International studies of mathematics achievement have revealed important cross-national differences. In this research, we focus on the mathematical problem-solving processes of students in Japan and the United States who have achieved equivalent levels of computational skill. Fifth-grade students in Japan and the United States took a 15-item test of mathematics achievement (covering basic arithmetic computation) and either an 18-item test of mathematical problem solving (covering analysis of word problems) or a 5-item test of non-routine problem solving (covering systematic testing of hypotheses about number sequences). As expected, students from Japan were more likely to attain high scores in mathematics achievement than students in the United States. However, when U.S. students were compared to Japanese students who scored at the same level of mathematics achievement, the U.S. students tended to perform significantly better than Japanese students on tests of problem-solving processes. The results are consistent with two aspects of the exposure hypothesis, concerning differences in overall amount and relative focus of instruction in Japan and the United States.

Key words: mathematical problem-solving processes, fifth graders, Japan, the United States, cross-cultural comparison