Análise histórica, epistemológica, curricular e didática do conceito de Função

Abstract

The present work aims to study the concept of Function, going through its historical, epistemological and didactic aspects. The research is justified both by the difficulties that basic education students have with this fundamental concept, which ends up reflecting difficulties in differential and integral calculus in higher education, as well as for their teaching and learning, in which teachers, aware of the link between the teaching of mathematics, the history of mathematics and didactics, can build a strategy to lead their students to acquire this notion. In addition, as the formation of the concept of Function required a lot of work and dedication, the teacher who is aware of this historical evolution, full of obstacles, will be able to build an adequate approach from the history of the concept of Function. Therefore, our theoretical and methodological contribution was through a bibliographic research, supported by Severino, Sousa and others, a literature review of existing works on the subject was developed. For this, we carried out a survey of reliable bibliographic sources, in order to obtain the necessary data for the development of the research and the solution of the research problem. Later, we studied the concept of Function in the Curriculum and Textbooks of Elementary and High Schools. Then we made a brief historical approach of this concept in several bibliographic materials found, physically and digitally, in which the two definitions of the concept of Function proposed by Euler were analyzed in particular. Finally, as an application, we present and analyze some activities to introduce the concept of Function both in basic education and in undergraduate mathematics teaching.