Elementary geometry split into different geometrical paradigms.

Géométrie élémentaire et ses différents paradigmes

Catherine Houdement (1) , Alain Kuzniak (1)

1 LDAR (URP_4434) - Laboratoire de Didactique André Revuz

Since several years, we have developed a scientific investigation on the teaching of Geometry, especially for pre-service teachers. This research is based on a specific theoretical frame. We have chosen to give some elements of our frame and we hope to present more consistent examples of our empirical studies during the working group. For us elementary geometry appears to be split into three various paradigms: natural geometry (Geometry I), natural axiomatic geometry (Geometry II) and formalist axiomatic geometry (Geometry III). We confront our approach with the approach of van Hiele, which to date is not used in France. We obtain a synthesis that we currently study in teachers training.

Mots clés: Geometry; Geometrical paradigms; Teacher Training

Domaines: Mathématiques [math]; Education

Catherine Houdement, Alain Kuzniak. Elementary geometry split into different geometrical paradigms.. CERME 3, European Research in Mathematics Education, Feb 2003, Bellaria, Italy. pp.1-10. ⟨hal-03214066⟩