All Positive Action Starts with Criticism : Hans Freudenthal and the Didactics of Mathematics

This study provides a historical analysis of Freudenthals 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 Freudenthals influence in this area considerable. He foresaw an essential, practical role for mathematics in everyones 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, Freudenthals approach seems to be passé. However, the outcome of this study (which is mainly based on documents from Freudenthals vast personal archive) shows a more refined picture. The direct identification of kindergarten-mathematics with Freudenthals 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.