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 provide a comprehensive presentation of the Theory. In order to facilitate the reading of certain points footnotes have been added, as well as preludes and interludes to place in context the chosen texts and clarify the construction of the book.

This work presents one of the original and fundamental experiments of Didactique, a research program whose underlying tenet is that Mathematics Education research should be solidly based on scientific observation. Here the observations are of a series of adventures that were astonishing for both the students and the teachers: the reinvention of fractions and of decimal numbers in a sequence of lessons and situations that permitted the students to construct the concepts for themselves. The book leads the reader through the highlights of the sequence's structure and some of the reasoning behind the lesson choices. It then presents explanations of some of the principal concepts of the Theory of Situations. In the process, it offers the reader the opportunity to join a lively set of fifth graders as they experience a particularly attractive set of lessons and master a topic that baffles many of their contemporaries.

This work presents one of the original and fundamental experiments of Didactique, a research program whose underlying tenet is that Mathematics Education research should be solidly based on scientific observation. Here the observations are of a series of adventures that were astonishing for both the students and the teachers: the reinvention of fractions and of decimal numbers in a sequence of lessons and situations that permitted the students to construct the concepts for themselves. The book leads the reader through the highlights of the sequence's structure and some of the reasoning behind the lesson choices. It then presents explanations of some of the principal concepts of the Theory of Situations. In the process, it offers the reader the opportunity to join a lively set of fifth graders as they experience a particularly attractive set of lessons and master a topic that baffles many of their contemporaries.

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."