Analysis of the relation between image and definition in a problem mediated by GeoGebra from non-examples of regular polyhedron

Abstract

Numerous regulatory documents express a revaluation of Geometry, not only when working with manipulative materials but also when dynamic geometric software mediates the work. We demonstrate it through the design of situations that allow exploration, formulation and validation of conjectures. To address the notion of regular polyhedron, we elaborated a problematic situation mediated by GeoGebra, due to the advantages that this dynamic environment provides when working with three-dimensional figures. This environment enables us to obtain a multiplicity of cases with a single construction provided geometric properties are used. We present an analysis of the tasks performed by prospective mathematics teachers during the resolution of the problem. Our aim is to determine whether their images are intrinsically governed by the concept, and to do so we have analyzed written records, audio and video recordings and the software construction protocol files. This analysis reveals that in the case of the polyhedron and/or of the regular polyhedron in particular, some students cannot achieve a complete integration between the image and the concept.