Geometric locus activities in a dynamic geometry system. Non-iconic visualization and instrumental genesis

Abstract

This paper presents a study on the use of geometric locus using a dynamic geometry system (GeoGebra) in order to pass from Geometry II (a natural proto - axiomatic Geometry) to Geometry III (a complete axiomatic Geometry). The research was conducted with 30 Spanish college prospective mathematics teachers. The Geometrical Working Space theory (GWS) was used as a theoretical framework to describe the figurative and instrumental genesis processes involved in the learning processes in computer environments. To study these two geneses, iconic visualization versus non - iconic visualization, along with instrumental and dimensional deconstruction concepts, was used. The authors identify typologies of images and visualization uses. Keywords: Problem - solving strategies, Visualization, Interactive learning, Diagrams, Loci, Teacher training, Visual representations, Reasoning, Geometry, GeoGebra.