Elaboration, Analysis, and Application of a Reference Epistemological Model for Teaching the Function Concept on a Mathematics Degree Course

Abstract

This article deals with the elaboration, analysis, and application of the reference epistemological model (REM) for the function concept, that was applied in the Functions I discipline of the Field Education Mathematics degree. For model elaboration, we used preliminary information about the function concept, as: a brief historical evolution of the concept; some difficulties in the teaching and learning processes; its organization in the Brazilian curriculum documents; and a praxeological analysis of a textbook used in the researched subject. As a theoretical basis for the elaboration of our REM, we used: a proposal by Lucas applied to the concept of elementary differential calculus; the mathematical modelling notion of Chevallard and Gascón and the functional modelling levels proposed by Ruiz-Munzón. With this organization, we proposed a schema of a REM for the function concept, that fundamented the application of Study and Research Path (SRP), which was applied by the teacher of the Functions I discipline to his students over a period of six sessions. During the application process, we were able to observe the development of the SRP fundamented by REM, which presents itself as a possibility for teaching the function concept. We highlight the transition process from discrete to continuous domain, as well as the study of families of functions. The results showed that the techniques do not take a prominent role in relation to the understanding of concepts, causing a change in the teacher’s perspective on how to teach and facilitate learning of the function concept.

Keywords
Anthropological Theory of the Didactic; Reference Epistemological Model; Function