As the authors say in their preface, "this book is about teaching and how to improve it" (p. ix). Their suggestions for improvement arise from their involvement in the Third International Mathematics, and Science Study usually referred to as TIMSS. TIMSS included students from 41 countries and compared their mathematics and science achievement. One component of TIMSS was a video study of eighth-grade mathematics teaching in three countries: Germany, Japan, and the United States. Teachers were videotaped teaching in their classrooms and these videotapes were analyzed to reveal a national profile of mathematics teaching practices. The authors discovered considerable homogeneity of teaching methods within each culture and significant differences in methods between cultures.
However, the teaching gap the authors describe "refers to more than cross-cultural teaching differences. It refers to the difference between the kinds of teaching needed to achieve the educational dreams of the American people and the kind of teaching found in most American schools" (p. x). The videotapes revealed that American teachers were very good at implementing American teaching methods. It is the methods themselves that are limited. Since other countries are continually improving their teaching methods and the United States has no mechanism in place to improve teaching, this teaching gap becomes even more pronounced. They conclude that the teaching gap will grow unless a mechanism for improving teaching practices is put in place. They argue that the involvement of teachers, with support from the stakeholders in education, is vital if we want to improve classroom teaching in the United States and close this gap. The goal of improving the quality of teaching must be our top priority.
In chapter two the authors review the goals of the TIMSS video study and their research methods for studying the videotapes from Germany, Japan and the United States. They describe how the data were collected in each country, claim that the sample "met the highest standards in statistical methodology" (p. 19), and describe the process of coding the data in the videos. This process yielded a profile of teaching in each country and how often certain characteristics of teaching occurred in each country.
In chapter three, the authors look at the details of typical lessons that the authors believe are fair representations of teaching in each country. The simplified images from Germany, Japan, and the United States were "developing advanced procedures", "structured problem solving", and "learning terms and practicing procedures" respectively. They concluded that teaching was a cultural activity and that if we are going to improve it we must recognize that, as such, it will be resistant to change. Furthermore, when change does happen it tends to be superficial. It will take time, but teachers must get out of their cubicles of isolation and begin to generate and share their knowledge about teaching.
In chapter four they discuss the advantage of comparing activities between the three countries to make obvious what would not be obvious if they simply investigated activities in, for instance, only the United States. American students, for example, encounter less challenging mathematics presented in a less coherent way and have to work a lot harder to make sense of it than their German and Japanese counterparts. In Japan, the teacher and the students share the mathematical work in contrast to the other two countries where students follow the teacher's lead.
Chapter five explains how lessons in the three countries can be described by a common pattern. These national patterns of teaching stem from the knowledge base of teachers who plan and implement lessons. This knowledge base might originate from teacher-training programs or from fourteen years of cultural preparation in the classroom. The authors, along with many researchers, lean towards the latter, claiming that teaching is a cultural activity that one learns to do more by being part of a culture (i.e., by being taught) than by formal training.
In chapter six, the authors focus "on Japan and the United States because this comparison is the most dramatic, and therefore illustrates well the role that beliefs can play in generating and maintaining cultural scripts [mental versions of teaching patterns] for teaching" (p. 88). For example, teaching in the U.S. is consistent with the belief that school mathematics is a mastery over a set of procedures, whereas Japanese lessons are developed from the perspective that mathematics is a set of relationships between concepts, facts and procedures. These beliefs have implications. Teachers in the U.S. try to minimize confusion by demonstrating every detail of solving a problem with their students attending to each step. As a result, they use the overhead in their classrooms more than their Japanese counterparts. Their lessons are more modular with few connections between them. Japanese teachers choose challenging problems to begin a lesson, and help students understand and represent the problem. Their role is to monitor solution methods, lead class discussion comparing and contrasting solution methods, and giving their own solutions. They prefer to use the chalkboard so that the students can see the connections between different pieces of the lesson at any time. The authors conclude the chapter stating that for change in teaching to occur efforts must be appropriate for changing a cultural activity. We must become aware of the cultural scripts that teachers are employing for "no matter how good teachers are, they will be only as effective as the script they are using. To improve teaching over the long run, we must improve the script" (p. 101).
Chapter seven looks at Japan's approach to improving teaching through explicit learning goals for students, a shared curriculum, administrative support, and teachers making gradual improvement in their practice. The Japanese system not only mentors and trains teachers, but also encourages teachers to function as researchers-in-context who develop and test new teaching techniques. The authors assert that instead of copying these ideas we must empower teachers to be leaders in supplying ideas to the research and development system in order to improve classroom teaching.
In chapter eight six principles are proposed for building such a system. The reader will enjoy reading how these principles apply to their own teaching situation and the impact they might have on the conventional methods of teacher development. Lesson study, they believe, is consistent with these principles. Thus, the authors propose a program based on the process of lesson study and three initiatives to help create a culture that would support the teacher-initiated improvement process. Of particular interest is the third initiative, where it is suggested that schools be restructured as 'places where teachers can learn'.
Chapter nine deals with how teachers would use their time in such a context. The authors admit that the Japanese model may have to be altered to work in the U.S. but they "believe it is better to start with an explicit model, even if it needs revisiting, than with no model at all" (p.150). The authors assert that lesson study is an ideal context for both teacher development and improving teaching. In order for lesson study to improve teaching, however, it must meet the needs of teachers and the educational system. The authors close the chapter by discussing how to establish the lesson study process and how to build an infrastructure for sharing professional knowledge. This accumulation of professional knowledge, a mechanism for developing new knowledge, and a sincere desire by teachers to improve their practice could lead, they believe, to society acknowledging teachers as professionals. They acknowledge that such a plan should start small, one district at a time, and may take many years.
The book is an easy read that stimulates the mind as to how we can improve teaching. The authors suggest that we try on a small scale to modify the teaching day and to make teaching improvement the work of teachers (initially with help from outside consultants).
The book is a must read for those responsible for the professional development of teachers. The book is also important for those in charge of faculty who teach undergraduate university mathematics classes. The model proposed here might help faculty solve some of the pedagogical problems that occur in these classrooms before they happen. As a secondary mathematics-education professor, I am following the book's lead and having my pre-service mathematics majors and minors engage in collaborative lesson-study experiences. I am eagerly awaiting the results.
There is a large web site devoted to The Teaching Gap. Among other things, it contains the full text of the first chapter and a discussion forum where visitors can interact with others who have read the book.