Study of the Real Numbers in a Course of Analysis under the Investigative Perspective of the History of Mathematics

Abstract

This paper presents an investigation carried out with a group of students in the fourth year of Mathematics, through the discussion of formalization of numerical sets in Real Analysis, under the History of Mathematics investigative perspective. By using the Research-Action methodology, the work aimed to lead students to a possible understanding of the structure of real numbers and, consequently, of its importance for the (theoretical) foundation of the concepts related to the subject through historical incursions. We also, concomitantly, evaluate the posture of these future teachers in investigative situations. Besides presenting an alternative way of working certain concepts of Analysis, we realize that the subsequent discussions were relevant to the formation of future Mathematics teachers. According to the evaluation of the actors involved in the process, the use of History of Mathematicsfavored the learning process, as well as motivated them to think about the role of Analysis in the curriculum and, in their formation.