Ratio, rate, and proportion in Japanese curriculum materials

Ratio, rate, and proportion are arguably the most important topics in the middle grades mathematics curriculum before algebra. The study reported here describes how Japanese mathematics curriculum materials treat these topics. The analyses were conducted on the official curriculum documents published by the Japanese Ministry of Education and one of the most widely used textbook series for Elementary and Lower Secondary School Mathematics. The results of the analyses show that the Japanese curriculum introduces and develops these topics across multiple grade levels as expected for such complex topics. However, the initial definition of a proportional relationship appears before students formally study ratios. Moreover, the Japanese materials emphasize solving missing-value proportion problems by using the definition of proportional relationships, rather than setting up a proportion equation with a missing value in the equation of the form [Formula: see text] where A, B, and D are given, and x is the unknown quantity. These and other aspects of how the Japanese curriculum materials approach these topics might be of interest to audiences outside of Japan.