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.

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 provides university teachers in charge of linear algebra courses with a wide range of information from works including theoretical and experimental issues.