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Math Education in the U.S., Germany, and Japan: What Can We Learn from This?

A recent study compared the videotaped teaching styles of 81 eighth-grade math teachers in the U.S. with those of teachers in Germany and Japan. What did educators learn from the study?

An April 27 Education World article (Math Wars!) reported that U.S. eighth graders scored below average in math on The Third International Mathematics and Science Study (TIMSS). In the study, the most comprehensive international comparison of math and science achievement levels ever attempted, U.S. math students were outperformed by students in the countries of some of our closest economic allies -- and major economic rivals. Many people -- including parents, politicians, educators, and business leaders -- wanted to know why. The results of another component of TIMSS have been released -- and they may help answer the question.


In a cross-cultural study of educational philosophy and teaching style, researchers at the University of California (Los Angeles) compared the instructional methods of 8th grade math teachers in the U.S. with those of teachers in the countries of two of its most important economic competitors -- Germany and Japan. The study had among its goals to:

  • learn how 8th grade mathematics is taught in the United States, Germany, and Japan.
  • develop objective measures for evaluating classroom instruction.
  • determine how teaching methods in the three countries conform with current U.S. reform recommendations.
  • determine U.S. teachers' perceptions of current reform recommendations.

To accomplish those goals, the UCLA researchers videotaped 231 eighth grade math lessons -- 100 in Germany, 50 in Japan, and 81 in the United States -- as they were being taught. The researchers then spent months viewing, analyzing, and discussing those lessons. The results of The TIMSS Videotape Classroom Study revealed striking differences in the teaching styles and educational focus of math teachers in the United States and of their German and Japanese counterparts.


According to the research team, the videotapes revealed major international differences in:

  1. Lesson goals--German and U.S. teachers stressed the development of problem-solving skills, while Japanese teachers stressed students' understanding of underlying concepts. More than 60 percent of U.S. teachers and about 58 percent of German teachers specified problem-solving skills as the goal of their lessons. More than 90 percent of Japanese teachers emphasized conceptual understanding over problem-solving ability.

  2. Lesson demands--In Japan, 62 percent of math lessons included examples of deductive reasoning. Only 21 percent of German lessons and 0 percent of U.S. lessons required deductive reasoning. Deductive reasoning is defined as the reasoning needed to draw logical conclusions from premises.

  3. Lesson difficulty--Topics covered in U.S. 8th grade classrooms were judged to be at a 7th grade level according to international standards. Topics covered in Germany were at an 8th grade level and topics taught in Japan were determined to be at a 9th grade level.

  4. Lesson focus--Math lessons in Japan appeared more specific and coherent than U.S. math lessons. In Japan, lessons focused tightly on a single mathematical concept and teachers provided clear connections between different parts of the lesson. U.S. math lessons contained significantly more topics than Japanese math lessons; U.S. teachers switched from one topic to another with greater frequency; and U.S. teachers were less likely to provide explicit links between topics.

  5. Lesson content--In the United States and Germany, about 90 percent of student seatwork involved practicing routine procedures. In Japan, 41 percent of working time was spent on routine practice and nearly half the time was spent "inventing new solutions and engaging in conceptual thinking."

  6. Lesson organization--U.S. and German math lessons generally had two separate steps or phases. The first was the acquisition phase, in which the teacher demonstrated how to solve a problem. That was followed by the application phase, in which students practiced solving sample problems while the teacher helped individual students. In Japanese lessons, the procedure was reversed. Students began by solving a problem on their own, using information learned in previous lessons. They then shared their solutions and methods with one another and worked together to develop an understanding of the underlying concept.

  7. Lesson development--In U.S. lessons, mathematical concepts and procedures were usually stated by the teacher. In German and Japanese lessons, concepts were generally developed through examples, demonstrations, and discussion.

  8. Lesson inviolability--U.S. lessons were more likely to be interrupted by announcements and visitors than were Japanese or German lessons. Twenty-eight percent of the U.S. lessons were interrupted by outside events, compared to 13 percent of the German lessons and 0 percent of the Japanese lessons.

  9. Reform implementation--In areas such as individual problem-solving, generating alternative solutions, and articulating conceptual understanding, Japanese teachers appeared more in line with the spirit of reform advocated in the U.S. than did U.S. teachers. Although most of the U.S. teachers believed their methods were consistent with reform recommendations, many still emphasized the "acquisition and application of skills" over conceptual understanding.

  10. Achievement level--Japanese students scored among the highest in the world on the TIMSS. U.S. and German students scored about, or a little below, average.


James W. Stigler, the UCLA psychology professor who directed the TIMSS classroom study, warns against drawing simple conclusions from these observations, however. In an article in Phi Delta Kappan, Understanding and Improving Classroom Mathematics Instruction: An Overview of the TIMSS Video Study, Dr. Stigler and co-author James Hiebert stress that teaching is a cultural activity that affects, and is affected by, a variety of social, economic, and political forces. One culture's educational system, however successful, can rarely be successfully imported into another culture, they say.

What we should learn from the Japanese educational system is not their style of teaching, but their approach to improving education through professional development. Japanese teachers, the authors point out, continuously participate in a formal process of collaboration and cooperation geared toward the refinement of individual lessons and the cumulative improvement of the educational process. No such organized approach to professional development exists in the U.S. "Our biggest long-term problem," the article states, "is not how we teach now but that we have no way of getting better."

As Dr. Stigler told Education World, U.S. educators focus too much on the teacher and not enough on the teaching. "We strive," he said, "to find the exemplary teacher when the real key is to improve the teaching of the average teacher." Dr. Stigler adds, "In this country, we need to develop a mechanism to improve teaching incrementally over time and we need to find a way to professionalize teaching by making professional development a part of every teacher's work week."


The TIMSS Video Classroom Study has resulted in a number of recommendations intended to improve math instruction in this country by fostering opportunities for professional development. They include

  • ensuring that teachers have a clear understanding of the spirit of recommended math reforms;
  • providing beginning teachers with more concrete guidance and direction;
  • assigning teachers lighter instructional loads; and
  • providing teachers with opportunities to interact, discuss, share, and develop ideas and procedures for effective teaching.

For teachers themselves, however, perhaps the most useful result of the study is the availability of the TIMSS videotapes. These concrete instructional models provide teachers with the opportunity to view, assess, and compare alternative methods of teaching; to become aware of elements of their own teaching that may have become automatic and unquestioned; and to develop ways of improving the level of teaching in their own classrooms.

According to Dr. Stigler, "Efforts to improve student learning succeed or fail inside the classroom....We must study directly the processes that lead to learning in the classroom, for if we do not understand these processes, we will have little chance of improving them."

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Article by Linda Starr
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