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On the Teaching of Linear Algebra

  • Book
  • © 2000

Overview

Editors:
  1. Jean-Luc Dorier

    1. Laboratoire Leibniz, Grenoble, France

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Part of the book series: Mathematics Education Library (MELI, volume 23)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xxii
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  2. Epistemological Analysis of the Genesis of the Theory of Vector Spaces

    1. Epistemological Analysis of the Genesis of the Theory of Vector Spaces

      • Jean-Luc Dorier
      Pages 3-81

  3. Teaching and Learning Issues

    1. The Obstacle of Formalism in Linear Algebra

      • Jean-Luc Dorier, Aline Robert, Jacqueline Robinet, Marc Rogalsiu
      Pages 85-124

    2. Level of Conceptualization and Secondary School Math Education

      • Aline Robert
      Pages 125-131

    3. The Teaching Experimented in Lille

      • Marc Rogalski
      Pages 133-149

    4. The Meta Lever

      • Jean-Luc Dorier, Aline Robert, Jacqueline Robinet, Marc Rogalski
      Pages 151-176

    5. Three Principles of Learning and Teaching Mathematics

      • Guershon Harel
      Pages 177-189

    6. Modes of Description and the Problem of Representation in Linear Algebra

      • Joel Hillel
      Pages 191-207

    7. On Some Aspects of Students’ Thinking in Linear Algebra

      • Anna Sierpinska
      Pages 209-246

    8. Presentation of Other Research Works

      • Michèle Artigue, Ghislaine Chartier, Jean-Luc Orier
      Pages 247-271

  4. Back Matter

    Pages 227-290
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Keywords

About this book

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 lycée (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.

Editors and Affiliations

  • Laboratoire Leibniz, Grenoble, France

    Jean-Luc Dorier

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