Construção do pensamento matemático no Ensino Médio

Abstract

This dissertation is about Euclidean Division, some items related to Congruence and Domain of Integrity. Each chapter contains the applied activity done at the classroom with high school students, as well as a basic summary of the mathematical objects that a graduation course may cover and some suggestions of other related points that the teacher may deepen. Besides that, there is an attachment that contains the activity of Chapter 1 which was crafted in the classroom, because it was a bit longer, while the examples used in Chapters 2 and 3 were less extensive and, because of that, are inside the chapter itself. Of course, a complete formalization is not suitable for this moment and the teacher can choose those of which s/he intends to go deeper. In Chapter 1, we will talk about the Euclidean Division and we will also discuss and give an answer as to why, when we are doing the division, we put the zero in the quotient and in the exercise called ER4, that is on the first list of exercises, this becomes clear when we will discuss the concept of uniquiness. Then in chapter 2, the exercises inside the activity will show a small effort to address Congruencies. Finally in chapter 3, we discuss Integrity domains. We draw attention to other points such as comutativity, since the matrix used is one of the examples and, in general, there is no commutativity in this ring of matrix. Our goal is to show that even in High School we can discuss such objects which usually we just have contact in undergraduate degree in mathematics. Of course we worked with simple examples that allow that to happen.