Skip to main content

The Hidden Role of Diagrams in Students’ Construction of Meaning in Geometry

  • Chapter
Meaning in Mathematics Education

Part of the book series: Mathematics Education Library ((MELI,volume 37))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Brousseau, G. (1992). Didactique: What it can do for the teacher. Recherches en didactique des mathematiques, Selected papers, 7–40 Grenoble: La Pensée Sauvage.

    Google Scholar 

  • De Villiers, M. (1990). The role and function of proof in mathematics. Pythagoras: Journal of the Mathematical Association of Southern Africa, 24, 17–23.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Fishbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24, 139–162.

    Article  Google Scholar 

  • Geometer’s Sketchpad [Computer software from the Visual Geometry Project]. (1993). Berkeley (USA): Key Curriculum Press.

    Google Scholar 

  • Greenberg, M. (1972). Euclidean and non Euclidean geometries: Development and history. New York: Freeman.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Hardy, G. H. (1940). A mathematician’s apology Cambridge: Cambridge University Press. (Republished 1992.)

    Google Scholar 

  • Hoelzl, R. (1994). Im Zugmodus der Cabri-Geometrie. Weinheim: Deutscher Studien.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Laborde, J.-M. & Straesser, R. (1990). Cabri-géomètre: A microworld of geometry for guided discovery learning. Zentralblattfuer Didaktik der Mathematik, 5(90). 171–177.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Mariotti M.-A. (2000). Introduction to proof: The mediation of a dynamic software environment. Educational Studies in Mathematics, 44(1–3), 25–53.

    Article  Google Scholar 

  • Noss, R. & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Dordrecht: Kluwer.

    Book  Google Scholar 

  • 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.

    Google Scholar 

  • Pluvinage, F. (1989). Aspects multidimensionnels du raisonnement géométrique. Annales de Didactique et de Sciences Cognitives (ULP et IREM de Strasbourg), 2, 5–24.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints 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

Publish with us

Policies and ethics