Torre de Hanói no estudo de recorrência e indução finita para o Ensino Médio

Abstract

The purpose of this work is to present a modern perspective on games to secondary level teachers in basic education, with the aim of approaching some concepts worked on at higher education that could be applied in basic education. Topics such as the principle of finite induction and linear recurrences can be treated in high school with the aid of games, with the purpose of reducing the gap of existing conceptual approaches between high school and higher education. In this regard, questions were elaborated based on the rule of a famous game known as “Tower of Hanoi”, created by the Frenchman Édouard Lucas. The concepts of mathematical induction and the recurrence relation are introduced from the patterns observed in the game, that is, how each move is constituted in relation to the previous move. Such subjects are used to demonstrate elementary properties of mathematics that are relevant to high school. This method consists in the historical presentation of the “Tower of Hanoi” and then the beginning of the game. A detailed teaching proposal is presented for application in the classroom. The goal of the proposal is to work with the mathematics teacher on possible ways to apply the study of recurrences and finite induction in high school. We want to take teachers along with their students to build a model to determine the smallest number of moves necessary to complete the game, applying the concepts of induction and recurrence in other problems. Everything that will be dealt with in this work will have the assistance of ludic approaches. The results obtained should be closer to the ideal puzzle resolutions to reach the perception if the concept of the principle of finite induction and the recurrence relation were well absorbed. So, the work presented here is committed to envisioning the way in which concepts can be treated in graduation, realizing that the ludic tool facilitates basic education students to understand mathematical content and solve problems, in addition to criticizing the approaches taken in higher and basic teaching.