Synopses & Reviews
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.
Synopsis
To a large extent, it lies, no doubt, in what is presented in this work under the title of meta lever, a method which it is certainly interesting to develop and further refine. There exists in mathematics courses a strange prudery which forbids one to ask questions such as, Why are we doing this? -, At what is the objective aimed? -, whereas it is usually easy to reply to such questions, to keep them in mind, and to show that one can challenge these questions and modify the objectives to be more productive or more useful. If we don t do this we give a false impression of a gratuitous or arbitrary interpretation of a discipline whose rules are far from being unmotivated or unfounded. One must also consider the time aspect. Simple ideas take a long time to be conceived. Should we not therefore allow the students time to familiarize themselves with new notions? And must we not also recognize that this length of time is generally longer than that ofthe official length of time accorded to this teaching and that we should be counting in years? When the rudiments of linear algebra were taught at the level of the lycee (college level), the task of first year university teachers was certainly easier: for sure the student's knowledge was not very deep, however it was not negligible and it allowed them to reach a deeper understanding more quickly."
Synopsis
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.
Table of Contents
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.