Japanese Mathematics Education Explained
By Professor Akihiko Takahashi
• The way mathematics is taught in Japan holds the key to the high-level performance of Japanese students, a DePaul University professor explained during a seminar in Chicago on August 29.
• The seminar, “Japanese Mathematics Education, How Japanese Mathematics Instruction Creates High-Performing Students” was hosted by the Japan America Society of Chicago. Akihiko Takahashi, Ph.D. and an Associate Professor at DePaul University in Chicago, was the featured speaker.
• According to international studies, math scores of Japanese elementary and middle school students are consistently high. A recent OECD study shows that not only Japanese students score high in math but gaps among them are much smaller than in the U.S. Why is that?
• Takahashi, who teaches mathematics and mathematics education, shared that there exists a substantial difference between the U.S. and Japan concerning the idea about teaching math. The Japanese approach, he argued, fosters problem-solving and reasoning capabilities, “better exemplifying” the current U.S. reform ideas for math education.
• Between the late 1990s and the early 2000s, the U.S.
Department of Education conducted a video survey, the Third International
Mathematics and Science Study (“TIMSS”), on 8th graders in the U.S., Germany
and Japan to see how mathematics was being taught in each country.
• The Department found that the teaching approach in
the U.S., while it was identical across the nation, was quite different
from the other two countries (The Teaching Gap, by J. Stigler and J. Hiebert,
Disasters of “Well-Taught” Math
• Alan H. Schoenfeld of University of California-Berkeley
argued in his 1988 book, Learning to Think Mathematically, that “well-taught”
students often end up in “disasters,” regarding development of students’
ability on discovery or invention.
• Schoenfeld also argued that students, when failing
to solve a problem, may resort to thinking that “only geniuses are capable
of discovering, creating or really understanding math; I don’t understand
math, but it’s OK.”
Japan’s Shift to Problem Solving
• By the early ‘90s, Japan’s math education “completely
shifted” to teaching the problem solving approach.
• According to the OECD’s 2015 Education Policy Outlook,
Japanese students were among the top performers in reading, math and science.
They weren’t the highest in the most recent study of March 2019, but were
still high enough.
• In the U.S., the survey showed that the proportion
of children from disadvantaged backgrounds achieving at least PISA (the
Program for International Student Assessment) level 2 in mathematics was
40% lower than that of the most advantaged peers.
• According to the 1982 book Thinking Mathematically
by J. Mason, L. Burton and K. Stacey, everybody can think mathematically,
and mathematical thinking can be improved through practice with reflection.
Furthermore, mathematical thinking is supported by an “atmosphere of questioning,
challenging and reflecting.” It can also be provoked by contradiction,
tension and surprise.
• For example, consider a problem like this (see Figure
• Takahashi is critical about U.S. math textbooks that
emphasize answers too much, and how to get the correct answer. He wants
to spend more time on how you “find and appreciate a variety of solutions.”
Once you find them, you can apply them to a new situation.
Three Levels of Math Teaching
• Lastly, Takahashi talked about the three levels in math teaching expertise, quoting from Lesson Study Alliance.
• Level 1 is where the teacher can convey to the students
important basic ideas of mathematics such as facts, concepts, procedures
• Level 2 is where the teacher can explain the meaning
of and logic behind important basic concepts and practices of mathematics
so that a student can understand them.
• It involves calculation with paper and pencil. Why
do teachers spend so much time to teach calculations with paper and pencil,
when we can get the answer easily by using a calculator?
• Finally, Level 3 is the professional level. This is
where the teacher can “provide students with opportunities to understand
basic mathematical contents and develop mathematical practices, and support
student learning so that they become independent learners.”
kihiko Takahashi is an Associate Professor at DePaul
University where he teaches mathematics and mathematics education. Before
coming to the U.S., he was a teacher in Japan and nationally active in
mathematics education reform. He received his Ph.D. from the University
of Illinois at Urbana-Champaign and has published over 80 journal articles
and book chapters in English and Japanese. Professor Takahashi has been
serving as an Honorary Reader of University College London and Specially
Appointed Professor of Tokyo Gakugei University in Tokyo.
Dr. Akihiko Takahashi, Associate Professor at DePaul University, explains Japanese Mathematics Education.