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Signs of Signification: Semiotics in Mathematics Education Research

Norma Presmeg, Luis Radford, Wolff-Michael Roth, and Gert Kadunz, editors
Publication Date: 
Number of Pages: 
ICME-13 Monographs
[Reviewed by
Annie Selden
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Semiotics is the theory of signs. It has recently been used by a number of mathematics education researchers to theorize their work. Having found this approach intriguing but not understandable, I approached this book seeking enlightenment. This book, however, is definitely not a primer on how semiotics is used in mathematics education research. 

I know the first three editors of this volume professionally and respect their work. Norma Presmeg has served as Editor-in-Chief of Educational Studies in Mathematics, considered the premier European journal of mathematics education research. Luis Radford is currently an Associate Editor of Educational Studies in Mathematics and the 2011 recipient of the International Commission on Mathematical Instruction’s prestigious Hans Freudenthal medal “in recognition of the theoretically well-conceived and highly coherent research program”. Wolff-Michael Roth is the Lansdowne Professor of Applied Cognitive Science at University of Victoria and the author or editor of seven books.

The parts of the book that I read were a “tough slog”, with many technical words. The collection of chapters by authors from a number of different countries seemed much more like a philosophical treatise than a collection of expository essays with mathematics education research data as exemplars of how/why semiotics is relevant to the everyday, run-of-the mill mathematics education researcher or mathematician. Some parts “boggled my mind”, such as Chapter 2, which introduces “life as a semiotic zone”. In it, the author, Luis Radford, includes in his discussion of semiotics not only various kinds of inscriptions, but also individuals, who coproduce themselves in “processes of subjectification”. He points out that

this way of conceptualizing individuals is certainly at odds with the conception of the individual that we have inherited from the philosophy of the Enlightenment… We have become used to the idea that we are equipped with an interior from where our true Being emanates. It is in this interior that our deepest feelings and meanings are allegedly formed, so that what we need in order to grow as human beings is simply a stimulating environment … The conceptualization of individuals that I am suggesting here, as reflective signs in an unfinished process of becoming, subsumed with dynamic symbolic ideological superstructure, goes in another direction. It is a direction that does not posit the student at the origin of knowing and becoming, as an essentially already given and already made entity. It rather conceives of the student as a continuously moving sign in the making. (pp. 22–23).

After perusing the other chapters very briefly, I gave up on learning more about semiotics as it relates to mathematics education research from this particular volume. Perhaps those with more patience and a more philosophical bent will persist in reading it and gain a great deal. Perhaps those who already use semiotics in their mathematics education research will become further informed. I wish them happy reading.

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.

See the table of contents in the publisher's webpage.