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Theory of Didactical Situations in Mathematics : Didactique des Mathematiques, 1970-1990 - Nicolas Balacheff

Theory of Didactical Situations in Mathematics

Didactique des Mathematiques, 1970-1990

By: Guy Brousseau, Nicolas Balacheff (Translator), Martin Cooper (Translator), Rosamund Sutherland (Translator), Virginia Warfield (Translator)

Hardcover Published: 30th September 1997
ISBN: 9780792345268
Number Of Pages: 306

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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 Mathematics is of interest for researchers in mathematics education, PhD students in mathematics education and mathematics educators.

Editors' Preface
Biography of Guy Brousseau
Prelude to the Introductionp. 1
Introduction: Setting the scene with an example: The race to 20p. 3
Introduction of the race to 20p. 3
First phase of the lesson: Instructionp. 6
Action - situation, pattern, dialecticp. 8
Formulation - situation, pattern, dialecticp. 10
Validation - situation, pattern, dialecticp. 13
Foundations and methods of didactiquep. 21
Objects of study of didactiquep. 21
Phenomena of didactiquep. 25
Elements for a modellingp. 29
Coherence and incoherence of the modelling envisaged: The paradoxes of the didactical contractp. 40
Ways and means of modelling didactical situationsp. 47
Adidactical situationsp. 54
Epistemological obstacles, problems and didactical engineeringp. 79
Epistemological obstacles and problems in mathematicsp. 79
Epistemological obstacles and didactique of mathematicsp. 98
Problems with teaching decimal numbersp. 119
Introductionp. 119
The teaching of decimals in the 1960s in Francep. 121
The teaching of decimals in the 1970sp. 131
Didactical problems with decimalsp. 149
General design of a process for teaching decimalsp. 149
Analysis of the process and its implementationp. 167
Analysis of a situation: The thickness of a sheet of a paperp. 195
Questions about didactique of decimalsp. 212
The didactical contract: the teacher, the student and the milieup. 227
Contextualization and decontextualization of knowledgep. 227
Devolution of the problem and "dedidactification"p. 227
Engineering devolution: subtractionp. 230
Institutionalizationp. 235
Conclusionsp. 246
Didactique: What use is it to a teacher?p. 253
Objects of didactiquep. 253
Usefulness of didactiquep. 255
Difficulties with disseminating didactiquep. 263
Didactique and innovationp. 267
The center for observations: The ecole Jules Michelet at Talencep. 275
Bibliographyp. 283
Referencesp. 287
Index of namesp. 295
Index of subjectsp. 299
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792345268
ISBN-10: 0792345266
Series: Mathematical Physics Studies
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 306
Published: 30th September 1997
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 1.91
Weight (kg): 0.64

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