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.
POSING 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.
SEARCHING FOR SOLUTIONS
According to the research team, the videotapes revealed major international differences in:
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.
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.
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.
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.
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."
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.
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.
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.
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.
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.
EVALUATING SOLUTIONS
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."
SHARING SOLUTIONS
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."
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?