Alturas Inacessíveis: Uma Análise Histórica em Livros Didáticos de Matemática

Abstract

Even with all the technological advancement and all the sources of information available, the textbook will become an important resource in the classroom, easily accessible for classes and teachers, and thus the most usual. This has a greater weight in searches on textbooks, each with its peculiarity. In this line, and to contribute to this analysis, this research intends to answer the following question: How did the textbooks of mathematics have approached, throughout history, the deductions of the height of objects, whose base is inaccessible? It has as general objective to discuss, historically, the deductions of the height of objects with inaccessible bases, present in the textbooks of Mathematics and, in the specific objectives, to present the history of the textbook in Brazil; talk about trigonometry in the triangle rectangle; illustrate the research proposal; present the proposed deductions for the teaching of trigonometry; and analyze the explanations, examples, textbook activities since 1929. As a theoretical foundation, the research focused on presenting the historical evolution of textbooks and then discussing the teaching of trigonometry in Brazil. The research is documentary in nature, carried out analysis in didactic books and sought, persistently, to reach the proposed objectives through the analyzes made in the explanations, deductions, examples, exercises and even figures. The analyzes showed that not always the content variations between notable angles were addressed in textbooks. There is a delay of two decades, until the early 1950s, when, finally, this part of trigonometry began to appear in these books. The analyzes indicate that the authors use three methods in their works: the general law, the system of equations and the properties of the triangle. The research proposes possible deductions to determine the height of objects whose distance to the base is inaccessible, through the variation of notable angles. Such proposals become important material for teachers of Mathematics, who can use them to stimulate in the student the learning of this content, as well as to bring it closer to other mathematical situations and/or patterns with this content and, thus, to increase its student achievement, among others.