Potencialidades pedagógicas da História da Matemática nos livros didáticos do Ensino Médio no conteúdo de trigonometria

Abstract

This study discusses the pedagogical potentialities of the History of Mathematics in the textbooks of High School in the content of Trigonometry. It is important to analyze the historical passages in the content of Trigonometry in the textbooks of High School, from the categories of meanings proposed by Alencar (2014) and of the pedagogical potentialities of the History of Mathematics, pointed out by Miguel (1993), and to verify which of the pedagogical potentialities of the History of Mathematics identified in textbooks have the potential to be more effective for the teaching of mathematics. It is characterized as a research of a qualitative nature in order to ascertain aspects regarding the nature of the content and the objective of the historical passages, describing the fundamental characteristics that made it possible to classify them according to the pedagogical potentialities of the History of Mathematics. The data were constructed from the analysis of the historical passages in the content of Trigonometry in the six textbooks of mathematics of the second year of High School, approved by PNLD 2015. Before the analysis, we observe that the History of Mathematics is used as an accessory to the mathematical content. Most of the historical passages extol the contribution or discovery of an important personality in the History of Mathematics, revealing as a pedagogical potential the history as a source of motivation and objectives for teaching-learning of mathematics, which seems to be the least interesting Understanding of mathematical concepts. The potentialities that treat the History of Mathematics as didactic strategy were identified in a reduced portion of historical passages. These potentialities should be further explored, since they contribute to a change of perception in relation to mathematics, they enable the demystification of mathematics as an isolated and finished science, as they show the motivations and applications of mathematical concepts in history. Another aspect revealed is that, in consonance with the literature, the potentiality "History as an instrument in the formalization of mathematical concepts" (MIGUEL, 1993), as having the potential to be more effective for teaching mathematics, plays The role of transforming the student into an active subject, leading him to an understanding of the content and the formalization of mathematical concepts. We observed a certain interest in using the History of Mathematics in the textbooks analyzed. However, we realize that this use should focus more on the pedagogical potentialities that deal with the importance of a mathematical concept throughout history that inserts the History of Mathematics within a sociocultural, political and economic context, contributing to the teaching- Learning and for a change of perception regarding Mathematics. We conclude that in the process of choosing the textbook, the teacher needs, besides the evaluation criteria of the PNLD, to find out which collections approach the History of Mathematics as a didactic resource. Which collections reveal the historical development of the content, evidencing its origin, evolution and the different formalizations of the same concept over time.