Taxonomy of errors in learning vector spaces

Abstract

As teachers of Linear Algebra concerned with some learning errors that frequently appear in our students’ productions, we decided to build a characterization of such errors based on the students’ learning of the concepts of vector spaces and subspaces. It is well-known that the teaching-learning process of Linear Algebra involves conceptual and cognitive difficulties due to the nature of concepts as well as the range of languages and representations used in the field. As discussed in the literature, reasoning and working with these languages and representations lead to different ways of addressing a concept; this in turn requires switching languages constantly. The abstract nature of concepts and the mastering of their various representations are the main reasons why learning difficulties and errors occur. It is in this context that we built a characterization of our students’ errors to find pedagogical approaches that help enhance the teaching-learning process. The taxonomy proposed in this paper consists of four categories that allow us to identify the possible causes of the students’ errors.