Japanese methods of teaching mathematics have been intensively studied in the United States since the Third International Mathematics and Science Study (TIMSS) revealed that Japanese students score significantly higher than students in the United States at both fourth and eighth grades. John Woodward, University of Puget Sound, and Ymiko Ono, Naruto University of Education, summarize Japanese methods for teaching mathematics and describe how the educational system addresses student diversity. There have been contradictory accounts of Japanese education. Woodward and Ono draw on a range of research conducted by both American and Japanese researchers to clarify Japan’s math curricula and its approach to teaching students at different skill levels.
U.S. mathematics texts typically present a great number of topics superficially and repeat the same topics over several grade levels with only minor increases in the difficulty of the concepts. In contrast, Japanese math texts follow strict guidelines established by the Ministry of Education and contain far fewer topics. Each grade level provides greater depth on a topic. Once students reach 6th grade in Japan, the number of topics covered per year decreases greatly. By seventh grade Japanese texts cover less than half as many topics as U.S. texts. By grade 8, Japanese curricula have moved students into relatively complex mathematics while U.S. curricula still emphasizes arithmetic. Japanese texts are slim volumes with few practice problems. It is assumed that well-established pedagogical practices will compensate for what is not presented in the text.
The TIMSS data shows that by eighth grade almost half of U.S. students were in schools that offered them three or more diff e rent math classes, while 99 percent of Japanese eighth-grade students were taught the same curriculum.
TIMSS reveals that teachers throughout the world tend to use a common set of teaching practices. They review previous lessons, go over homework, provide instruction on new concepts, have students work on exercises, and allow time for homework. But the major difference between Japan and the United States is the amount of time set aside for each activity. U.S. teachers, especially at the secondary level, spend more time going over homework and allow more time for homework in class. They spend less time explaining new concepts and allocate far less time for students to work on interactive classroom activities or thought-provoking problems.
Studies of Japanese elementary mathematics teaching describe carefully implemented practices that are passed on from experienced to novice teachers t h rough extensive apprenticeships. Math lessons begin slowly and build methodically in an attempt to engage students in a challenging problem. Japanese teachers place a much greater emphasis on thinking about the problem than on quickly coming up with a solution. Students are directed to work in small groups on one or two problems. At the elementary level, students use mathematics kits that contain visual aids and manipulatives. These are considered important elements in re p resenting and discussing mathematical solutions. Japanese students are four times more likely than U.S. students to work on exercises or challenging problems for 15 minutes or more each class. Japanese teachers interrupt small-group work to discuss diff e rent groups’ solutions to problems. They examine and extend a group’s solution regardless of its correctness. In contrast, U.S. teachers are reluctant to present errors or incorrect thinking as the basis for class discussion. Japanese teachers move back and forth from whole-class to group work, using whole-class discussions to raise questions and re v e a l inconsistencies. Japanese teachers are three times more likely than U.S. teachers to discuss alternative perspectives on a problem. Japanese teachers give feedback during seatwork. U.S. teachers tend to allow students to do seatwork or homework for an extended period at the end of the lesson, with much less interactive instructional time.
Research has revealed no major differences in cognitive abilities between U.S. and Japanese students. In Japan as well as in the United States, there is a wide range of performance on the TIMSS at the fourth- and eighth-grade levels. However, the Japanese levels of performance are significantly higher. Japanese classes are often much larger than U.S. classes and provide few formal programs for low-achieving students or students with learning disabilities. Slightly more than 1 percent of school-age Japanese children are in special education. However, a report by the National Institute of Special Education indicated that 10 percent of fifth- and sixth-grade students were two or more years behind in mathematics. This disparity in performance is one of the reasons given by teachers who reported having difficulty controlling their classrooms and conducting lessons effectively.
Woodward and Ono looked at several factors they believe reveal how Japan manages academic diversity. Japan has one of the most highly developed preschool systems in the world. Seventy percent of all children attend preschool for three years. Young children are gradually trained in important school-related behavior, practicing routines that will be used throughout elementary school. Teachers delegate authority to children , and young students learn to work with others and identify with the group. Everyone is expected to participate in activities and discussions. Groups are composed of students with diverse abilities. Teachers see great benefit in mixing slow learners with faster learners. Low-achieving children learn by listening to more capable peers, and fast learners benefit from explaining their mathematical thinking to others.
Two traits pervade the culture and are taught by both parents and teachers: effort and persistence. In a study of a puzzle-like game with a series of increasingly difficult stages, Japanese students persisted significantly longer than U.S. students. Researchers in a previous study saw the emphasis on effort that permeates Japanese education as one of the reasons that academically low-achieving Japanese students do better in school than their U.S. peers. Students are encouraged to put in extra effort to keep up, and Japanese teachers in that study were three times more likely than U.S. teachers to work with struggling students outside of class.
Education changes significantly in Japan during middle school. Instruction intensifies, and an increasing number of tests assess mastery of content, leading up to the high school entrance test given in eighth grade. Enrollment in after-school tutoring programs increases. These programs provide the remedial assistance and individualized instruction not found in Japanese schools. The three years of high school are not mandatory, but 97 percent of students attend high school and between 91 and 99 percent graduate. Struggling students can attend three alternative types of high school: evening, correspondence or special-education high schools. However, less than 5 percent of students attend an alternative school.
Trial efforts to serve students with learning disabilities began in 1990 in Japan. Current educational reform in Japan is focused on individual differences. A method called Suido appears to be effective for students struggling in mathematics. Similar to the national curricula, the Suido method focuses on the relationship between mental and written calculations; between the concept of number and the four basic operations; and the principles that should guide the calculation system. This method uses tiles to make quantities explicit. By working with tiles, children associate quantity with place value and written symbols. Once students have been shown the interrelationship between the tiles, place value, and the written symbol, they can be shown each operation on the number. The Suido method underscores the importance of teaching the four operations separately and demonstrates that tiles can be an effective mechanism for showing basic concepts such as uniting, taking away, and distributing. There is a significant emphasis on visual representations and on the careful analysis of mathematical problems. Unlike the strong emphasis on procedural fluency in arithmetic found in U.S. curricula for students with learning disabilities, in Japan significant attention is given to important concepts such as place value.
“Mathematics and Academic Diversity in Japan”, Journal of Learning Disabilities, Volume 37, Number 1, February 2004, pp. 74-82.
Published in ERN March 2004 Volume 17 Number 3