Variations et variables de la démonstration géométrique

Abstract We examine the practice of mathematical proof in geometry in the work of Euclid, Hilbert, and Legendre, each illustrated with specific examples. Our study shows the great variation in the forms of geometric proof, even in Hilbert’s books, according to variables that we enumerate. These differences come not so much from the underlying logic … Lire la suite

Ecologie des problèmes de construction dans l’espace

Abstract In this article, we propose to study the history of construction problems in solid geometry. First, we will show that construction problems have evolved during the two periods from 1920 to 1969 and from 1982 to the present and that the drawing has served different functions in the solution of these problems. To that … Lire la suite

Problèmes d’articulation de cadres théoriques : l’exemple du concept de milieu

Abstract This paper is the written version of a talk given at the summer school on the didactics of mathematics held at Houlgate, France, in August 1999. The topic for the day was to examine the domain of validity of different didactical approaches. I chose to approach the subject by starting from two questions, treating … Lire la suite

L’analyse des pratiques enseignantes en théorie anthropologique du didactique

Abstract This paper originated in a series of lectures given at the summer university for in-service mathematics teachers held in La Rochelle (France) in july 1998. It provides a straightforward presentation of some key concepts of the anthropological approach to the teaching of mathematics. It is mainly intended to help the practising didactician come into … Lire la suite