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Third International Handbook of Mathematics Education

M. A. (Ken) Clements, Alan J. Bishop, Christine Keitel, Jeremy Kilpatrick, and Frederick K. S. Leung, editors
Publication Date: 
Number of Pages: 
Springer International Handbooks of Education 27
[Reviewed by
Annie Selden
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This behemoth of a book is 2¼ inches wide and 1120 pages long. It has 33 chapters by 84 authors from 26 countries, making it truly international by representation. It is divided into four parts which describe: 1) social, political, and cultural dimensions in mathematics education; 2) mathematics education as a field of study; 3) technology in the mathematics curriculum; and 4) international perspectives in mathematics education. When I inquired of a Springer editor why it had not been printed in the more customary two volumes, she said that Springer was now able to bind larger volumes.

This volume is not a successor to the Second International Handbook of Mathematics Education, but that was not intended from the “get-go”. As the volume’s editors state in the introduction, the intent was not “merely an update of the earlier handbooks”, and I can say that they got what they wanted. For whatever else it is, this volume is not a handbook of research on the teaching and learning of mathematics — something which I, personally, found to be a disappointment. Some of the reasons will be given below.

One can go 200 pages into the volume and not find a single mathematical symbol. Indeed, just a few functions and a few computer-generated graphs can be found in the chapters on technology and mathematics — the rest is mostly verbiage. I also found it disappointing that many authors of the chapters in this volume almost entirely ignored the large body of research on the learning and teaching of university mathematics, instead choosing to focus on school level mathematics and adult mathematics education. Also, I find it strange that the word “cognition” is not mentioned very often. Instead, this volume focuses on the “social turn” that some mathematics educators generally, and some mathematics education researchers, have emphasized lately.

Why was individual cognition ignored?

There has been much mathematics education research, beginning in about the 1980s and going on into the present, that has focused on the way individual students’ learn, and sometimes do not learn, various mathematical concepts.

I have great respect for the more recent socio-cultural studies within mathematics education, which add much to our understanding of how the teaching and learning of mathematics is fostered in classrooms and other social situations. But as Paul Cobb (the 2005 recipient of ICMI’s Freudenthal Medal which recognizes a major cumulative research program in mathematics education) has observed, “Each of the two perspectives, the sociocultural and the constructivist, tells half of a good story, and each can be used to complement the other.” [“Where Is the Mind? Constructivist and Sociocultural Perspectives on Mathematical Development”, Educational Researcher, 23(7), 13-20.]

In particular, I object to the view stated in Chapter 4 that “deficit models were previously in the foreground of research designs” suggesting that much, if not all, of the research into cognitive issues of mathematical learning and teaching were assuming a “deficit” model of students. That is, as the authors state, that previous researchers assumed “people of low socio-economic background, or of different genders or ethnic groups, are intellectually less capable” (p. 102). I do not believe this was the case, and saying so maligns many capable mathematics education researchers such as Les Steffe (who received the Senior Research Award given by the American Educational Research Association’s Special Interest Group on Research in Mathematics Education), Richard Skemp (who introduced the concepts of relational and instrumental understanding into the field), Pirie and Kieren (whose model of mathematical understanding was insightful and much used), and numerous other leaders in the field. If I can say so, painting prior research in this way amounts to an unfortunate kind of “revisionist history”. I think the authors of various chapters could have emphasized the advantages of taking a socio-cultural perspective, while acknowledging past, and current, cognitively-based research. That is not to say that nothing can be gained from this Handbook.

Who was this Handbook written for?

Ken Clements, the overall editor, states in his introduction that “all mathematics educators, including mathematics teachers at all levels, should read some or all of the chapters.” I asked myself: Why would an individual mathematics teacher be interested in reading this volume, when there are no, or almost no, pedagogical suggestions? To be clear, Clements suggests the Handbook can provide insights into questions such as, “What can a school do if it wants engage all of its students actively and productively in relevant mathematics learning?” It seems to me that such insights would interest heads of school mathematics departments, school principals, and other school administrators, but would not help an individual teacher in day-to-day practice.

One can learn from this Handbook a lot of information on the “social turn” in mathematics education and a good bit about international assessments in mathematics, such as PISA and TIMMS. International organizations are also discussed in the volume, so beginning on page 937, one can find a glossary for an “alphabet soup” of 87 organizations, such as AFRICME, CIAEM, CLAME, EMF, IACME, ICMI, ICTMA, MEAS, NORMA, RDM, SERJ, and YESS, to name just a few.

