Relationships between the spatial and theoretical in geometry: the role of computer dynamic representations in problem solving

  • Colette Laborde
Part of the IFIP — The International Federation for Information Processing book series (IFIPAICT)


Diagrams play an important role in geometry teaching. An analysis of tasks and students’ behaviour in solving problems in two different environments, paper-and-pencil or computer, indicated that the dynamic nature of the software changes the relationship between diagrams and the theoretical aspects of the subject. Learning geometry seems to involve not only learning how to use theoretical statements in deductive reasoning, but also learning to recognise visually relevant spatial-graphical invariants attached to geometrical invariants. Observations of students revealed that this was not easy for them—moving between the spatial and the theoretical domains was not spontaneous and they tended to consider each domain independently.


Geometry software direct manipulation problem solving case studies. 


  1. Balacheff, N. and Sutherland, R (1994). Epistemological domain of validity of microworlds: the case of Logo and Cabri-géomètre In R Lewis and P.Mendelsohn (eds) Lessons from Learning. IFIP Transactions, A 46, 137–150. Amsterdam: North Holland and Elsevier Science B.V.Google Scholar
  2. Bartolini Bussi, M. (1991). Geometrical proofs and mathematical machines: an exploratory study, Proceedings of the XVIlth Conference of the International Group for Psychology of Mathematics Education. Tsukuba, Japan: University of Tsukuba, 97–104.Google Scholar
  3. Brousseau, G. (1992). Didactique: what it can do for the teacher. Recherches en didactique des mathématiques. Selected Papers. 7–40.Google Scholar
  4. Dreyfus, T. (1993). Didactic design of computer based learning environments. In C. Keitel and K. Ruthven (eds.), Learning from Computers. Nato ASI Series, Heidelberg: Springer Verlag, 101–130.Google Scholar
  5. Duval, R (1995). Geometrical pictures-kinds of representation and specific processings. In R Sutherland and J. Mason Exploiting Mental Imagery with Computers in Mathematics Education. NATO ASI Series, Berlin, Heidelberg: Springer Verlag, 142–157.Google Scholar
  6. Fishbein, E. (1993). The theory of figural concepts, Educational Studies in Mathematics, 24 (2), 139–62.CrossRefGoogle Scholar
  7. Jackiw N. (1993). Geometer Sketchpad (1993) The Visual Geometry Project (software). Swarthmore College and Berkeley: Key Curriculum Press.Google Scholar
  8. Laborde, J-M. and Straesser, R (1990). Cabri-géomètre: a microworld of geometry for guided discovery learning, Zentralblatt fuer Didaktik der Mathematik 5, 171–77.Google Scholar
  9. Mariotti, M. (1995). Images and Concepts in Geometrical Reasoning. In R Sutherland and J. Mason (eds.) Exploiting Mental Imagery with Computers in Mathematics Education. NATO ASI Series, Berlin, Heidelberg: Springer Verlag, 97–116.CrossRefGoogle Scholar
  10. Salin, M-H. and Berthelot, R (1994). Phénomènes liés á l’insertion de situations adidactiques dans l’enseignement élémentaire de la géométrie. In M. Artigue, R Gras, C. Laborde and P Tavignot (eds.), Vingt ans de didactique des mathématiques en France. Grenoble: Editions La Pensée Sauvage, 275–82.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Colette Laborde
    • 1
  1. 1.Laboratoire Leibniz-IMAGGrenobleFrance

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