Teoria dos números no ensino básico : um estudo de caso no 2º ano do ensino médio

Abstract

We present in this project a proposal to include basic concepts of number theory in the secondary school curriculum. Numbers theory is an area of mathematics of great importance, which has numerous applications, such as cryptography, and which can be useful in solving problems that would have a rather complex solution without the mathematical tools studied in this theory . This work originated considering the need to make the teaching-learning process of mathematics more pro table by solving challenging problems that arouse students' interest in this science and foster, in them, the development of logical reasoning, critical thinking and the understanding of conceptual ideals, which would be the key point in learning mathematics. In this context, working on some concepts of Numbers Theory would be one way of generating such results. Therefore, in this work will be presented a proposal of a didactic sequence where they will be worked, without abandoning mathematical rigor, but at the same time respecting the level of the student's learning process, mathematical concepts such as divisibility, GCD and LCM, fundamental arithmetic property, modular arithmetic, and diophantine equations. In the current context of Brazilian education, where the results of assessments of students' learning level in relation to mathematics are poor, it is necessary to rethink the current pedagogical practice in which only the memorization of formulas has been prioritized in mathematics teaching. Thus, this work consisted of developing a basic course in Numbers Theory with students of a 2nd grade high school class at the Federal Institute of Education and Science of Pernambuco - IFPE, Campus Caruaru. Before the course, the students underwent an initial test, called "Test 1" and, at the end of the course, they performed a new test, called "Test 2" to measure the students' possible progress. During the course, several themes of the study of Number Theory as well as their application of Numbers Theory were worked on, either in mathematics itself or in some everyday situations, and which will serve as motivational tools for the development of classes.