But this is not the end of the acronyms to be found in this volume. There are FAME (formal adults’ mathematics education), NFAME (non-formal adults’ mathematics education), and IFAME (informal adults’ mathematics education), all of which are parts of AME (adults’ mathematics education), and all of which were unfamiliar to me before. Perhaps this is because university students are not the subject of adult education. There are also acronyms that are more familiar to mathematics educators and mathematics education researchers, but probably not to mathematicians, such as PCK (pedagogical content knowledge), DGE (dynamic geometry), CCK (common content knowledge), SCK (specialized content knowledge), KCS (knowledge of content and students), and KCT (knowledge of content and teaching). These are illustrated in a diagram on page 395 of Chapter 13 titled, “Teachers Learning from Teachers”. Thus, if one is not in the field, one needs to have a glossary of such terms, but none is provided.

I am not sorry to have had the chance to review this tome, and to obtain a complimentary copy, but I would not have purchased it for myself, given what I now know of its contents.

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.

Past, present and future dimensions of mathematics education: Introduction to the Third International Handbook of Mathematics Education: M. A. (Ken) Clements



Introduction to Section A: Social, Political and Cultural Dimensions in Mathematics Education: Christine Keitel
1. From the few to the many: Historical perspectives on who should learn mathematics: M. A. (Ken) Clements, C. Keitel, Alan J. Bishop, Jeremy Kilpatrick and Frederick Leung
2 Theories for studying social, political and cultural dimensions of mathematics education: Eva Jablonka, David Wagner and Margaret Walshaw
3. Understanding and overcoming “disadvantage” in learning mathematics : Lulu Healey and Arthur B. Powell
4. Beyond deficit models of learning mathematics: Sociocultural directions for change and research: Cristina Frade, Nadja Acioly-Régnier and Li Jun
5. Studying learners in intercultural contexts: Yoshinori Shimizu and Gaye Williams
6. Learners in transition between contexts: Tamsin Meaney and Troels Lange.-7. Critical perspectives on adults’ mathematics education: Jeff Evans, Tine Wedege and Keiko Yasukawa
8. The politics of equity and access in teaching and learning mathematics: Neil A. Pateman and Chap Sam Lim


Introduction to Section B: Mathematics Education as a Field of Study: Alan J. Bishop
9. From mathematics and education to mathematics education: Fulvia Furinghetti, José Manuel Matos and Marta Menghini
10. Theories for education: mathematics: Some developments and ways forward: Bharath Sriraman and Elena Nardi
11. Research methods in mathematics teacher education: Uwe Gellert, Rosa Becerra Hernández and Olive Chapman
12. Linking research to practice: Teachers as key stakeholders in mathematics education research: Carolyn Kieran, Konrad Krainer and J. Michael Shaughnessy
13. Teachers learning from teachers: Allan Leslie White, Barbara Jaworski, Cecilia Agudelo-Valderrama and Zahra Gooya
14. Developing mathematics educators: Jarmila Novotná, Claire Margolinas and Bernard Sarrazy
15. Institutional contexts for research in mathematics education: Tony Brown and David Clarke
16. Policy implications of developing mathematics education research: Celia Hoyles and Joan Ferrini-Mundy



Introduction to Section C: Technology in the mathematics curriculum: Frederick Leung
17. From the slate to the Web: Technology in the mathematics curriculum: David Lindsay Roberts, Allen Yuk Lun Leung and Abigail Lins
18. Modelling with mathematics and technologies: Julian Williams and Merrilyn Goos
19. Technology and the role of proof: The case of dynamic geometry: Nathalie Sinclair and Ornella Robutti
20. How might Computer Algebra Systems change the role of algebra in the school curriculum?: M. Kathleen Heid, Mike Thomas and Rose Mary Zbiek
21. Technologies for enhancing statistical reasoning at the school level: Rolf Biehler, Dani Ben-Zvi, Arthur Bakker and Katie Makar
22. Learning with the Use of the Internet: Marcelo C. Borba, Philip Clarkson and George Gadanidis
23. Technology and assessment in mathematics: Kaye Stacey and Dylan Wiliam
24. Technology-driven developments and policy implications for mathematics education: Luc Trouche, Paul Drijvers, Ghislaine Gueudet and Ana Isabel Sacristán


Introduction to Section D: International Perspectives on Mathematics Education: Jeremy Kilpatrick.