Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abrougui, H. (1995). Impact de ’environnement Cabri-géomètre sur les démarches de preuve d’élèves de 5ème dans un problème de construction impossible. Lyon (France), University of Lyon 1, Mémoire de DEA de Didactique des Disciplines Scientifiques.
Bartolini Bussi, M. (1991). Geometrical proofs and mathematical machines: An exploratory study. In I. Hirabayashi, N. Nohda, K. Shigematsu, F. L. Lin (Eds.), Proceedings of the XVIIth Conference of the International Group for Psychology of Mathematics Education (Vol. II, pp. 97–104). Tsukuba (Japan): University of Tsukuba.
Bazin, J.-M. (1994) Géométrie: le rôle de la figure mis en évidence par les difficultés de conception d’un résolveur de problèmes en EIAO. In M. Artigue et al. (Eds.), Vingt ans de didactique des mathématiques en France (pp. 371–377). Grenoble: La Pensée Sauvage.
Brousseau, G. (1992). Didactique: What it can do for the teacher. Recherches en didactique des mathematiques, Selected papers, 7–40 Grenoble: La Pensée Sauvage.
De Villiers, M. (1990). The role and function of proof in mathematics. Pythagoras: Journal of the Mathematical Association of Southern Africa, 24, 17–23.
Duval, R. (1995). Geometrical pictures: Kinds of representation and specific processes. In R. Sutherland & J. Mason (Eds.), Exploiting mental imagery with computers in mathematics education (pp. 142–157). Berlin: Springer.
Fishbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24, 139–162.
Geometer’s Sketchpad [Computer software from the Visual Geometry Project]. (1993). Berkeley (USA): Key Curriculum Press.
Greenberg, M. (1972). Euclidean and non Euclidean geometries: Development and history. New York: Freeman.
Hadas N., Hershkowitz R. & Schwarz B. (2000). The role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments. Educational Studies in Mathematics, 44(1–3), 127–150.
Hardy, G. H. (1940). A mathematician’s apology Cambridge: Cambridge University Press. (Republished 1992.)
Hoelzl, R. (1994). Im Zugmodus der Cabri-Geometrie. Weinheim: Deutscher Studien.
Hoelzl, R. (1995). Between drawing and figure. In R. Sutherland & J. Mason (Eds.), Exploiting mental imagery with computers in mathematics education (pp. 117–124). Berlin: Springer.
Jones K. (1998) Deductive and intuitive approaches to solving geometrical problems In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century (pp. 78–83). Dordrecht: Kluwer.
Jones K. (2000). Providing a foundation for deductive reasoning: students’ interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44(1–3), 55–85.
Laborde, J.-M. & Straesser, R. (1990). Cabri-géomètre: A microworld of geometry for guided discovery learning. Zentralblattfuer Didaktik der Mathematik, 5(90). 171–177.
Marrades R. & Guttierez, A. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics 44(1–3), 87–125.
Mariotti, M. A. (1995). Images and concepts in geometrical reasoning. In R. Sutherland & J. Mason (Eds.), Exploiting mental imagery with computers in mathematics education (pp. 97–116). Berlin: Springer.
Mariotti M.-A. (2000). Introduction to proof: The mediation of a dynamic software environment. Educational Studies in Mathematics, 44(1–3), 25–53.
Noss, R. & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Dordrecht: Kluwer.
Otte, M. (1995). Mathematik und Verallgemeinerung. In Arbeiten aus dem Institut für Didaktik der Mathematik der Universität Bielefeld, Occasional Paper 158. Bielefeld: University of Bielefeld.
Pluvinage, F. (1989). Aspects multidimensionnels du raisonnement géométrique. Annales de Didactique et de Sciences Cognitives (ULP et IREM de Strasbourg), 2, 5–24.
Rauscher, J. C. (1993). L’hétérégonéité des professeurs face à des élèves hétérogènes. Le cas de l’enseignement de la géométrie au début du collège. Strasbourg (France), Université des Sciences Humaines de Strasbourg, Thèse de l’université de Strasbourg.
Salin, M.-H. & Berthelot, R. (1994). Phénomènes liés à l’insertion de situations adidactiques dans l’enseignement élémentaire de la géométrie. In M. Artigue et al. (Eds.), Vingt ans de didactique des mathématiques en France (pp. 275–282). Grenoble: La Pensée Sauvage.
Straesser, R. (1995). Euclidean versus descriptive: On social needs and teaching geometry. In C. Mammana (Ed.), Perspectives on the teaching of geometry for the 21st century (pp. 246–249). Catania (Italy): University of Catania.
Sutherland, R. & Balacheff, N. (1999). Didactical complexity of computational environments for the learning of mathematics. International Journal of Computers for Mathematical Learning, 4, 1–26.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Laborde, C. (2005). The Hidden Role of Diagrams in Students’ Construction of Meaning in Geometry. In: Kilpatrick, J., Hoyles, C., Skovsmose, O., Valero, P. (eds) Meaning in Mathematics Education. Mathematics Education Library, vol 37. Springer, New York, NY. https://doi.org/10.1007/0-387-24040-3_11
Download citation
DOI: https://doi.org/10.1007/0-387-24040-3_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-24039-8
Online ISBN: 978-0-387-24040-4
eBook Packages: Humanities, Social Sciences and LawEducation (R0)