The books in this series present “relevant research and innovative international developments with respect to the preparation and professional development of mathematics teachers.” While this book is clearly intended for mathematics education researchers who investigate the preparation and teaching of K–12 mathematics teachers, it would also be of interest to mathematics teacher educators and curriculum designers. The authors of the individual chapters come from thirteen countries — the U.S, the U.K., New Zealand, South Africa, the Netherlands, France, Canada, Mexico, Italy, Norway, Germany, Australia, and Denmark — and the divergence of views can be both stimulating and unsettling. While textbooks remain the mainstay of mathematics instruction and are considered, what counts as curriculum resources for these authors is very broad: not only textbooks, but also problem sets, tasks, artifacts, digital resources (including the internet), software, learning goals, programs, interactions with students and colleagues, and professional development. By “lived resources” is meant how teachers make use of such resources in the classroom. The book is organized into four parts — each part has an introductory chapter and is followed by an “expert’s reaction.” There is also a final closing reaction by Deborah Ball.

Gone are the attempts of the 50s and 60s to produce “teacher proof” materials. The authors of these chapters see teachers as creative users of resources and document their professional growth. Almost all authors propose their own theoretical perspectives and illustrate them with excerpts from empirical studies. If there is one disturbing element, it is the authors’ use of terms, derived from the French. They refer to *documentation system*, *documentation work*, and the *documentational approach* by which they mean how “the teacher interacts with resources, selects them, and works on them (adapting, revising, reorganizing, etc.).” In reading this book, I had to keep reminding myself that the authors’ use of these terms was not the same as the standard English usage, where “documentation” means “material that provides official information or that serves as a record.” By *documentational genesis*, the authors refer to “becoming a teacher” (p. 343), and “becoming a professional” with “rich and varied perspectives” (p. 353).

Some chapters’ empirical evidence includes case studies. For example in Chapters 2 and 16, Ghislaine Gueudet and Luc Trouche discuss two teachers, Myriam and Pierre. These two teachers, followed over several years, are used to illustrate the authors’ theoretical concepts and the two teachers’ integration of both digital and non-digital resources. The authors report the extent of Myriam’s and Pierre’s integration and modification of resources, such as email and spreadsheets, and their professional growth. These and the other case studies report the specific experiences of teachers, and in particular, are much easier to read and digest than the more theoretical parts of these chapters. One of the conclusions of the chapters is that the new standards-based curricula (whether *NCTM Standards* or *Common Core State Standards*) present “challenges for many teachers” and “require considerable reorientation” (p. 105) on their part, and that teacher change happens over long periods of time.

One particular piece of information that was new to me was contained in William H. Schmidt’s chapter, namely, that there exists a TIMMS Mathematics Textbook Classification System. It “is built on a set of content categories developed by groups of mathematicians and mathematics teachers representing numerous countries … [and] includes mathematics content topics that are commonly found in elementary and lower secondary schools in participating countries” (p. 146). There is also an Index of Mathematical Exposure. Using this index, Schmidt concludes “it is clear that [U.S.] students in the top mathematics track [of four] are exposed to significantly more challenging mathematics earlier than the other students and that this initial advantage grows during the 6 years of middle and high schools.”

This book can be a worthwhile read for those who are interested in how teachers use a variety of resources, material and non-material, digital and non-digital. However, the theoretical parts might be “tough slog” for those uninitiated into the language of mathematics education research, and might be skipped or skimmed.

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.