Teaching linear algebra at university

TL;DR

This paper reviews recent research on teaching linear algebra at university, focusing on epistemological, cognitive, and pedagogical issues, and discusses innovative teaching methods and their implications.

Contribution

It provides a synthetic overview of recent developments in mathematics education research related to linear algebra, highlighting new principles and teaching designs.

Findings

Emphasizes the epistemological and historical aspects of linear algebra teaching.

Identifies three principles for effective linear algebra instruction.

Describes an original teaching design tested in practice.

Abstract

Linear algebra represents, with calculus, the two main mathematical subjects taught in science universities. However this teaching has always been difficult. In the last two decades, it became an active area for research works in mathematics education in several countries. Our goal is to give a synthetic overview of the main results of these works focusing on the most recent developments. The main issues we will address concern: the epistemological specificity of linear algebra and the interaction with research in history of mathematics; the cognitive flexibility at stake in learning linear algebra; three principles for the teaching of linear algebra as postulated by G. Harel; the relation between geometry and linear algebra; an original teaching design experimented by M. Rogalsk.