Geometria Euclidiana e geometria Hiperbólica em um ambiente de geometria dinâmica : o que pensam e o que sabem os professores

Abstract

This research approaches the teaching of Non-Euclidian Geometries, especially Hyperbolic Geometry and the software use of GeoGebra Dynamic Geometries. The research main goals consist of checking the knowledge from a group of teacher over Euclidian Geometry and Hyperbolic Geometry; identifying some epistemological obstacles during the activities performance that use the Poincaré disc model; verify that the study of this model allows that he teachers abandon the focused view that Euclidian Geometry is the only Geometry possible and, finally, check the possible contributions of GeoGebra software for the learning of Geometry contents. In order to achieve our goals we chose qualitative research type and we proposed a short-term course on Euclidian Geometry and Hyperbolic Geometry with the support from the GeoGebra software for a group of forty Mathematics teachers from public schools in towns from the North of Paraná state. We also had a historical, mathematic and philosophical discussion on Euclidian and Hyperbolic Geometry, concerning the teaching of these kinds of Geometry and the use of new Technologies in the educational field. Starting from interactions and reports from the teachers, some difficulties in the Geometry contents were confirmed, as well as the existence of epistemological obstacles - general and verbal - besides the lack of knowledge on educational possibilities of technological resources available in the schools and the difficulties in using them.