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La démarche de découverte expérimentalement médiée par Cabri-Géomètre en mathématiques: un essai de formalisation à partir de l'analyse de démarches de résolutions de problèmes de boîtes noires

Jean-Jacques Dahan 1, 2
2 IAM - Informatique et Apprentissage des Mathématiques
LIG - Laboratoire d'Informatique de Grenoble, Inria - Institut National de Recherche en Informatique et en Automatique
Abstract : Our work is focused on the process of discovery in the context of experimentations with Cabri-Geometry. The analysis of a corpus going beyond mathematics enlightens the way discovery happens, is possibly transmitted as well as the role of experimentation in this process. This analysis validates our initial hypothesis breaking out the experimental process of discovery into macro-stages before and after conjecture including micro-stages of “exploration-interpretation”.
The analysis of the solving process of a particular black box task allows us to refine our a priori model of discovery process by clarifying the role of the figure (Duval), the levels of geometry (Parzysz's praxeologies: G1 and G2) and the extensions we have developed (G1 and G2 information), the frames of inquiry (Millar) and the state of the experimental proof (Johsua).
The analysis of the experimentations we carried out provides an improved model that allows teachers to have a minimal knowledge about the heuristic stages of their students' work, to develop analytical studies and research activities with precise aims that are linked with the formalised stages of our model and possibly to evaluate this work.
At last, current activities have been analysed with our model and show its adequacy. Activities built to improve specific stages of the process of discovery, show the viability of our model as a basis for creating pedagogic scenarios according to the model.
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Submitted on : Monday, January 26, 2009 - 3:55:59 PM
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Jean-Jacques Dahan. La démarche de découverte expérimentalement médiée par Cabri-Géomètre en mathématiques: un essai de formalisation à partir de l'analyse de démarches de résolutions de problèmes de boîtes noires. Autre [cs.OH]. Université Joseph-Fourier - Grenoble I, 2005. Français. ⟨tel-00356107⟩

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