Skip to main content
SpringerLink
Log in

Dynamic and Tangible Representations in Mathematics Education

  • Chapter
  • First Online:
Transformation - A Fundamental Idea of Mathematics Education

Abstract

Dynamic geometry environments offer a new kind of representation of mathematical objects that are variable and behave “mathematically” when one of the elements of the construction is dragged. This chapter addresses three dimensions of transformations brought about by this new kind of representation in mathematics and mathematics education: an epistemological dimension, a cognitive dimension, and a didactic dimension.

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

Access this chapter

Log in via an institution
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 EPUB and 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

References

  • Abd El All, S. (1996). La géométrie comme un moyen d’explication de phénomènes spatio-graphiques: une étude de cas, Mémoire de DEA de Didactique des Disciplines Scientifiques, Grenoble: University of Grenoble 1, Laboratoire Leibniz-IMAG.

    Google Scholar 

  • Artigue, M. (2002). Learning mathematics in a CAS environment: the genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7(3), 245–274.

    Article  Google Scholar 

  • Arzarello, F., Micheletti, C., Olivero, F., Robutti, O., & Domingo, P. (1998a). A model for analysing the transition to formal proofs in geometry. In A. Olivier & K. Newstead (Eds.), Proceedings from the 22nd annual conference of the international group for the psychology of mathematics education (Vol. 2, pp. 24–31). South Africa: University of Stellenbosch.

    Google Scholar 

  • Arzarello, F., Micheletti, C., Olivero, F., Robutti, O., Paola, D., & Gallino, G. (1998b). Dragging in Cabri and modalities of transition from conjectures to proofs in geometry. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd conference of the international group for the psychology of mathematics education (Vol. 2, pp. 32–39). South Africa: University of Stellenbosch.

    Google Scholar 

  • Bosch, M., & Chevallard, Y. (1999). La sensibilité de l’activité mathématique aux ostensifs. Recherches en didactique des mathématiques, 19(1), 77–124.

    Google Scholar 

  • Brousseau, G. (1997). Theory of didactical situations in mathematics. N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (Trans., Eds.). Dordrecht: Kluwer.

    Google Scholar 

  • D’Amore, B. (2003). Le basi filosofische, pedagogiche, epistemologiche e concettuali della Didattica della Matematica. Bologna: Pitagora Editrice.

    Google Scholar 

  • Duval, R. (2000). Basic issues for research in mathematics education In T. Nakahara & M. Koyama (Eds.), Procedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol 1, pp. 55–69). Hiroshima: Hiroshima University.

    Google Scholar 

  • Duval, R. (2005). Les conditions cognitives de l’apprentissage de la géométrie: développement de la visualisation, différenciation des raisonnements et coordination de leurs fonctionnements, In: Annales de didactique et sciences cognitives, 5–53. Strasbourg, France: IREM, Université Louis Pasteur.

    Google Scholar 

  • Falcade, R., Laborde, C., Mariotti, A. (2007). Approaching functions: Cabri tools as instruments of semiotic mediation. Educational Studies in Mathematics, 66(3), 317–333.

    Article  Google Scholar 

  • Goldenberg, E. P. (1995). Rumination about dynamic imagery. In R. Sutherland & J. Mason (Eds.), Exploiting Mental Imagery with computers in mathematics education, (Vol 138, pp. 202–224). (NATO ASI series F). Heidelberg: Springer.

    Chapter  Google Scholar 

  • Hattermann, M. (2011). Explorative Studie zur Hypothesengewinnung von Nutzungsweisen des Zugmodus in dreidimensionalen dynamischen Geometriesoftwaresystemen. Giessen: Dissertation der Justus Liebig Universität.

    Google Scholar 

  • Hilbert, D., Cohn-Vossen, S. (1952). Geometry and the imagination, (2nd ed., 1990), New York: Chelsea, translation by P. Nemenyi of Anschauliche Geometrie, Berlin, 1932: Springer.

    Google Scholar 

  • Hölzl, R. (1996). How does the dragging affect the learning of geometry? International Journal of Computer for Mathematical Learning, 1(2), 169–187.

    Article  Google Scholar 

  • Hoyles, C., & Jones, K. (1998). Proof in dynamic geometry contexts. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century—An ICMI study (chap. 4, section II, pp. 121–128). Dordrecht: Kluwer.

    Google Scholar 

  • Hoyles, C., & Noss, R. (2003). What can digital technologies take from and bring to research in mathematics education? In J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Second international handbook of mathematics education (Part 1; pp. 323–349). Dordrecht, The Netherlands: Kluwer.

