Ebook: Theory of Didactical Situations in Mathematics: Didactique des Mathématiques, 1970–1990

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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This book is unique. It gathers texts which give the best presentation of the principles and key concepts of the Theory of Didactical Situations that Guy Brousseau developed in the period from 1970 to 1990. These texts have been edited and organised so that they provide a comprehensive presentation of the Theory. Concepts such as didactical contract, didactical variable and epistemological obstacle are presented in detail. At the heart of the book, one will find two works which demonstrate in detail the articulation between theoretical work and experimental research which is the source of the richness of the Theory.
Although referenced by many research texts, up to now the original texts of Guy Brousseau were unknown, or known only with difficulty, in the non- French-speaking world. This book is a response to these difficulties. In order to facilitate the reading of certain points, or elucidate them for the reader, footnotes have been added to the original text, as well as preludes and interludes to place in context the chosen texts and clarify the construction of the book.
Theory of Didactical Situations in Mathematicsis of interest for researchers in mathematics education, PhD students in mathematics education and mathematics educators.