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Une étude du rapport entre connaissance et preuve : le cas de la notion de symétrie orthogonale

Abstract : This research presents an analysis of the relationship between knowledge and proof through a mathematical concept: reflective symmetry (in a situation of construction of a proof). We propose to clarify the cognitive distance which would exist for the students, between geometrical construction and the theoretical geometry by the specification of knowledge.

Tools for analysis (conception, rule, support, etc.) are adopted and developed from the knowledge model (cK¢ model) of Balacheff and other models of reasoning and argumentation (Toulmin's model, etc), in order to establish the comparative relationship between the problem of proof and the other problems (geometrical construction, recognition of figures) in terms of knowledge investigated.

In order to identify the effective knowing mobilized by the pupils in a situation of proof construction, an experiment is carried out at a junior high school, at a class of 9th grade in France. This experiment follows a theoretical analysis of certain types of problems which allows us to clarify the various functionalities of components of conception in the sense of Balacheff. The problems of construction and proving are proposed there. The analysis of obtained data illuminates a gap in the state of students' knowledge. In fact, students succeed the construction problem of symmetrical figures, whereas they fail the analogue problem (the same rule is required) in which a proof is required. The absence of a well organized "control" in the construction which is required in proving is identified.
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https://tel.archives-ouvertes.fr/tel-00076565
Contributor : Takeshi Miyakawa <>
Submitted on : Thursday, May 25, 2006 - 5:06:40 AM
Last modification on : Thursday, March 12, 2020 - 11:58:02 AM
Long-term archiving on: : Monday, April 5, 2010 - 8:58:37 PM

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Takeshi Miyakawa. Une étude du rapport entre connaissance et preuve : le cas de la notion de symétrie orthogonale. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2005. Français. ⟨tel-00076565⟩

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