Guy Brousseau - Böcker

This is a collection of 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 organized 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. 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.

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.

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.