As Geometrias e a Formação de Professores de Matemática: uma Terapia em quatro movimentos sobre o cenário nas Universidades Federais brasileiras entre 2021–2022

Abstract

This research proposes a four-movement therapy on the presence and participation of geometries in the training of Mathematics teachers at Brazilian federal universities. Based on Wittgenstein's Philosophical Therapy and Language Games, the work starts from the initial observation of a hegemony of Euclidean Geometry to the detriment of non-Euclidean geometries, which motivated the development of this investigation. We initially chose to analyze the curriculum framework of Mathematics Teacher Education programs at Brazilian federal universities. During this investigation, we observed that the data revealed a greater complexity than previously assumed. This led us to modify the research theme, focusing instead on how geometries are present and participate in the training of Mathematics teachers. Thus, we decided to organize our research into therapeutic (Wittgensteinian) movements, which allowed us to explore different language games and produce diverse perspectives on the proposed theme. The first movement was based on systematic bibliographical research guided by the following question: in which way(s) do geometry subjects participate in Mathematics Degree courses and/or Mathematics Teacher Training at Brazilian Federal Universities. The second therapeutic movement focused on the textbooks used in the Flat Geometry discipline. In the third therapeutic movement, we place Analytical Geometry on the couch and explore bibliographical investigations on this topic. Finally, the fourth therapeutic movement opened space for a relevant agent in the process of teaching/learning geometries: the teacher. The therapeutic movements generated different images and language games, which in the end served as an object of comparison. The results indicate that, although some authors point to a deficiency in the teaching of geometries at federal universities, there is a growing increase in research in this area; on the other hand, we identified the prevalence of axiomatic approaches as the main bibliographical reference for Flat Geometry disciplines; we also have the recognition of Analytical Geometry as a relevant subject beyond Mathematics teacher training courses; and, finally, the understanding of geometry teachers in training courses that does not point to the need to increase the number of geometry hours in their teacher training courses, but indicates the changes caused by legislation, the expansion of the teachers coming from Mathematics Education and the importance of other spaces and projects for the study of geometries. This research is linked to the Postgraduate Program in Mathematics Education at the Federal University of Mato Grosso do Sul and the History of Mathematics Education in Research Group (Hemep).