ICME 8: Topic Group 19 Presentation Summary

This is an abstract of a presentation at The 8th International Congress on Math Education (ICME 8)

July 14-21, 1996 in Seville, Spain..

We present two computer-based open learning environments for geometry problem solving: CALQUES which is widely used in French secondary schools, then CHYPRE which is an experimental improvement with reasoning tools. Our aim is to give freedom to explore a problem in any way and to test any plan of problem-solving.

With CALQUES, the user creates any Euclidean construction. He obtains a diagram which could be separated into several diagrams and the sequence of these diagrams may be considered as an obvious visual proof.

CHYPRE is based on the relevance of basic configurations (e.g. a parallelogram) in a figure. The student designates a configuration directly on the figure. This action will be translated into a statement (ex.: "ABCD is a parallelogram"). After checking the accuracy of the statement, the system creates "implicit", i.e. statements which can be inferred naturally from the entered statement, and add logical links between existing statements. For example, an implicit of "ABCD is a parallelogram" is "AB and CD are parallel".

The solution representation is obtained by a graph which only contains the relevant elements of this solution. This graph is a reduction of the full resolution graph. It only represents the elements really declared by the user and not the implicit elements created by the system. This graph is in accordance with principles which assure the consistency of the presentation with regard to logic deductions it induces. The student is absolutely free to explore the problem. He can begin with inferences from hypothesis (top-down) or from goal (bottom-up) or with a fact in the "middle". When using CHYPRE, the student focuses on the key steps of a demonstration and skips the less important ones. CHYPRE accepts solutions explanations which are not highly formalized.

Philippe Bernat, Bernat@loria.fr

Université Henri Poincaré Nancy I

Centre de Recherche en Informatique de Nancy BP 239

54506 Vandoeuvre les Nancy - FranceTel (33) 83 59 20 57

Fax (33) 83 41 30 79

http://www.loria.fr/~bernatSecretariat : (33)83 59 30 87