Conference Material

Understanding and Improving Classroom Mathematics Instruction

By James W. Stigler and James Hiebert

Page 2

Beware of Simple Solutions

Given the high mathematics achievement of Japanese students,11 it is tempting to conclude that U.S. teachers should teach more like their Japanese counterparts. Although there are probably many useful ideas for U.S. classrooms in the Japanese videos, we are pessimistic that such ideas can simply be imported. Indeed, if teaching could be changed by just disseminating ideas, the record of reform in the U.S. would be more successful than it is. The data on how teachers view reform, presented above, are quite sobering in this regard.

Besides the ineffectiveness of just disseminating prescriptions, systems of teaching are not easily transported from one culture into another. Teaching, as a cultural activity, fits within a variety of social, economic, and political forces in our society. The effects of teaching are determined, in part, by all of these forces. Thus if one imports a system of teaching into a different culture, one cannot expect that system to produce the same results. The Japanese system of teaching is enmeshed within Japanese culture -- the social and behavioral norms; the expectations and involvement of parents; the national curriculum; outside educational activities such as juku (so-called cram schools); values of education held by students, parents, and the public; and so on. All these factors no doubt play important roles in supporting the kind of teaching we see on the Japanese videotapes.

An additional problem with simple solutions for improving teaching is that they often focus on individual features of teaching, such as using concrete materials, asking higher-order questions, or forming cooperative groups. But teaching is not just a collection of individual features. It is a system composed of tightly connected elements. And the system is rooted in deep-seated beliefs about the nature of the subject, the way students learn, and the role of the teacher. Attempts to change individual features are likely to have little effect on the overall system. The changes often get swallowed up or reshaped.

If we cannot improve teaching by importing another system or by manipulating individual features, what can we do? A recently popular approach is to create content and performance standards and then hold teachers accountable for achieving them. Although we firmly believe that such standards are necessary, a focus on standards and accountability that ignores the processes of teaching and learning in classrooms will not provide the direction that teachers need in their quest to improve.

Another common American approach is to ask experts to meet and discuss the problem and issue written documents to guide a reform. Reforms are needed, presumably, because past policies have failed. The experts decide that we need to break with current practice and try something new. Current documents contain recommendations for such things as how schools should be structured, how market forces should drive improvements, and how technology should change the classroom. This approach, too, is problematic because it assumes that these changes will automatically improve the quality of teaching.

Improving Classroom Teaching

What we need to improve teaching over time is an approach that recognizes that teaching can be studied and improved but at the same time acknowledges the cultural complexity and embeddedness of teaching. How can we break out of our conventional approaches and imagine more productive alternatives? Comparative studies are especially helpful here, and this is where we can learn something from the Japanese.

The approach to improving teaching used in Japan is not based on distributing written reports, or on reforming features of instruction, or on assuming that teaching will change when surrounding elements change. It is based on the direct study of teaching, with the goal of steady improvement in the mathematics learning of students.12

The process of professional teacher development in Japan begins with clearly stated goals for student learning. Japanese mathematics teachers are very familiar with the widely shared goals for student learning at each grade level. The documents that present these goals are similar to the content standards that have received so much attention in the U.S. in recent years. To the extent that American teachers share these goals and understand their meaning and intent, these standards can set the stage for improving teaching. Unfortunately, the reading of the standards documents is often the end of the process in the U.S.; in Japan, becoming familiar with the learning goals is only the beginning.

