Teorema de Pick e aplicação em jogos geométricos

Abstract

This research explores the potential of Pick’s Theorem and its extensions, applied at game developing for teaching mathematics. Advancing the development of games aimed at teaching, is an action of great relevance, as games, when used correctly, contribute to the improvement of students’ understanding of mathematical concepts as well as develops their reasoning skills, some of which are indicated in official documents such as the BNCC and DC-GOEM. With a view to contributing in this direction, we began our activities with a detailed study of Pick’s Theorem and some of its extensions. Pick’s Theorem presents a formula for calculating areas on a mesh in the plane. In this initial study, we identified promising possibilities for game creation. Moreover, we study in detail some games already proposed on this subject. The proposal of games for teaching must be supported by solid scientific evidence, so that, rather than being fun for the students, we obtain powerful tools contributing to the teaching and learning process. This concern led us to study current trends in games for teaching. We studied trends such as classical formalist, empirical-activist, modern formalist, technicist, constructivist and socio-ethnocultural. We used some elements of the empirical-activist and technicist trends combined to select some games and to design others. Didactic sequences for using games in the classroom are proposed. Both the games and the didactic sequences represented contributions to improve teaching and learning of mathematics