Geometrias Não-Euclidianas: reflexões na Licenciatura em Matemática sobre aplicações no Ensino Médio

Abstract

This dissertation is qualitative in nature, more specifically quasi-experimental. It was developed with the aim of reflections on the teaching of Non-Euclidean Geometries in undergraduate mathematics courses. The as specific objectives were to report on its emergence, introduce the creators, define the concepts, review the literature in order to provide support for other works, and analyze an intervention in a Mathematics degree course in order to demonstrate the viability of applications in secondary education. With the summaries of the work and the implementation of activities through a workshop, with questionnaires, practices and applications using the Geogebra software and face with a panorama of verifications of the answers and interactions with undergraduate, it was concluded that Non-Euclidean Geometries can, in addition to being approached in High School, Non-Euclidean Geometries can be taught from elementary school onwards, depending on how they are presented, considering the assumption of the existence of other environments and surfaces, surpassing initial expectations.