© 1987

Three Dimensions

A Model of Goal and Theory Description in Mathematics Instruction — The Wiskobas Project


Part of the Mathematics Education Library book series (MELI, volume 3)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Mathematical Material for Chapter I: “Gulliver”

    1. Front Matter
      Pages 1-7
    2. Adrian Treffers
      Pages 8-29
  3. Mathematical Material for Chapter II: “Counting Problems”

    1. Front Matter
      Pages 31-36
    2. Adrian Treffers
      Pages 37-73
  4. Mathematical Material for Chapter III: “Grains on the Chessboard”

    1. Front Matter
      Pages 75-82
    2. Adrian Treffers
      Pages 83-111
  5. Mathematical Material for Chapter IV: “The Land of Eight”

    1. Front Matter
      Pages 113-118
    2. Adrian Treffers
      Pages 119-158
  6. Mathematical Material for Chapter V: “Freckleham”

    1. Front Matter
      Pages 159-166
    2. Adrian Treffers
      Pages 167-195
  7. Mathematical Material for Chapter VI: “Algorithms”

    1. Front Matter
      Pages 197-210
    2. Adrian Treffers
      Pages 211-219
  8. Mathematical Material for Chapter VII: “The Wiskobas Curriculum”

    1. Front Matter
      Pages 221-238
    2. Adrian Treffers
      Pages 239-296
  9. Back Matter
    Pages 297-351

About this book


In Dutch "WISKOBAS" stands for a particular kind of mathematics in the elementary school (ages 6-12). In tum Wiskobas was one of the depart­ ments in the IOWO, the Institute for the Development of Mathematics Education. This institute was concerned with the development of material for mathematics education as well as the related research on the possibility of change from the then existing arithmetic instruction to the future mathematics education. The present publication Three Dimensions has three aims: to give a picture of the goals Wiskobas set for future mathematics education, at the same time to show how such goals can be described, and to show the theoretical framework of the Wiskobas curriculum. The problem at hand is not at all simple. What is more, Wiskobas' ideas about mathematics education cannot literally be translated into strings of words. So how can we face the accusation that our objectives are unattain­ able and the goal itself irrational? In order to avoid this vagueness as much as possible and for the sake of clarity, this book makes continuous use of illustrations of mathematics education. In these examples both the subject-matter and the methods of description of the goals are illustrated as explicitly as possible, while at the same time creating the opportunity to read between the lines. The reader is urged to follow carefully the mathe­ matical material at the start of each chapter. This advice applies both to the more general education oriented, and to the more mathematical! didactical reader.


Arithmetic Counting Integration education function mathematics mathematics education socialisation

Authors and affiliations

  1. 1.Mathematics Education Research Group (OW & OC)State University of UtrechtThe Netherlands

Bibliographic information

  • Book Title Three Dimensions
  • Book Subtitle A Model of Goal and Theory Description in Mathematics Instruction — The Wiskobas Project
  • Authors A. Treffers
  • Series Title Mathematics Education Library
  • DOI
  • Copyright Information Springer Science+Business Media B.V. 1987
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-90-277-2165-5
  • Softcover ISBN 978-94-010-8160-3
  • eBook ISBN 978-94-009-3707-9
  • Edition Number 1
  • Number of Pages XVI, 352
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published in Dutch
  • Topics Mathematics Education
    Education, general
  • Buy this book on publisher's site