definition of the notion of limit in the high school classes, advocating a simple use of the "language of the limits". In practice, this teaching is reduced to an algebraic work on the limits. Graphical calculators, which are not taken into account by the educational institution, are increasingly used by students. A survey conducted in Terminale and in the first year of university shows the influence of these tools which reinforce in students a monotonous concept of limits, linked to the kinematic point of view. The "approximation" point of view does not emerge either from the teaching received or from the use of calculators. An observation followed by a class in which graphical and then symbolic calculators are integrated by the teacher indicates that the influence of calculating tools is greater or smaller according to the pupils: the instrumentation processes depend on the cognitive characteristics of the pupils. This thesis highlights: - five student profiles (related to essential meta-knowledge: investigation, storage, comparison, interpretation, inference and general control over the activity); - different relationships for each of these types between instrumentation processes and conceptualization processes. This thesis leads to the need, to control the tools, of three taken into account: - an epistemological consideration: we can not speak of a concept - the limits - without being interested in its meaning; - technological consideration: the integration of calculation tools is the responsibility of the professor; - a psychological consideration: attention to student profiles is a prerequisite for classroom management, even more necessary in an activity with instruments.
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Contributor : Luc Trouche <>
Submitted on : Tuesday, December 3, 2019 - 12:32:22 PM
Last modification on : Monday, October 19, 2020 - 10:41:19 AM
Long-term archiving on: : Wednesday, March 4, 2020 - 1:19:58 PM

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  • HAL Id : tel-02374810, version 1

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Luc Trouche. A propos de l'apprentissage des limites de fonctions dans un "environnement calculatrice" : étude des rapports entre processus d'instrumentation et processus de conceptualisation. Histoire et perspectives sur les mathématiques [math.HO]. Université Montpellier 2, 1996. Français. ⟨tel-02374810⟩

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