LANGUAGE GAMES AND GEOMETRY PLANE EUCLIDIAN: A WITTGENSTEIN’S THERAPY IN MATHEMATICS GRADUATE COURSE

Abstract

This work reports an investigation, based on the doubt that flat Euclidean geometry is approached differently in different books, used in the formation of mathematics teachers at the Federal University of Mato Grosso do Sul - UFMS. Thus, based on the survey of menus and bibliographies of geometry disciplines in the Mathematics Degree courses at UFMS, the books Euclidean Flat Geometry, by João Lucas Barbosa (2006), which had been used for many years in practically all degree courses that were analyzed. For logistical reasons, UFMS replaced this book with Euclidean Flat Geometry and Geometric Constructions, by Eliane Quelho Frota Rezende and Maria Lúcia Bontorim de Queiroz (2000), in search of similarities and differences between both. Anchored in the perspective of Ludwig Wittgenstein's language games, the aforementioned analysis of these two manuals was based on the investigation of how language games were constituted in these manuals. For this research, a Bibliographic Therapy with Flat Euclidean Geometry, its axioms, postulates and theorems was practiced, considering that language games are always based on life forms. Thus, the reading was inspired by the possible uses of these textbooks in mathematics teacher training classrooms. Several dissimilarities were found, such as different words used in the same sense, use of the same word in their own ways and unique logical chains, thus characterizing different language games, different Flat Euclidean Geometries.