On the Teaching of Linear Algebra

Abstract

This book presents the state-of-the-art research on the teaching and learning of linear algebra in the first year of university, in an international perspective. It aims at giving to university teachers in charge of linear algebra courses a wide range of information from works including theoretical and experimental issues. These works try to better understand the meaning of linear algebra in an epistemological approach, as well as the constraints and the difficulties in its teaching and learning. They also present teaching designs with the analysis of their experimentation. However, it would be vain to expect a miraculous way for teaching linear algebra, rather elements of reflection are given to the reader with keys for his or her own experimentation. Through the variety of the works presented, this book also discusses theoretical issues which are consistent for all research in maths education at tertiary level. Foreword to the English Edition -- Preface -- Introduction -- Part I: Epistemological Analysis of the Genesis of the Theory of Vector Spaces. 1. Introduction. 2. Analytical and Geometrical Origins. 3. Towards a Formal Axiomatic Theory. 4. Conclusion. 5. Notes -- Part II: Teaching and Learning Issues. 1. The Obstacle of Formalism in Linear Algebra. 2. Level of Conceptualization and Secondary School Math Education. 3. The Teaching Experimented in Lille. 4. The Meta Lever. 5. Three Principles of Learning and Teaching Mathematics. 6. Modes of Description and the Problem of Representation in Linear Algebra. 7. On Some Aspects of Students' Thinking in Linear Algebra. 8. Presentation of Other Research Works. Conclusion. Notes on Contributors. Index.