Theory of Didactical Situations in Mathematics

1. Front Matter

   Pages i-xix

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2. Prelude to the Introduction

   Pages 1-1

3. Introduction Setting the Scene with an Example: the Race to 20

   Pages 3-18

4. Prelude

   Pages 19-19

5. Foundations and Methods of Didactique

   Pages 21-75

6. Prelude

   Pages 77-77

7. Epistemological Obstacles, Problems, and Didactical Engineering

   Pages 79-117

8. Prelude

   Pages 117-117

9. Problems with Teaching Decimal Numbers

   Pages 119-146

10. Interlude

    Pages 147-147

11. Didactical Problems with Decimals

    Pages 149-222

12. Postlude Didactique and Teaching Problems

    Pages 223-224

13. Prelude

    Pages 225-225

14. The Didactical Contract: The Teacher, the Student and the Milieu

    Pages 226-249

15. Prelude

    Pages 251-251

16. Didactique: What Use is it to a Teacher?

    Pages 253-274

17. Back Matter

    Pages 275-304

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On the occasion of the celebration of “Twenty Years of Didactique of Ma- ematics” in France, Jeremy Kilpatrick commented that though the works of Guy Brousseau are known through texts referring to them or mentioning their existence, the original texts are unknown, or known only with difficulty, in the non-Fren- speaking world. With very few exceptions, what has been available until now have been interpretations of the works of Brousseau rather than the works themselves. It was in response to this need that two of us, in the euphoria of an unforgettable Mexican evening at the time of the 1990 PME conference, decided to undertake the task of translating into English most of the works of Guy Brousseau. The ceuvre is immense, and once past the initial moments ofenthusiasm, with the accompanying ambition to produce the entire of it, we recognized the need to choose both the texts and a method of proceeding. As far as the texts go, we chose to take the period from 1970 to 1990, in the course of which it seemed to us that Brousseau had forged the essentials of the Theory of Didactical Situations. But even there the collection is huge. So, after an initial translation of most of the publications of the period, we carved out a selection, retaining the texts which gave the best presentation of the principles and key concepts of the Theory.

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