A geometria não euclidiana e formação do professor de Matemática - Sousa, Alexandre Pereira (2019)
This work aims to collaborate in the insertion of the teaching of Non-Euclidean Geometries in the formation of the mathematics teacher. In this context, we carry out bibliographical research on the teacher formation and on the Euclidean Geometry history, observing the facts about the fifth postulate, until the appearance of Non-Euclidean, Hyperbolic and Elliptic Geometries in their particular case of Spherical Geometry. Next, there is a sequence of contents linked to Hyperbolic Geometry and Spherical Geometry where we approach the main hyperbolic models, in particular Eugenio Beltrami's model that confirms the consistency of this Geometry, as well as some of the main topics of Spherical Geometry that we list as the basic structure in the Mathematics Teacher formation. In the text structure, we try to show that the Euclidean theory was deficient in relation, for example, to the calculation of great distances, but also does not support revolutionary knowledge as the theory of relativity. Our goal is through the Didactics of Anthropological Theory – DAT to build a praxeology that should be understood as a proposal, through which the Questioning Question and the research objective, which permeate the insertion of these contents, related to Hyperbolic Geometry and Spherical Geometry, as Current model of mathematics teacher formation. The result of the research is stimulated through Mathematical Practice Workshops - MPW, which demonstrate that our hypothesis is confirmed.