U.S. students, on average, score lower than Japanese students in math. In particular, U.S. students perform significantly worse than Japanese student in math problem solving. Previous studies have shown that Japanese schools tend to emphasize the process of problem solving and spend twice as many hours per week on mathematics. U.S. schools tend to emphasize the mastery of facts and procedures for computing the correct answer.
Instruction in most math classes relies heavily on textbooks. Therefore, in their effort to explain differences in math performance between Japanese and U.S. students, Richard E. Mayer and Valerie Sims, University of California/Santa Barbara, and Hidetsuga Tajika, Aichi University, Japan, compared textbooks used in the two countries. Specifically, they compared lessons on adding and subtracting positive and negative whole numbers in three Japanese and four U.S. seventh-grade textbooks.
Significant differences were apparent. Japanese textbooks were less than half as long as the U.S. texts (200 pages versus 475 pages) and better integrated. They averaged only seven chapters, each divided into two or three coherent sections. U.S. texts contained an average of 12 chapters that often included a dozen loosely related topics. U.S. lessons on addition and subtraction of positive and negative whole numbers were presented in short fragments within several diverse chapters throughout the text; the Japanese text covered them in depth in one section.
Japanese texts devote more space to problem-solving
These researchers discovered that Japanese texts devote significantly more space to problem solving — 81 percent compared to 36 percent in U.S. texts. The Japanese texts integrated words, symbols and pictures to demonstrate how to solve problems. Explanations were organized inductively, beginning with a familiar, everyday situation and ending with a formal statement of the solution rule. Only one of the four U.S. texts used a similar instructional method (Invitation to Mathematics, Bolster et al., Scott, Foresman & Co.).
The instructional lesson in Japanese texts is much longer, and relevant illustrations are more common. Of the 81 percent of the page space that is devoted to problem-solving explanation in Japan, 63 percent is devoted to worked-out problems and 18 percent to their corresponding illustrations.
In U.S. texts, only 36 percent of the space is given over to explaining problem solving, 25 percent of which is worked-out problems and 11 percent illustrations. U.S. texts also devote 19 percent of their space to interest-grabbing illustrations not relevant to the lesson. Irrelevant illustrations are nonexistent in Japanese tests.
Japanese texts emphasize the coordination of multiple representations of a problem. All three Japanese texts built connections among verbal, symbolic and pictorial representations for each step in solving a problem. Each lesson used at least two worked-out problems, beginning with a familiar analogy and ending with a general principle.
These researchers believe that textbooks serve as a sort of de facto national curriculum in mathematics. This comparison of U.S. and Japanese texts illustrates the differences in instruction we provide our respective students.
Mayer et al. conclude that the coherent, in-depth coverage of problem solving in Japanese texts, integrating symbolic, verbal and pictorial representations, is at least partly responsible for that country’s outstanding performance in mathematics. They suggest that improvement of U.S. textbooks would lead to improved performance by U.S. students.
“A Comparison of How Textbooks Teach Mathematical Problem Solving in Japan and the United States”, American Educational Research Journal, Volume 32, Number 2, Summer 1995, pp. 443-461.
Published in ERN September/October 1995 Volume 8 Number 4