Cross-national comparison of representational competence

Flexible use of multiple representations has been described as it key component of competent mathematical thinking and problem solving. In this study, 6th-grade American students are compared to 3 samples of Asian (Chinese, Japanese, and Taiwanese) 6th graders to determine if the well-documented mathematical achievement of students from these Asian nations may be due in part to a greater understanding of mathematical representations. The results show that, among all groups, Chinese students generally scored highest on the representation tasks and, except on items about the visual representations of fractions, all Asian samples scored significantly higher than the American sample. The results are discussed in terms of possible instructional antecedents and textbook differences.