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Déconstruction instrumentale et déconstruction dimensionnelle dans le contexte de la géométrie dynamique tridimensionnelle

Abstract : This work is about geometry teaching in secondary school, from a practical geometry to a more theoretical one. We show that 3D dynamic geometry environments make this evolution easier, which we detail here. Our hypothesis about learning lie on Theory of Didactical Situations (Brousseau, 1998). Moreover, our first questions were reformulated considering two main theoretical frameworks. With the geometrical paradigms' epistemological point of view (Houdement&Kuzniak, 2006), we identified that it is fundamental for pupils to use a GII paradigm. Duval (2005) cognitive approach highlighted that this requires them to leave iconic visualization and to use dimensional deconstruction for geometry problems interpretation and resolution. 3D dynamic geometry environments are supposed to be helpful for this, and instrumental deconstruction plays a central role. This was made more accurate with a theoretical study, based on cKc (Balacheff, 1995; Balacheff & Margolinas, 2005), and an experimental one, based on the didactics engineering method. We show that in this context two kinds on instrumental deconstructions have to be distinguished, which bridges the gap between iconic visualization and dimensional deconstruction. 3D dynamic geometry make pupils use GII and dimensional deconstruction, and cKc helps to describe this progressive evolution.
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https://tel.archives-ouvertes.fr/tel-00590941
Contributor : Joris Mithalal <>
Submitted on : Friday, May 6, 2011 - 3:19:09 PM
Last modification on : Thursday, November 19, 2020 - 12:59:53 PM
Long-term archiving on: : Friday, November 9, 2012 - 10:50:14 AM

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  • HAL Id : tel-00590941, version 1

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Joris Mithalal. Déconstruction instrumentale et déconstruction dimensionnelle dans le contexte de la géométrie dynamique tridimensionnelle. Mathématiques [math]. Université de Grenoble, 2010. Français. ⟨tel-00590941⟩

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