Possibilidades e dificuldades da utilização da história da matemática para o ensino e aprendizagem da equação do primeiro grau na educação básica

Abstract

First Degree Equations, which are often studied in grade school (primary school), are fundamental to conceptually understanding certain aspects of Algebra. Studies show that students frequently have difficulties learning First Degree Equations because, as Algebraic functions, they differ from simple Arithmetic. Given this fact, new ways of teaching these equations should be studied, and the study of the History of Mathematics (HM) may serve as an auxiliary in this process. Many studies in the existing literature point to the effectiveness of studying the History of Mathematics in math classes. We conducted an investigation to better understand the advantages and disadvantages of using the History of Mathematics for teaching First Degree Equations in primary school. We have carried out set of activities that addressed teaching First Degree Equations from within a historical context using the False Position Method and Inversion. These activities, consisting in five stages, were conducted at a State school with 7th graders. Students carried out the activities, and data were collected using audio recordings and observational annotations made in a daily register. The data were analyzed according to four criteria set forth in existing literature. The results indicate that the elements related to HM contributed to the learning of mathematics and about mathematics, as it brought contributions to: the motivation of some students to learn mathematics; the contextualization of the studied concept; the learning of resolution procedures for solving a first degree equation and a change in perception in relation to mathematics. It is worth mentioning that we encountered some of the same difficulties already mentioned in existing literature with respect to the fact that HM does not motivate all students. Nonetheless, this study highlights the effectiveness of using historical methods for teaching First Degree Equations in a way that gives students a greater understanding of what it means the resolution of a First Degree Equation.