To cover 30 years of the psychology of mathematics education from the perspective of the International Group for the Psychology of Mathematics Education (PME) and to include parts of the research knowledge base from that perspective are daunting tasks. The volume intends to present “a consolidated report on important PME research interests, questions and methodologies, findings and conclusions, as well as some hints of possible future activity in the field.”
To examine the volume, this reviewer chose to concentrate on a few of the areas including research on the learning and teaching of algebra, proof and proving in mathematics education and the teaching and learning of geometry through technology. The reviewer chose these areas because of previous, and different, work in these areas. The personal work provided a base to help achieve an understanding of some of the research being reported here. Unfortunately, the base may have provided a reviewer bias in these specific areas.
While reading in the chosen areas, this reviewer kept coming back to some of the goals of the editors of the book:
- Avoid the “list style” of review of research that could survey the field and avoid the “unilateral reconstruction style” in which authors interpret research from their personal viewpoints over time.
- Finding a representative set of authors who could be removed enough from a field to take an unbiased view of different approaches while being both culturally and regionally diverse
The first goal listed by the editors appears to have been achieved and that may be the more important of the two. However, it is distressing in this international volume to see that one-third of the chapters have single authors. And while writers of the single-author-chapters are certainly knowledgeable in the fields where they wrote, they are far from representative of either the membership of PME or of the native languages used around the world. With the broad membership of PME, with the stated goals of the editors, and with a book that took over four years from conception to publishing, it is almost inconceivable that more representative authors could not be found. This weakness, and with it the appearance of potential biases of the authors, should have been overcome and, if so, would have given the appearance of a more worldwide view than the volume currently has.
That having been said, the reviewer-focus-chapters were in depth and were broad in their scope and understanding of research at many levels. The reviewer was able to find some personal favorite studies discussed and, as expected, others that were less well known. All of the focus chapters appeared to have the requisite knowledge base, and referred-to studies were generally given without author evaluation. (It is noted that the studies mentioned were likely evaluated by the authors before their inclusion.). The focus chapters had varying depths of hints and notions of research yet to be done. As in other non-focus-chapters in the book, some of the focus-chapters gave in-depth suggestions of future research in the Freudenthal style with lists; others gave very brief notes and hints in some (but not all) sections about what research might be needed in the future. This reviewer wanted a consistency in the form of conclusions to the chapters with the authors’ best guesses at where the research is headed. These best guesses are generally in the chapters, but a summary would have helped.
A major strength of this volume is the extensive reference list at the end of each chapter. A reader wanting to find a good collection of resources in one place will find a treasure trove here. While some chapters are heavy with Proceedings of PME Conferences references as expected in such a volume, there are enough other resources to make the work valuable to researchers and doctoral students.
This reviewer strongly believes that the volume was a worthwhile endeavor and is a fitting tribute to the 30 years of the PME organization. It would be a good contribution to any library’s core mathematics education collection. The chapter bibliographies alone make the resource an inexpensive but notable book for mathematics educators to own.
Johnny W. Lott is Director of the Center for Excellence in Teaching and Learning at the University of Mississippi. Additionally, he holds the titles of Professor of Mathematics and Professor of Education. A past president of the National Council of Teachers of Mathematics, Dr. Lott is Professor Emeritus of the Department of Mathematical Sciences at The University of Montana. He may be reached at firstname.lastname@example.org.