During their careers, Japanese teachers engage in a relentless, continuous process of improving their lessons to improve students' opportunities to achieve the learning goals. A key part of this process is their participation in "lesson study groups." Small groups of teachers meet regularly, once a week for about an hour, to plan, implement, evaluate, and revise lessons collaboratively. Many groups focus on only a few lessons over the course of the year with the aim of perfecting these.13

A group of fourth-grade teachers, for example, might be dissatisfied with its current lessons on adding fractions with unlike denominators. So this study group sets the goal of replacing these lessons. The group designs several lessons, one group member tries them out while the others observe and evaluate what is effective and what is not, and they revise the lessons. Maybe they change the wording of the opening problem, or maybe they change the kinds of follow-up questions they ask, or maybe they learn more about what methods students are likely to invent and then build these methods into the whole-class discussion. Then they try out the lessons again, perhaps with other teachers observing. This process may go on for several years. When the replacement lessons are ready, they are shared with other teachers, in other schools. Through the lesson study groups, teachers improve their own pedagogy and they improve the curriculum. More than that, they improve the collective practice of teaching as they share their work with others.

The belief that drives these lesson study groups is that students' opportunities to learn will improve with better lessons and that better lessons come through collaborative planning and testing. Japanese teachers assume that this task is so big that every teacher must be involved; the wisdom and experience of all teachers are needed to make progress. Further, they assume that improvement will come through a steady, gradual, cumulative process. As they learn from their experiences and pool their information, they will become more highly skilled teachers who have access to increasingly more effective lessons. By focusing on lessons, the Japanese teacher development system formulates and assesses new ideas in the same context in which these ideas will be applied. In this way, the Japanese lesson study group respects the cultural complexity of teaching, focusing on contexts in which all relevant parts of the system of instruction are naturally incorporated.

The True Profession of Teaching

The Japanese approach to teacher development stands in stark contrast to the American approach. Our biggest long-term problem is not how we teach now but that we have no way of getting better. We have no mechanism built into the teaching profession that allows us to improve gradually over time. We have reports of individual teachers who, through heroic efforts of their own, become unusually effective. But these are individuals, not large numbers of teachers, and, sadder still, we have no way of learning from their experiences. Indeed, we have no way of harvesting the best ideas of the thousands of teachers who work, by themselves, to improve their own teaching.

There are many reasons for the absence of a systemic approach to teacher development in the U.S. For example, Americans hold the notion that good teaching comes through artful and spontaneous interactions with students during lessons. This kind of on-the-fly decision making is made possible by the innate intuitions of "natural" teachers. Such views minimize the importance of planning increasingly effective lessons and lend credence to the folk belief that good teachers are born, not made. If we really believe this, it is no wonder that teacher development is not a high priority. Unfortunately, it is not just one belief, but an entire cluster of beliefs, some of them contradictory, that dampen our commitment to improving teaching. Beliefs about teacher autonomy; about the intractable complexity of teaching, on the one hand, and its common simplicity, on the other; about the unlikelihood that it will ever change, on the one hand, and the persistent optimism of reformers, on the other - all these tenets work against efforts to institute mechanisms for continuous, long-term improvement.

We are not arguing for simply importing the Japanese method of teacher development. Just as the Japanese method of teaching mathematics is embedded in a particular culture, so is the Japanese system of teacher development. However, in both cases, we can study these alternative systems to gain new insights into our own systems, and we can use these insights to challenge the status quo.

We believe that our failure to take teacher development seriously is closely tied to the issue of professionalism. For years, educators have called attention to the relatively low status of teaching and have bemoaned the lack of respect bestowed on teaching by the media and the public. Much rhetoric has been devoted to this issue, as if demanding higher status or labeling teaching a profession would solve the problem. A true profession of teaching will emerge as teachers find ways and are given the opportunities to improve teaching. By improving teaching, we mean a relentless process in which teachers do not just improve their own skills but also contribute to the improvement of Teaching with a capital T. Only when teachers are allowed to see themselves as members of a group, collectively and directly improving their professional practice by improving pedagogy and curricula and by improving students' opportunities to learn, will we be on the road to developing a true profession of teaching. The TIMSS videotape study points us beyond the data, not to a critique of how we currently teach but to a recognition of the need to implement a mechanism whereby we can, over time, improve our teaching.

