Generating multiple solutions for a problem: A comparison of the responses of U.S. and Japanese students

A task involving simple mathematics, yet complex in its call for the generation of multiple solution methods, was administered to about 150 U.S. students, most of whom were in fourth grade. Written responses were examined for correctness, evidence of strategy use and mode of explanation. Results for the U.S. sample were also compared to those obtained from about 200 Japanese fourth-grade students. Students in both countries (a) produced multiple solutions and explanations of their solutions, (b) exhibited almost identical patterns and frequency of strategy use across response occasions, and (c) used the same kinds of explanations, with a majority of the responses involving solution explanations that combined both visual and verbal/symbolic features. Nevertheless, Japanese students tended to produce explanations involving more sophisticated mathematical ideas (multiplication rather than addition) and formalisms (mathematical expressions rather than verbal explanations) than did U.S. students.