proposal for teaching the abstract concept of vector spaces

Abstract

Due to its known conceptual difficulty among students, there are many investigations that study linear algebra in the discipline of mathematics education. However, researches that focus on the specific concept of vector space from the perspective of teaching are not abundant and it is a recent research field. As a part of a broader investigation that considers the fundamentals of the Anthropological Theory of Didactics (ATD), in this article a proposal of activities that allows to study how students will initially face the concept of vector space is presented. This proposal also allows students to explore the properties of vector spaces, so that the algebraic structures presented are similar to those that have worked in other courses. Thus, the introduction to the abstract concepts of linear algebra may not be as sudden as it usually is in traditional teaching.