They have workbooks for this purpose. This success comes with practice. It is likely that the kind of mathematics that students learn is related to the nature of the mathematics that they are asked to study. Although constructing proofs and reasoning deductively are important aspects of mathematics, American students lacked opportunities to engage in these kinds of activities. Part of the REAL difference between the U.S. and Japan is the organization of schools.
Teachers concentrate on their subject matter lessons much more.
The focus on the content of the lessons is the subject of the film Polished Stones. This is part of the REAL difference between the U.S. and other countries. There are national standards in both Japan and Singapore. In Japan, these standards are not very detailed, but they really don't need to be because they have a standardized curriculum. This is the case in Japan.