O ensino da Geometria através de resolução de problemas: Explorando possibilidades na formação inicial de professores de Matemática

Abstract

The main goal of this paper was to (re)construct geometric knowledge utilizing the Methodology of Teaching-Learning-Evaluation of Mathematics through Problem Solving. For that a extension course was offered with twenty vacancies to students in Mathematics Graduation from the Universidade Estadual da Paraiba and Universidade Federal de Campina Grande, called: Geometry Teaching in the context of Problem Solving having in mind both Theory and Practice. As scientific methodology for the research was employed the outline of the ten activities presented by Romberg (2007). The theoretical reference used to develop the research was based on Initial Formation of the Mathematics Professor, Problem Solving and Geometry. The field research was of qualitative nature, where the tools utilized were observation, written material by the students-participants, audio recordings, filming,questionnaire and log book, plus the problems proposed on the extension course. Initially, the Methodology of Teaching-Learning-Evaluation of Mathematics through Problem Solving was presented in the course. In this methodology the problem is the starting point to the construction of mathematical knowledge, being the generator of new concepts, procedures and geometric content. The participants, themselves being Mathematics graduates and a teacher, had the chance to participate during ten encounters in the (re)construction of geometric knowledge in relation to geometry: Perpendicularity of Straight and Flat, Congruence and Triangles similarities, Graphs, Circle and Circumference, Relative Position between Straight and Flat, Euler’s Formula, Tales’ Theorem, Pythagorean Theorem, External Angle Theorem, Parallelepiped and pyramid, cylinder, Cone and Sphere, and Topology. The results indicated that the referred methodology, worked on in the extension course, provided students- participants with the experience of a new way to work on Geometry through Problem Solving, made possible for the graduates to share experiences and productive participation during the extension course. The students-participants would go up to the board, without any trouble, to defend their solutions, showing reflection about their practice and/or future practice in the classroom. We noticed then that our work created a bond between Problem Solving, the Initial Formation of Teachers and Geometry, besides the interest shown for the contents seen. This way, this research contributed in the formation of this group of graduates.