As conjecturas como instrumentos de ensino de matemática

Abstract

Conjectures are fundamental in the development of Mathematics. Each result that we know, it arose initially from assumptions formulated by deducting of problem situations, and after much analysis, their statements were constructed then. However, there are several claims that mathematicians have still not been able to prove or to refute them, some of them are several centuries old. In this work we present some of thes conjectures, namely: Beal’s Conjecture, Collatz’s Conjecture, Goldbach’s Conjecture and Toeplitz’s Conjecture in which, although they have proved to be extremely complex to demonstrate or to refute them, they present simple comprehension statements and have properties that allow us to explore a few concepts that can be used in Elementary and High school Mathematics classes.