Epistemological Reference Model for Factoring Implemented through a Study and Research Path in Elementary Education

Abstract

In this article, we present a partial study on the Epistemological Model of Reference proposed in our research aligned with its objectives, which were to identify the existing didactical and mathematical praxeology for the study of factorization, to understand the relations of students and teachers with this object, and to explore activities that can favor its applications in varied intra and extra mathematical contexts in the final years of Elementary School in Brazil. This is to implement a didactical engineering of the Study and Research Path (SRP) type. The SRP was developed through Study and Research Activities (SRA) related to the identified mathematical praxeology (MP). We take as a reference Chevallard's Anthropological Theory of Didactics, the notions of SRP and SRA introduced by Barquero, Bosch, and Gascón, MP defined by Bosch and Gascón. In this research extract, we consider the first part of the research objective, namely: Identifying the existing mathematical and didactical praxeology for the study of numerical and algebraic factorization, highlighting the possible difficulties that may be encountered in some applications and showing the functioning of this praxeology when applying the SRP to high school students and those studying for a Mathematics degree. The epistemological reference model allowed us to establish the reference mathematical praxeology that helped in the prior analysis of the SRA used in the development of the SRP. Results show that the personal relations of students from both groups is centered on the direct application of the techniques, and they had difficulties in recognizing the proto-mathematical role of factorization in the proposed applications.

Epistemological Reference Model; Mathematical and Didactical Praxeologies; Numerical and Algebraic Factorization