    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: An ICMI study (pp. 78–83). Dordrecht: Kluwer.

    Google Scholar 

  • Kadunz, G., & Straesser, R. (2007). Didaktik der Geometrie in der Sekundarstufe I, Hildesheim. Berlin: Franzbecker.

    Google Scholar 

  • Laborde, C. (1991). Zu einer Didaktik des Geometrie-Lernens unter Nutzung des Computers in Intelligente Tutorielle Systeme für das Lernen von Geometrie, Proceedings des Workshops am IDM, März 1991, Occasional Paper 124, Bielefeld, Germany: Universität Bielefeld, Institut für Didaktik der Mathematik.

    Google Scholar 

  • Lagrange, J.-B. (2002). Etudier les mathématiques avec les calculatrices symboliques: quelles places pour les techniques? In D. Guin & L. Trouche (Eds.), Calculatrices symboliques, transformer un outil en un instrument du travail mathématique: un problème didactique (ch. 5, pp. 151–185), Grenoble: La Pensée Sauvage Editions.

    Google Scholar 

  • Mariotti, A. (2001). Justifying and proving in the Cabri environment. International Journal of Computers for Mathematical Learning, 6(3), 257–281.

    Article  Google Scholar 

  • Mithalal, J. (2010). Déconstruction instrumentale et déconstruction dimensionnelle dans le contexte de la géométrie dynamique tridimensionnelle. Thèse de l’Université Grenoble 1.

    Google Scholar 

  • Moreno, J. (2006). Articulation des registres graphique et symbolique pour l’étude des équations différentielles avec Cabri-géomètre: analyse des difficultés des étudiants et rôle du logiciel. Thesis, Université Joseph Fourier, Grenoble, France.

    Google Scholar 

  • Moreno Armella, L. (1999). Epistemologia ed Educazione matematica. La Matemetica e la sua Didattica, 1, 43–59.

    Google Scholar 

  • Netz, R. (1999). The shaping of deduction in Greek mathematics Cambridge Univ. Press

    Google Scholar 

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

    Book  Google Scholar 

  • Parzysz, B. (1988). Knowing vs. Seeing, Problems of representation of space geometry figures. Educational Studies in Mathematics, 19(1), 79–92.

    Article  Google Scholar 

  • Restrepo, A. (2008). Genèse instrumentale du déplacement en géométrie dynamique chez des élèves de 6ème. Thèse Université Grenoble 1.

    Google Scholar 

  • Schneidermann, B. (1983). Direct manipulation: A step beyond programming languages. IEEE Computer, 16, 57–69.

    Article  Google Scholar 

  • Smith, D., Harslem, E., Irby, C., & Kimball, R. (1982). Designing the star user interface. Byte, 74, 242–282.

    Google Scholar 

  • Strässer, R. (1991). Dessin et Figure Géométrie et Dessin technique à l’aide de l’ordinateur. (Juni 1991) Occasional paper n°128. Bielefeld, Germany: Universität Bielefeld, Institut für Didaktik der Mathematik.

    Google Scholar 

  • Strässer, R. (1992). Didaktische Perspektiven auf Werkzeug-Software im Geometrie-Unterricht der Sekundarstufe I. Zentralblatt für Didaktik der Mathematik, 24(5), 197–201.

    Google Scholar 

  • Vérillon, P., & Rabardel, P. (1995). Cognition and artifacts. A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10(1), 77–101.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University Joseph Fourier, Cabrilog, Grenoble, France

    Colette Laborde & Jean-Marie Laborde

  2. Chemin du Chateau, 38160, Saint Sauveur, France

    Colette Laborde & Jean-Marie Laborde

Authors
  1. Colette Laborde
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jean-Marie Laborde
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Colette Laborde .

Editor information

Editors and Affiliations

  1. IEIM - Institut für Mathematik, Universität Paderborn, Paderborn, Germany

    Sebastian Rezat

  2. Fakultät für Mathematik - IDM, Universität Bielefeld, Bielefeld, Germany

    Mathias Hattermann

  3. Fakultät für Mathematik - IDM, Universität Bielefeld, Bielefeld, Germany

    Andrea Peter-Koop

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Laborde, C., Laborde, JM. (2014). Dynamic and Tangible Representations in Mathematics Education. In: Rezat, S., Hattermann, M., Peter-Koop, A. (eds) Transformation - A Fundamental Idea of Mathematics Education. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3489-4_10

Download citation

Publish with us

Policies and ethics

Search

Navigation