“Locus” and “Trace” in Cabrigéomètre: relationships between geometric and functional aspects in a study of transformations

Abstract

The present text describes and characterises the tools “Locus” and “Trace” of Cabri-geometre II, in relations to a study of geometric transformation, more precisely, the passage from the notion of transformation of figures to the notion of applications1 that map points on the plane onto the plane itself. In particular it discusses how the conception of image of a figure under a transformation can evolve—through interaction in a “milieu” organised around Cabri-geometre—such that students move from views of figure-images as undecomposible entities to see them as sets of image-points. Moreover, the study allowed the identification that the notion of trajectory (in a dynamic interpretation) has an important role in this conceptually difficult passage and that dynamic geometry environment renovate this notion.