All Positive Action Starts with Criticism

Hans Freudenthal and the Didactics of Mathematics

  • Sacha la Bastide-van Gemert

Table of contents

  1. Front Matter
    Pages i-xv
  2. Sacha la Bastide-van Gemert
    Pages 1-9
  3. Sacha la Bastide-van Gemert
    Pages 37-59
  4. Sacha la Bastide-van Gemert
    Pages 61-80
  5. Sacha la Bastide-van Gemert
    Pages 81-132
  6. Sacha la Bastide-van Gemert
    Pages 133-177
  7. Sacha la Bastide-van Gemert
    Pages 179-204
  8. Sacha la Bastide-van Gemert
    Pages 205-282
  9. Sacha la Bastide-van Gemert
    Pages 283-359
  10. Sacha la Bastide-van Gemert
    Pages 361-366
  11. Back Matter
    Pages 367-386

About this book


This study provides a historical analysis of Freudenthal’s didactic ideas and his didactic career. It is partly biographical, but also contributes to the historiography of mathematics education and addresses closely related questions such as: what is mathematics and where does it start? Which role does mathematics play in society and what influence does it have on the prevailing views concerning its accompanying didactics?

Hans Freudenthal (1905–1990), professor in mathematics, scientist, literator, but above all mathematics-educator, was inextricably  linked to the changes which took place in mathematics education and didactics during the second half of the last century. His diversity as a scientist and his inexhaustible efforts to establish the didactics of mathematics as a seriously pursued science, made Freudenthal's influence in this area considerable. He foresaw an essential, practical role for mathematics in everyone’s life, encouraging students to discover and create mathematics themselves, instead of imposing a ready-made mathematical system. The theory of mathematics education thus developed in the Netherlands would gain world fame in the following decades.

Today, in the light of the discussions about mathematics education, in which the call for `genuine’ mathematics instead of the so-called 'kindergarten'-mathematics can be heard, Freudenthal's approach seems to be passé. However, the outcome of this study (which is mainly based on documents from Freudenthal’s vast personal archive) shows a more refined picture. The direct identification of 'kindergarten'-mathematics with Freudenthal’s view on mathematics education is not justified. 'Realistic mathematics' as advocated by Freudenthal includes more than just a practical introductory and should, among other things, always aim at teaching 'genuine' mathematics in the end.


Educational Studies of Mathematics FIsme Freudenthal Institute Hans Freudenthal History of ICMI ICMI New Math Rekendidactiek Wiskunde Werkgroep didactics of arithmetic didactics of mathematics mathematics education realistic mathematics realistisch rekenen

Authors and affiliations

  • Sacha la Bastide-van Gemert
    • 1
  1. 1.GarmerwoldeThe Netherlands

Bibliographic information