O tratamento dos números reais na disciplina de análise real na licenciatura: um olhar a partir dos livros didáticos.

Abstract

This work was derived from the concerns that arose in the Real Analysis course of the undergraduate course in Mathematics, considering that even as a student the objectives of this one were not perceptible to the students, thus causing a questioning regarding the reflexes of the Real Analysis in the teacher training. In this perspective, we have looked at the textbooks of Higher Education in Real Analysis, since they play a fundamental role in the teaching-learning process, both by students and by teachers. According to Moreira and Viana (2008), three textbooks that are usually used in undergraduate courses in mathematics are analyzed (Mathematical Analysis for the Degree - Geraldo Ávila, Analysis I - Djairo G. de Figueiredo and Introduction to Analysis Real - Elon L. Lima). This research can be characterized as qualitative, since we have as a purpose to perform a descriptive analysis of the three works listed, presenting aspects that contribute to the learning of the future teacher of Mathematics. In addition, it can also be classified as pedagogical, since we are concerned about the mathematics that is being taught to the licenciandos in mathematics. It is observed that the contents that are being offered by both teachers and textbooks in this discipline do not effectively contribute to the formation of the future teacher. For the development of this work, we divide the research into two moments: the first stage comprises the analyzes of the works, in which we categorize the studies according to the following topics: (Preface, chapter organization, examples, historical notes, ; the second moment, consists of the reflections on the analysis of the Books of Real Analysis. Based on the results, we verified that the books of the authors Lima and Figueiredo translate their works directed to the baccalaureate in mathematics, since the pedagogical aspects that helps the future teacher in the professional development are little perceptible, presenting a Mathematics that is not destined to the licenciando in mathematics. However, Ávila’s book, specifically aimed at the degree in Mathematics, shows a fear of working with rigor and formalism, leaving aside the essential characteristics of the discipline, working on numerical concepts that are distant from the objective of the course. Thus, we find that the chapters experienced on the Real Numbers, that concepts of great utilities belonging to these are not presented, or little worked for the contribution of teacher training. Finally, we conclude that the works analyzed do not approach the needs of mathematics graduates, since the material needed for these students needs to present pedagogical aspects and a mathematics that is compatible with the reality of the future teacher of Mathematics.