Artículos
Vol. 17 No. 4(II) (2014): Diciembre
TO INITIATE A MATHEMATICAL PROOF PROCESS IN AN 3D DYNAMIC GEOMETRY ENVIRONMENT
Abstract
This paper concerns the topic: “The mathematical work and the social and institutional aspects.” We have attempted to analyze how, in a geometrical construction activity context, the use of intellectual proof can be justified and which way it contributes to stably insert the students’ activity in a natural geometrical axiom. In our thesis project we have shown that situations built on a 3D dynamic geometrical environment can lead the students to rely on this type of geometry. Nonetheless, this evolution would proof itself unstable, and we propose here to examine where the social interactions, and especially via discursive genesis, play a fundamental role in terms of this stability. The proof issue is central to this concern, as it seems to be consubstantial with the transition of assumed Geometry GI to parceled Geometry GII. We propose to analyze the work of three groups of students, inspired on a thesis experiment (Mithalal, 2010), with the purpose of highlighting the interactions between the material activity and the discursive genesis in the geometrical working spaces.
References
- Balacheff, N. (1999). Apprendre la preuve. Le concept de preuve à la lumière de l’intelligence artificielle, 197-236. (J. Sallantin, & J. J. Szczeciniarz, Éds.) Paris: PUF.
- Bartolini Bussi, M. (1991). Social interaction and mathematical knowledge. Proceedings of the 15th PME International, (pp. 1-16). Assisi, Italia.
- Bulf, C., Mathé, A. - C., & Mithalal, J. (2011). Language in geometrical classroom. Proceedingof the 7th Congress of the European Society for Research in Mathematics Education (CERME 7), (pp. 649-659). Rzeszow, Pologne.
- Bulf, C., Mathé, A. - C., Mithalal, J., & Wozniak, F. (2012). Le langage en classe de Mathématiques : quels outils d’analyse en didactique des mathématiques? Questions vives en didactique des mathématiques : problèmes de la profession d’enseignant. Grenoble: La pensée sauvage.
- Duval, R. (2005). Les conditions cognitives de l’apprentissage de la géométrie: développement de la visualisation, différenciation des raisonnements et coordination de leurs fonctionnements. Annales de Didactique et de Sciences Cognitves, 10, 5 - 53.
- Houdement, C., & Kuzniak, A. (2006). Paradigmes géométriques et enseignement de la géométrie. Annales de Didactique et de Sciences Cognitives, 11, 175 - 193.
- Kuzniak, A. (2010). Un essai sur la nature du travail géométrique en fin de la scolarité obligatoire en France. Proceedings of the First French - Cypriot Conference of Mathematics Education, (pp. 71 - 89).
- Laborde, C. & Capponi, B. (1994). Cabri - géomètre constituant d’un milieu pour l’apprentissage de la notion de figure géométrique. Recherches en didactique des mathématiques 14 (1.2), 165-210.
- Legrand, M. (1993). Débat scientifique en cours de mathématiques et spécificité de l’analyse. Repères IREM, 123-158.
- Mithalal, J. (2010). Déconstruction instrumentale et déconstruction dimensionnelle dansle contexte de la géométrie dynamique tridimensionnelle. Grenoble: Thèse de l’Université de Grenoble.
- Rabardel, P. (1995). Les hommes et les technologies. Approche cognitive des instruments contemporains. Paris: Armand Collin.
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