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Place de la validation dans la conceptualisation, le cas du concept de fonction

Abstract : This work analyses the interactions of the classical adidactical system: a subject in interaction with a “milieu”. We explore the place of knowledge as a regulator on these interactions. For that, we choose the mathematical concept of function and the subject activity is characterised by means of conceptions (cKc model). We focus our attention on the “control” aspect of conceptions, in relation with others, in particular with the “operator” aspect. Our framework is presented in relation with two other frameworks: the “Théorie des Situations Didactiques” et the “Théorie des Champs Conceptuels”. We also explain the classical distinction between operational and structural conceptions of mathematical concept and we show the interest of such a distinction in a validation perspective. We also point out the sound difference between this approach and our approach. We have built experimentation for engineer students (INPG) and trainee teachers (PLC2). The experimentation problem has been built to reveal the controls and require the concept of function. The data analysis is based on a methodology which explains the relations between the choices of the analysis and the problematic. The interactions complexity leads us to distinguish two levels of controls: referent control and instrumentation control. In particular, we demonstrate the effects of the lack of controls on the subject activity.
Keywords : conception, function, validation, control, operator, cK¢ model.
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https://tel.archives-ouvertes.fr/tel-00113100
Contributor : Nathalie Gaudin <>
Submitted on : Friday, November 10, 2006 - 3:45:31 PM
Last modification on : Friday, November 6, 2020 - 4:13:44 AM
Long-term archiving on: : Tuesday, April 6, 2010 - 6:58:59 PM

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  • HAL Id : tel-00113100, version 1

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Nathalie Gaudin. Place de la validation dans la conceptualisation, le cas du concept de fonction. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2005. Français. ⟨tel-00113100⟩

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