Curiculum Vitae
Other Writings
Book reviews
from the
Dutch Mathematical
Book reviews
from the journal
Acta Applicandae

Book review

Author(s) Bishop, A.J. (ed.)
Mellin-Olsen, S. (ed.)
Dormolen, J.van (ed.)
Title Mathematical Knowledge: Its Growth Through Teaching
Publisher Kluwer Academic Publishers
Year of publication 1991
Reviewed by C.I.Gheorghiu

The work is the tenth issued in the Mathematics Education Library - managing editor A.J.Bishop, Cambridge UK - and the second delivered by BACOMET.

It is developed over the period 1985 - 9 and it focuses on the genesis of mathematical knowledge in classroom.

An introduction, nine articles (named entr'actes) an index of names and an index of subjects are the contents.

Here are the names of authors and of their contributions: G.Brousseau and M.Otte, The Fragility of Knowledge; S.Mellin-Olsen, The Double Bind as a Didactical Trap; W. Dörfler, Forms and Means of Generalization in Mathematics; J. van Dormolen, Metaphors Mediating the Teaching and Understanding of Mathematics; R. Douady, Tool, Object, Setting, Window: Elements for Analysing and Constructing Didactical Situations in Mathematics; T. Werner, Observing Conceptual Complexity; C. Hoyles, Developing Mathematical Knowledge Through Microworlds; N. Balacheff, The Benefits and Limits of Social Interaction: The Case of Mathematical Proof; A.J.Bishop, Mathematical Values in the Teaching Process.

The book as a whole deals with some very keen aspects in mathematical education. It represents the efforts of BACOMET group on new research strategies in mathematical education, new tools for innovative work and new perspectives and possibilities for promoting the learning of mathematics. The authors come from different countries and are raised in different research traditions. Nevertheless, they all try to identify and analyze the really significant aspects of the process of growth of mathematical knowledge in classroom. Finally, they have succeeded.

"What problems do classroom situations in learning mathematics have in common? What issues are always present irrespective of milieu, content, players? And what, of these, are the most significant for developing mathematics educators' understanding in order that mathematics education itself can develop fruitfully?" - are the questions the authors are faced with here. It is of benefit for all mathematics education community.

All in all, this collection of essays proves to be a good investment for didactic libraries, as well as for individuals working within this exciting field of research.