Desenvolvimento do raciocínio dedutivo ao nível do ensino secundário: recurso a geometrias planas

Abstract

The present curricular guidelines of the secondary school level goes towards a diversified approach promoting the understanding of Geometry as an axiomatic system. What is currently documented may not be sufficiently rich to cover important aspects in the understanding of what is an axiomatic system, as well as aspects related to the development of mathematical reasoning (e.g., the meaning given in known situations working on distinct models of plane geometries). This text presents the results of a research carried out in the context of alternated approaches in the processes of teaching and learning Euclidean geometry, at a secondary education level, in order to promote structured levels of mathematical thinking. In particular, the potential of other models of Plane Geometries (e.g. hyperbolic geometry, geometry of taxi driver) in relation to this problem were considered. The research consisted in the classroom implementation of a geometry task folder to generate some understanding on the following question: How can other models of Plane Geometries, other than the Euclidean one, help Secondary School students to develop deductive reasoning?