Abstract

In this thesis, we evaluate the effectiveness of a basic tool for the teaching of linear algebra at university level: the administration of weekly quizzes. These tests, each made of two short, conceptual questions, are believed to have the potential of developing students' theoretical thinking. At the start of our research we believed that this kind of thinking is necessary for the understanding of linear algebra and that it represents, in general, an important educational aim in university teaching. To see if, indeed, the quizzes can contribute to the development of students' theoretical thinking, we have analyzed students' solutions to the weekly quizzes administered in a Linear Algebra II course at Concordia University in Montreal, over a one-semester time span. We have used, for this purpose, a model of thinking that characterizes theoretical thinking by certain properties, which contrast practical and theoretical thinking. Our study shows that the administration of weekly quizzes could not account for the development, in general, of theoretical thinking, with all the characteristics that it encompasses. We have found that the group's engagement with certain features of thinking is directly influenced by the mathematical content of the questions in the quizzes, and thus it is impossible to evaluate their development in time. However, the quizzes do have the potential of developing other features of theoretical thinking, that we have called, more generally "habits of the mind", because they are less conditioned by content specificities.