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Étude des effets de la symétrie axiale sur la conceptualisation des isométries planes et sur la nature du travail géométrique au collège

Abstract : Our study focuses on didactical effects of symmetry on teaching and learning of the others transformations of the plan at secondary school. We refer to Vergnaud's theory, the conceptual field theory and to the Houdement and Kuzniak's theoretical framework of geometrical paradigms and Geometrical Working Space (GWS) in order to describe the nature of geometrical work in student's activity. The main research question deals with the symmetry's play in the figural treatment, according to Duval meaning, in students' personal GWS. We propose a common test to the students at two different levels: at the second year (students are 12-13 years old), and at the fourth year of secondary school (students are 14-15 y. o.). This research points out that the personal GWS is more stabilized for a student at the end of secondary school than for a student at the beginning of secondary school. The schemes of the concept of symmetry are more flexible and can be adapted to the task. These symmetry's schemes contrast to the rotation's ones and reveal a different figural treatment according to the transformation at stake. Several analysis classrooms' practices from the same teacher at different levels at secondary school explain a part of these results from student's productions. Some schemes built in classroom reveal shift in meaning which seem negligible in classroom but crystallize students' practices. Our research concerns the nature of geometrical work in a vocational context too, through an investigation with craftsmen. This study describes how symmetry is a “naturalized” concept and how symmetry organizes craftsman's behaviour through geometry in action.
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Submitted on : Friday, March 20, 2009 - 10:26:52 AM
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  • HAL Id : tel-00369503, version 1

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Caroline Bulf. Étude des effets de la symétrie axiale sur la conceptualisation des isométries planes et sur la nature du travail géométrique au collège. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2008. Français. ⟨tel-00369503⟩

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