This book is part of the *Studies in Mathematics Thinking and Learning Series*, edited by Alan Schoenfeld. After having my preservice mathematics teachers read The Teaching Gap, by James W. Stigler and James Hiebert (published by Free Press in 1999), I asked them to apply the concept of Japanese lesson study to improve upon the lessons they microtaught. This process was well received, and I found that they became more receptive to teaching suggestions from cooperating teachers, both during their internship and when working with other teachers to improve their lessons.

As James W. Stigler states in his Foreword to this book, "we cannot implement lesson study in the United States the same way it is implemented in Japan. But we also cannot implement lesson study unless we understand it in a deep sense" (p. xi). I could not agree more, and I could hardly wait to read further and learn from the observations that are part of Makoto Yoshida's doctoral dissertation.

Lesson study in Japan is seen as a form of professional development. This book gives the reader insights into a lesson study that was conducted by first- and second-grade elementary teachers at one Japanese school. Beginning in October and continuing until March, Yoshida focused on collecting data from students, teachers and administrators, using videotaped observation, field notes and audio taped interviews.

Lesson study, the authors say in chapter two, "consists of the study or examination of teaching practice" (p. 7). The authors proceed to explain the steps involved in the lesson study process. It is part of a school-based form of in-service professional development where the teaching staff works on an important school goal that is normally guided by the school's mission statement. As a result, the goal may not necessarily be academic. Of interest to the reader/educator is how lesson study is then organized for each school, when Japanese teachers involved in the lesson study have their meetings, and what kind of financial support they might receive from outside sources.

Chapter three sets the context for the lesson study to be described in this book and chapter four sets out what the four first- and second-grade teachers decided upon for their lesson study. They picked the first lesson from a 12-lesson unit on subtraction, which introduces students to the concept of subtraction with regrouping. Although this lesson study is restricted to grades one and two, the reader will be able to learn about the lesson study process at any level.

Chapters five and six describe the planning and preparation of the initial lesson plan/unit. It is suggested that problems used be based on students' daily lives in order to motivate them to want to learn the mathematics involved. The conversation on what manipulatives the students should be provided reinforces the strength of working with others on a lesson study. The choice between teaching mathematics for understanding or to comply with time constraints is discussed; this discussion continues throughout the remainder of the book.

"Listening in" on these lesson study participants provides a rich learning experience for both those involved in teaching mathematics and preservice mathematics teachers. The lesson plan/unit continues to be refined in chapter seven. Of interest within the lesson plan is the "related items" section, which indicates where the lesson is situated in the grades one to five elementary curriculum. This is an important inclusion for those involved in the lesson study, but it also gives the reader/educator a snapshot of the mathematical expectations of this part of the Japanese curriculum.

Chapter eight, with the aid of pictures, diagrams and dialogue, describes the actual lesson taught; improving the lesson plan is the focus of chapter nine. Of interest is the discussion by those involved with the lesson study concerning the use of time, getting the right answers, and student understanding. The conversation touches on redesigning handouts, clarifying of the focus on subtraction, and refining the manipulative involved. Comparing the revised lesson plan in chapter ten with its beginnings powerfully demonstrates how a lesson plan can be improved by working with other educators.

Chapters nine and ten are an excellent resource to stimulate the discussion of planning and teaching mathematics with preservice mathematics teachers. Chapter 11 describes the teaching of the revised lesson and is followed with a description of the feedback about the lesson in chapter 12. The first time the lesson was taught, only the lesson study group and the principal offered feedback. With the revised lesson, all of the teachers in the school, the principal, the vice-principal and an outside advisor attended the debriefing. The conversation returned to the issues regarding time allotment during the lesson, referring to it as a "catch 22", and focusing on how students solve problems. Working together, it was recognized how difficult it is to develop the "perfect" lesson. As a result of these discussions, the principal was able to formulate what the topic for next year's lesson study might be.

Chapter 13 describes the year-end reflection about the lesson study and the work teachers in the school do to put on a lesson study open house that is open to outside educators. At the open house, teachers handed out a "research bulletin" about their year's work. One recommendation contained in the report that is of interest is the "curricular plan for how to sequence, across Grades 1 through 6, instruction related to numbers and basic operations" (p.192). Teachers recognized the importance "that learning across the grades was a coherent and well-connected experience for students" (p. 224). Chapter 14 describes the next step in which lesson study groups share the results of their work with other educators. The system of teacher transfers — on the average of every four years — to facilitate the sharing of what has been learned from lesson studies sounds good in theory. I am not convinced, however, that this is the way to go. Open houses and the "Stop Motion" (p. 220) method of lesson evaluation also has the potential for sharing with other schools that could be just as valuable.

Chapter 15 delves into the question of what we can we learn from Japanese lesson study. Focusing on planning the "perfect" lesson with colleagues in a risk-free academic environment is a very powerful experience. Sharing their experiences with outside educators makes the learning that much deeper. As the authors assert, "the most important take-home message for us in Japanese lesson study is about the huge disservice that we do to teachers when we deprive them of a professional life. How can we expect teachers to grow and develop if they do not have opportunities to do the kind of work that lesson study allows?" (p. 231)

I look forward to sharing with my preservice mathematics teachers the ideas and experiences of the educators involved in this Japanese lesson study as they strived to develop the "perfect" lesson. This book is derived from Yoshida's doctoral dissertation, but this is one dissertation whose observations won't gather dust on a bookshelf!

Rick Seaman (Rick.Seaman@uregina.ca) is Associate Professor of Mathematics Education at the University of Regina in Regina, SK, Canada.