1. Ronald Gallimore, "Classrooms Are Just Another Cultural Activity," in Deborah L. Speece and Barbara K. Keogh, eds., Research on Classroom Ecologies: Implications for Inclusion of Children with Learning Disabilities (Mahwah, N.J.: Erlbaum, 1996), pp. 229-50; and Roland G. Tharp and Ronald Gallimore, Rousing Minds to Life: Teaching, Learning, and Schooling in Social Context (New York: Cambridge University Press, 1988).

2. A number of researchers have pointed out that teachers teach much in the way they were taught. See, for example, Daniel C. Lortie, Schoolteacher: A Sociological Study (Chicago: University of Chicago Press, 1975); and Sharon F. Nemser, "Learning to Teach," in Lee Shulman and Gary Sykes, eds., Handbook of Teaching and Policy (New York: Longman, 1983), pp. 150-70.

3. A complete description of sampling procedures can be found in James W. Stigler et al., The TIMSS Videotape Classroom Study: Methods and Findings from an Exploratory Research Project on Eighth-Grade Mathematics Instruction in Germany, Japan, and the United States (Washington, D.C.: National Center for Education Statistics, 1997).

4. For a full description of videotaping considerations and procedures, see Stigler et al., op. cit.

5. Professional Standards for Teaching Mathematics (Reston, Va.: National Council of Teachers of Mathematics, 1991).

6. Richard E. Nisbett and Lee Ross, Human Inference: Strategies and Shortcomings of Social Judgment (Englewood Cliffs, N.J.: Prentice-Hall, 1980).

7. For a complete report of the 41-country curriculum analysis, see William H. Schmidt et al., Many Visions, Many Aims: A Cross-National Investigation of Curricular Intentions in School Mathematics (Boston: Kluwer, 1997).

8. The Math Group was led by Alfred Manaster of the University of California, San Diego. Other members of the group were Phillip Emig, Wallace Etterbeek, and Barbara Wells.

9. A videotape with examples from German, Japanese, and U.S. lessons, together with an accompanying study guide, can be obtained by phoning the National Center for Education Statistics at 202/219-1333 or by sending e-mail to timss@ed.gov.

10. Other studies have also shown that reform recommendations are often implemented in superficial ways. See, for example, the case studies of California teachers conducted by researchers from Michigan State University and reported in a special issue of Educational Evaluation and Policy Analysis (Fall 1990).

11. TIMSS achievement results for eighth grade are published in Lois Peak, Pursuing Excellence: A Study of U.S. Eighth-Grade Mathematics and Science Teaching, Learning, Curriculum, and Achievement in International Context (Washington, D.C.: Office of Educational Research and Improvement, U.S. Department of Education, 1996).

12. Our description of the Japanese process of improving teaching comes from our conversations with Japanese educators and a number of written sources, including Nobuo K. Shimahara and Akira Sakai, Learning to Teach in Two Cultures: Japan and the United States (New York: Garland, 1995); and two special issues of the Peabody Journal of Education devoted to Japanese teacher education (Spring and Summer 1993).

13. For more information on lesson study in Japan, see Catherine Lewis and Ineko Tsuchida, "Planned Educational Change in Japan: The Shift to Student-Centered Elementary Science," Journal of Educational Policy, in press.

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    JAMES W. STIGLER is a professor of psychology at the University of California, Los Angeles (e-mail: stigler@psych.ucla.edu). JAMES HIEBERT is a professor of education at the University of Delaware, Newark. The research reported in this article was funded by the National Center for Education Statistics, U.S. Department of Education. The study was conducted in collaboration with Jurgen Baumert and Rainer Lehmann in Germany and Toshio Sawada in Japan. The authors gratefully acknowledge the assistance of Patrick Gonzales, Takako Kawanaka, Steffen Knoll, and Ana Serrano, all of whom functioned as primary researchers on the study, and of Eric Derghazarian, Gundula Huber, Fumiko Ichioka, and Nicole Kersting, among many, many others. The writing of this article was supported, in part, by a grant from the American Federation of Teachers.