European Traditions in Didactics of Mathematics

This open-access book is one of several monographs published after the 13th International Congress on Mathematical Education (ICME-13), which I attended. I very much enjoyed the opportunity to learn about and understand various international approaches to mathematics education, and this book provides just such an opportunity. This book grew out of the Thematic Afternoon on European Didactic Traditions, and includes contributions from a total of 23 international experts in the didactics of mathematics.

This book is a grand tour through mathematics education research in Europe. Each of the seven chapters presents a different country’s (or region’s) traditions in “the didactics of mathematics” -- a term common to many European traditions, denoting the art and science of teaching and learning, and research into the same. Four major cross-cutting themes unify the chapters: “a strong connection with mathematics and mathematicians, the key role of theory, the key role of design activities for learning and teaching environments, and a firm basis in empirical research” (p. 2). The presentation is clear, well-organized, and readable. The introduction is excellent; as a thousand-foot overview of the landscape of European didactics, it’s worth the price of admission all by itself.

This is mostly useful as a reference text for experienced mathematics educators interested in further understanding the European traditions; the reader is presumed to be acquainted with the canon of mathematics education literature. Some chapters are more accessible to novices than others. For instance, the chapter on the Dutch tradition includes an extensive and helpful discussion of the principles underlying RME and walks through several useful examples, while the French chapter can only hope to provide a brief gloss of three major “theoretical pillars.”

Each chapter ends with a carefully-curated reference list, which I think is a major selling point of this book. These lists are excellent, comprehensive, and extensive, with many English-language references. They might be particularly useful for Ph.D. students in mathematics education, or others interested in gaining a comprehensive understanding of the didactical traditions summarized in this book.

These traditions have been very influential in American mathematics education, both in research and in practice. For instance, I’ve employed Brousseau’s Theory of Didactical Situations (TDS) as a theoretical lens in some of my own research, and my own classroom practice is strongly influenced by the Dutch tradition of Realistic Mathematics Education (RME) pioneered by Hans Freudenthal. This book led me to a deeper understanding of didactical traditions I was already familiar with, and exposed me to other traditions I hadn’t yet heard of, especially the Czech and Slovak tradition inspired by Jan Amos Comenius.

Reflecting on how the didactics of mathematics have developed in other countries provided me with a useful lens on the development of mathematics education in America -- the theoretical traditions that have informed our development; the influence of government and politics, especially relating to international comparative studies such as TIMSS and PISA, on our systems of mathematical education; the specific place teachers and education have inhabited in American culture and society, etc. Further, I think such reflection can provide the broader American mathematics education community with valuable ideas for new paths forward.

A particular example of a great idea that I wish existed in America is the French network of Institutes of Research on Mathematics Teaching (IREMs) -- “university structures [that] welcome university mathematicians, teachers, teacher educators, didacticians, and historians of mathematics who collaboratively work part-time in thematic groups, developing action-research, teacher training activities based on their activities, and producing material for teaching and teacher education” (p. 13). This system provided important structure that helped scaffold the development of French didactics at multiple levels, and I found myself wishing that there was a similar system and structure available to American mathematicians, educators, and math education researchers.

The book demonstrates the usefulness and value of international collaboration through several inspiring and instructive examples, including: the strong collaboration between the Nordic countries; joint doctoral programs crossing the border between France and Italy; RME in the United States, Indonesia, England, the Cayman Islands, South Africa, and Belgium; collaborations between German and Polish researchers; and even the influence of Italian didactics in China. I believe this is a lesson American math education researchers could profitably take to heart; especially in the age of the internet, we have many exciting opportunities for collaborating with our colleagues across the world.

I could provide a few small critiques -- the authors of Chapter 4 appear to have misinterpreted the work of Cobb and Yackel; I was surprised to not hear very much about the foundational work of Felix Klein; the portrayal of the relationships between established and emerging didactical traditions is often uncomfortably colonialist -- but overall, this is an excellent and useful book. As the authors of the chapter on French didactics argue: “All these connections and collaborations allow us to see our tradition from the outside, to better identify its strengths and weaknesses, ... and to envisage ways to jointly progress, at a time when the need of research in mathematics education is more important than ever” (p. 49).

Spencer Bagley is an assistant professor in the Mathematics Department at Westminster College. He lives in Salt Lake City with his husband and three cats. He was previously an assistant professor at the University of Northern Colorado. He holds a Ph.D. in mathematics education from San Diego State University and UC San Diego. He promotes active learning pedagogy in his teaching and research. He enjoys cooking, baking, good food, and a nice cup of tea. Email him at sbagley@westminstercollege.edu, find him on Twitter @sbagley, or read his blog at https://sbagleyteaches.wordpress.com/.