A new way for visual reasoning in geometry education

  • Philippe Bernat
  • Josette Morinet-Lambert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1086)


In this paper, we describe two open learning environments for geometry problem solving: CALQUES which is widely used in French secondary schools for mathematical courses, then CHYPRE which is an experimental improvement with reasoning tools. Our aim is not to imitate an expert method nor to implement an existing pedagogical approach but to give freedom to explore a problem in any way and to test any plan of problem-solving. Visual reasoning plays an important role in geometry and provides a far different approach of problem-solving than standard formal proofs. We will explain that a student using CHYPRE focuses only on the main statements that could be observed on the problem diagram and has the opportunity to skip the less important ones. To students, as well as to mathematicians, mathematical concepts are not mere definitions, but they consist of individuals' intuitions. These intuitions are formed by imagination and understanding.


visual reasoning direct manipulation problem solving geometry 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    ANDERSON, J.R.-BOYLE, C.F.-YOST, G.: The Geometry Tutor. Proceedings of IJCAI 85, Los Angeles, pp. 1–7, 1985Google Scholar
  2. [2]
    BERNAT, P.: CALQVES2, Topiques Edition, 1994Google Scholar
  3. [3]
    CUNNINGHAM, s.-HUBBOLD R.J.: Interactive Learning Through Vizualisation, IFIP Series on Computer graphics, Springer-Verlag 1992.Google Scholar
  4. [4]
    DREYFUS, T.: Imagery and Reasoning in Mathematics and Mathematics Education, Selected Lectures from the 7th International Congress on Mathematical Education, Les Presses de l'Université Lavai, Sainte-Foy, pp. 107–122, 1994Google Scholar
  5. [5]
    FISCHBEIN, E.: The Theory of Figural Concepts, Educational Studies in mathematics 24, pp. 139–162, 1993Google Scholar
  6. [6]
    GUIN, D.: Modélisation des connaissances pour un système d'aide à la démonstration géométrique, Université d'été Informatique et Enseignement de la Géométrie, IREM de Toulouse, pp. 61–72, 1990Google Scholar
  7. [7]
    JACKIW, N.: The Geometer's Sketchpad (version 3.0), Visual Geometry Project, Key curriculum Press, 1995Google Scholar
  8. [8]
    KOEDINGER, K.R.-ANDERSON, J.R.: Effective Use of Intelligent Software in High School Math Classrooms, Proceedings of AI-ED 93, P.Brna, S. Ohlsson, H. Pain (Ed), pp. 241–248, 1993Google Scholar
  9. [9]
    LABORDE, J.M.-BELLEMAIN, F.: Cabri 2 — Texas InstrumentsGoogle Scholar
  10. [10]
    LARKIN, J.H.-SIMON, H.A.: Why a Diagram is (Sometimes) Worth Ten Thousand Words, Cognitive Science 11, pp. 65–99, 1987[BP1]Google Scholar
  11. [11]
    PY, D.: Geometry problem solving with Mentoniezh, Computers in Education, vol. 20 n°l, Pergamon Press, pp. 141–146, 1993Google Scholar
  12. [12]
    TAURISSON, A.: Pensée mathématique et gestion mentale, Pour une pédagogie de l'intuition mathématique. Bayard Editions, 1993Google Scholar
  13. [13]
    WERTHEIMER, R.: The Geometry Proof Tutor: An Intelligent Computer-based Tutor in the Classroom, Mathematics Teacher, pp. 308–317, April 1990Google Scholar
  14. [14]
    YERUSHALMY, M.-CHAZAN, D.: Overcoming Visual Obstacles with the Aid of the Supposer. Educational Studies in Mathematics n°21, pp. 199–219, 1990Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Philippe Bernat
    • 1
  • Josette Morinet-Lambert
    • 1
  1. 1.Centre de Recherche en Informatique de Nancy/CNRSUniversité Henri Poincaré - Nancy IVandoeuvre les Nancy CedexFrance

Personalised recommendations