Situações didáticas olímpicas aplicadas a problemas de geometria plana da Olimpíada Brasileira de Matemática das Escolas Públicas (OBMEP)

Abstract

This research aims to present to the Brazilian Public Schools Mathematics Olympiad (OBMEP), in a complementary way, a methodological proposal of teaching named Olympic Didactic Situation (SDO), recent in the literature, but which is based on the French mathematical didactics that emerged in the late 60's of the twentieth century. SDO is based on Michèle Artigue's Didactic Engineering (ED), research methodology, and embodied in Guy Brousseau's Theory of Didactic Situations (TSD). Accompanying this work is a workbook consisting of an Educational Product (PE) where ten SDOs applied to OBMEP Flat Geometry Olympic Problems (POs) were elaborated according to Brousseau's dialectical phases, mediated by Geogebra software, using the first two phases of ED which are Previous Analysis and Priori Analysis, and in the body of this dissertation, in order to validate the research, two of these SDOs are described using all four phases of ED, the two already mentioned, plus the phases Experimentation and Analysis. The research was applied at the Johnson Full-Time High School (EEMTI) with first year students, and the research results were analyzed and validated. The aim of this work is to contribute to improving the quality of the teaching and learning process focused not only on the mathematical Olympiads, but on mathematical didactics in general, since SDOs have as a differential mobilizing students' intuitive reasoning from of a didactic mediation process.