Characterising the teaching of university mathematics: a case of linear algebra

This paper focuses on university mathematics teaching where the topic is linear algebra. The research team includes two mathematics educators and a mathematician who collaborate to study the teaching approach and the issues it raises for teaching-learning at university level. We see university mathematics to constitute a community of practice in which the practitioners are those who do mathematics. Such a perspective draws sociohistorically on established practices in doing, learning and teaching mathematics within a university. The paper offers an interpretation of these theoretical perspectives in relation to a first year course on Linear Algebra. We look at how teaching is constructed within the particular setting, with a critical eye on the learners, on learning outcomes and on the tensions experienced by the lecturer in satisfying student needs and mathematical values.