Algebra and its role: reflections based on the works of SBEM GT04

Abstract

In this article, we present part of the results of an interpretative analysis carried out adopting as corpus of work five studies on the Algebra subject, developed by members of the Working Group for Mathematical Education in Higher Education (GT04), linked to the Brazilian Society of Mathematical Education (SBEM). To collect, categorize, and analyze the data, we consulted precepts of Content Analysis in the conception of Bardin. Five categories of analysis were built and this article focused on two: C1: What is Algebra? and C2: The role of Algebra. For each category, in addition to presenting the reflections present in the analyzed works, we established dialogues among these considerations and others presented in the reference studies in Algebraic Education. Regarding C1, the data highlights that answers to the question What is Algebra? contemplates historical and structural aspects related to generalization, contents, and observations commonly associated to Algebra, the relation between Arithmetic and Algebra, and the permeability of Algebra in different fields of Mathematics and knowledge. As for category C2, the results point to the fact that Algebra plays a role in the construction of mathematical knowledge, as well as in the teacher's work, who will mediate this construction process in the classroom. These roles are linked to the knowledge of structures, demonstrations, symbolism, the centrality of generalizations, and the appropriation of the algebraic language and thought to enable the person to think and communicate mathematically.

Keywords
What is Algebra; The role of Algebra; Work Group Mathematical Education in Higher Education; Interpretative Analysis