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The Teaching and Learning of Mathematics at University Level: An ICMI Study

Derek Holton, editor
Publication Date: 
Number of Pages: 
New ICMI Study Series 7
[Reviewed by
Teri J. Murphy
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The Kluwer website says that "This book arose from the ICMI Study into the teaching and learning of mathematics at university level that began with a conference in Singapore in 1998." This edited book is thus the culmination of several years of conversations. The book has seven sections: Introduction, Practice, Research, Mathematics and Other Disciplines, Technology, Assessment, and Teacher Education. Each section contains some half dozen loosely-related chapters, written by different authors who may or may not have read or built on each others' work. This structure is common among publications sometimes called "Handbooks" (e.g., NCTM's Handbook of Research on Mathematics Teaching and Learning, AERA's Handbook of Research on Teaching). With this structure, each section reads much like a special issue (minus a clear peer-review process) of an education-related journal (e.g., PRIMUS, Research in Collegiate Mathematics Education, The Journal of Mathematics Teacher Education).

Like an article, each chapter is a separate entity and can be read in isolation from the rest of the book. As with most edited books comprised of chapters by different authors, some chapters are more appealing, more compelling, written better, and/or more informative than other chapters. The lack of abstracts at the beginning of the chapters added to my difficulty understanding what to expect from each chapter or each section as a whole. However, many of the authors used the first paragraph or two to give an overview of the chapter. In the absence of actual abstracts, I recommend that readers use these introductory paragraphs to help determine the level of interest/usefulness of the chapter.

A few of the chapters are reports from ICMI working groups; others are descriptions of the state of practice or knowledge in a specific geographic or disciplinary area; still others appear to be expository writings by experienced practitioners. Some chapters describe specific perspectives or approaches; others raise more general issues. Some chapters discuss practice at an instructor level, some at a program level. Some research-related chapters appear in the section entitled "Research" and other research-focused chapters (vs. anecdotal descriptions of practice) appear scattered throughout other sections. In many cases, it was unclear to me why a particular chapter was placed in a particular section instead of another section; it was also unclear to me how the ordering of chapters within each section was decided (e.g., Hodgson, "The Mathematical Preparation of School Teachers," was separated from Wittmann, "The Alpha and Omega of Teacher Education," by two chapters specifically addressing the professional development of tertiary instructors). I do not recommend reading the book from front to back.

The opening chapter (Alsina, "Why the Professor Must Be a Stimulating Teacher") caught my attention right away with its no-bones-about-it writing that presented "myths", discussed their impact, and offered alternate perspectives. In the end, though, the title did not match the content. I felt this way about many of the chapters.

The "Assessment" section was my favorite. I enjoyed all three chapters and they each provided good information and made me think. I was surprised by this, because assessment is not usually my favorite topic. As is the case in general, I would have liked to see more research referred to in practice chapters and more practices referred to in research chapters. I did enjoy, and learned a lot from, the chapters in the "Case Studies" at the end of the Introduction section and the Practice section. These chapters offered concise, well-described examples of situations from around the globe. If busy people have time to read no other pieces of this book, I recommend these chapters to enhance awareness of situations, models, and issues in multiple geographical contexts. I am not sure why the other five sections did not also include "case study" chapters (in some instances, it seemed to me that some of the "regular" chapters were actually "case studies" but were not labeled as such).

In addition to the inclusion of chapter abstracts, a second structural change could have made the book more compelling: I would have liked brief biographies of each author. In the absence of an explicit peer review process, it is not clear from the book why these are the people whose writings we should spend our limited and precious time reading. I am not saying that the ideas presented are not worth considering, nor am I questioning the credentials of the authors (many of whom I know). I am merely pointing out that academics are more likely to pay attention to ideas when the credentials of the authors are clear and that it should not be assumed that all potential readers are familiar with the credentials of the authors.

The book suffers from an additional annoying editorial problem: several of the chapters are missing things that I am sure the authors intended to be there. For example, Wood's chapter, "The secondary-tertiary interface," skips from the end of a paragraph on the first page to the middle of a paragraph on the second page. This is not the only chapter that has this particular problem. I found it not only distracting and disruptive, but also confusing, because I think sometimes those missing words or sentences were part of the set-up for the chapter. In addition, Kessel and Ma, "Mathematicians and the preparation of elementary teachers," refers several times to a figure that I could not find anywhere in the chapter. At least these authors indicated in the chapter where else a reader could find the figure. These unprofessional editorial mistakes make the book frustrating to read.

I returned over and over again to the Preface that says "... this Study was commissioned to provide a forum for discussing, disseminating and interchanging, educational and pedagogical ideas between and among, mathematicians and mathematics educators" (p. v.). I am still unclear who the target audience(s) is (are) for the book. I am convinced that discussions happened at ICMI meetings and in the preparation of this book. I am, however, unconvinced that very many people are going to read this book from cover-to-cover as I did. I fear that this book, like so much academic writing, will receive attention primarily from a small group who are already engaged in discussion; I am not sure that the book will attract new participants to these discussions. (I would love to be wrong.) Yet, overall, I would say that every academic library should own a copy, much as they own copies of journals and magazines, and that people interested in specific topics should include the relevant chapters in their personal literature databases.

Teri J. Murphy ( is associate professor of mathematics at the University of Oklahoma. She has an M.S. in mathematics, an M.S. in applied mathematics, and a Ph.D. in mathematics education from the University of Illinois at Urbana-Champaign. Her research specialty is undergraduate mathematics education.