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On the teaching of linear algebra

Author: Jean-Luc Dorier
Publisher: Dordrecht ; Boston : Kluwer Academic Publishers, ©2000.
Series: Mathematics education library, v. 23.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic book
Electronic books
Additional Physical Format: Print version:
Enseignement de l'algèbre linéaire en question. English.
On the teaching of linear algebra.
Dordrecht ; Boston : Kluwer Academic Publishers, ©2000
(DLC) 00061288
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jean-Luc Dorier
ISBN: 6610207720 0306472244 9780306472244 9786610207725 9780792365396 0792365399
OCLC Number: 1017993476
Description: 1 online resource (1 electronic recource (xxii, 288 pages)) : illustrations.
Contents: Cover --
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 --
REFERENCES --
PART I --
PART 11. TEACHING AND LEARNING ISSUES --
CHAPTER 1. THE OBSTACLE OF FORMALISM IN LINEAR ALGEBRA --
1. INTRODUCTION --
2. FIRST DIAGNOSIS, A 1987 STUDY --
3. A SECOND SURVEY MADE IN THE 1990 : IS FORMALISM A DIDACTICAL OBSTACLE RELATED TO THE LACK OF PREREQUISITES? 3. A SECOND SURVEY MADE IN THE 1990 : IS FORMALISM A DIDACTICAL --
4. THE LAST SURVEYS FROM 1991 TO 1994: THE OBSTACLE STILL HAS NOT BEEN OVERCOME --
5. ANNEX --
MATHEMATICAL SOLUTION OF THE HYPERPLANES PROBLEM (1992, QUESTION (a) --
6. NOTES --
CHAPTER 2. LEVEL OF CONCEPTUALIZATION AND SECONDARY SCHOOL MATH EDUCATION --
1. WHAT DO WE CALL 'LEVEL OF CONCEPTUALIZATION'? --
2. LEVELS OF CONCEPTUALIZATION IN SECONDARY EDUCATION --
3. CONCEPTUALIZATION --
CHAPTER 3. THE TEACHING EXPERIMENTED IN LILLE --
1. THE UNDERLYING PRINCIPLES OF THE COURSE DESIGN IN LILLE --
2. THE DETAILED PLAN OF THE COURSE DESIGN --
3. THE POSITIVE EFFECTS OF THE LILLE EXPERIMENT --
4. ANNEXES --
5. NOTES --
CHAPTER 4. THE META LEVER --
1. DEFINITIONS AND EDUCATIONAL POSITIONS --
2. INTRODUCTION TO THE STRUCTURE OF VECTOR SPACE --
3. AN EXAMPLE OF THE USE OF META FOR TEACHING THE GREGORY FORMULA --
4. UNDERSTANDING LINEARITY AND NON-LINEARITY --
5 . CONCLUSION: AN IMPORTANT METHODOLOGICAL PROBLEM, PERSPECTIVES --
6 . NOTES --
CHAPTER 5 . THREE PRINCIPLES OF LEARNING AND TEACHING MATHEMATICS --
1. BACKGROUND --
2 . THE CONCRETENESS PRINCIPLE --
3 . THE NECESSITY PRINCIPLE --
4 . GENERALIZIBILITY PRINCIPLE --
5 . SUMMARY --
6 . NOTES --
CHAPTER 6 . MODES OF DESCRIPTION AND THE PROBLEM OF REPRESENTATION IN LINEAR ALGEBRA --
1 . INTRODUCTION --
2 . MODES OF DESCRIPTION IN LINEAR ALGEBRA --
3. THE PROBLEM OF REPRESENTATIONS --
4. APPLICABLITY OF THE GENERAL THEORY --
5. CONCLUDING COMMENTS. --
6. NOTES --
CHAPTER 7. ON SOME ASPECTS OF STUDENTS' THINKING IN LINEAR ALGEBRA --
1. INTRODUCTION --
2. PRACTICAL, AS OPPOSED TO THEORETICAL, THINKING --
A SOURCE OF DIFFICULTY IN LINEAR ALGEBRA STUDENTS --
3. SYNTHETIC-GEOMETRIC, ANALYTIC-ARITHMETIC AND ANALYTICSTRUCTURAL MODES OF THINKING IN LINEAR ALGEBRA --
4. CONCLUSIONS --
5. NOTES --
CHAPTER 8. PRESENTATION OF OTHER RESEARCH WORKS --
1. COORDINATION OF SEMIOTIC REPRESENTATION REGISTERS --
2. ARTICULATION PROBLEMS BETWEEN CARTESIAN AND PARAMETRIC VIEWPOINTS IN LINEAR ALGEBRA --
3. STUDIES WITH FIRST-YEAR UNIVERSITY STUDENTS IN VANNES. --
4. STRUCTURING OF KNOWLEDGE --
5. USING GEOMETRY TO TEACH AND LEARN LINEAR ALGEBRA --
6. NOTES --
REFERENCES --
PART II --
CONCLUSION --
NOTES ON CONTRIBUTORS.
Series Title: Mathematics education library, v. 23.
Other Titles: Enseignement de l'algèbre linéaire en question.
Responsibility: edited by Jean-Luc Dorier.

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.

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