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All Positive Action Starts with Criticism

Sacha la Bastide-van Gemert
Publication Date: 
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[Reviewed by
Annie Selden
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What sort of book is this? Originally written as a dissertation (in Dutch) and then translated into English, it concentrates on the historical development of Freudenthal’s ideas on the didactics of mathematics. As the author states, this dissertation study tried to answer the question, “What was Freudenthal’s role in mathematics education?” (p. 3). To answer this question, the author offers a reconstruction of the development of Freudenthal’s ideas, based primarily on documents found in Freudenthal’s 16 meter long personal archive. It is not meant to be a biography, but rather a historical analysis of the development of his didactical ideas.

The book proceeds chronologically, first describing the situation in mathematics education (mainly in the Netherlands) between the two World Wars. This is followed by a very short chapter containing the broad outlines of Freudenthal’s life to provide some context for what follows. During the final years of WWII, Freudenthal wrote an unpublished manuscript, “Didactics of arithmetic” (in Dutch), which was his first work on the didactics of mathematics. This unpublished manuscript is described and analyzed in Chapter 4, taking into account Freudenthal’s later ideas of the 1970s.The next chapter describes the period just after WWII when Freudenthal took his first actual steps into the field of mathematics education and the didactics of mathematics and published his first manuscript in the field. Also, during this period, he moved from Amsterdam to Utrecht and became an active member of the mathematics working group, Wiskunde Werkgroep (WW).

Chapter 6 covers the period from 1950 to 1957 when Freudenthal’s national and international reputation as a mathematics educator grew enormously. Also, towards the end of the period, his mathematical-didactical ideas were greatly influenced by the pedagogical dissertation studies of Pierre and Dina van Hiele on geometry. Their work, and its influence on Freudenthal who was their dissertation advisor, is further discussed and analyzed in Chapter 7. Of special interest to mathematics education researchers who use realistic mathematics education (RME) as their theoretical framework is Section 7.4 titled, “Freudenthal and the theory of the van Hieles: From ‘level theory’ to ‘guided re-invention’”. According to the author, it was during this time period that Freudenthal introduced the ideas of “guided re-invention” and the “anti-didactical inversion”. These terms “did not come out of the blue. … [B]oth concepts were already mentioned before in more guarded terms. But it is the first time that Freudenthal mentioned and defined them explicitly.” (p. 195).

Chapter 8 deals with the period of the 1960s during which Freudenthal was “the lonesome opponent of the New Math.” (p. 7). The final chapter describes the years around 1970 during which Freudenthal consolidated his ideas on the didactics of mathematics. And, despite the fact that Freudenthal continued to work on the didactic of mathematics until his death in 1990, the book ends here, except for a short epilogue.

I suspect, given the academic nature of this book, that it would primarily be of interest to mathematics education researchers, especially those who use RME as their theoretical framework and to those interested in the history and development of the field, as seen from Freudenthal’s, and the author’s, perspectives.

One caveat, the book is replete with acronyms and abbreviations, such as APS, CMLW, HAV0, IOWO, MULO, SVO, and WISKOBAS — indeed there are so many that the author provides a 2½ page list of abbreviations (in both Dutch and English equivalents) at the beginning.

Annie Selden is Adjunct Professor of Mathematics at New Mexico State University and Professor Emerita of Mathematics from Tennessee Technological University. She regularly teaches graduate courses in mathematics and mathematics education. In 2002, she was recipient of the Association for Women in Mathematics 12th Annual Louise Hay Award for Contributions to Mathematics Education. In 2003, she was elected a Fellow of the American Association for the Advancement of Science. She remains active in mathematics education research and curriculum development.