Elementary geometry split into different geometrical paradigms.

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