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Mary E. Brenner, Sally Herman, Hsiu-Zu Ho and Jules M. Zimmer

Flexible use of multiple representations has been described as a 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.

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Hsiu-Zu Ho, Deniz Senturk, Amy G. Lam, Jules M. Zimmer, Sehee Hong, Yukari Okamoto, Sou-Yung Chiu, Yasuo Nakazawa and Chang-Pei Wang

In this study we focus on math anxiety, comparing its dimensions, levels, and relationship with mathematics achievement across samples of 6th-grade students from China, Taiwan, and the United States. The results of confirmatory factor analyses supported the theoretical distinction between affective and cognitive dimensions of math anxiety in all 3 national samples. The analyses of structural equation models provided evidence for the differential predictive validity of the 2 dimensions of math anxiety. Specifically, across the 3 national samples, the affective factor of math anxiety was significantly related to mathematics achievement in the negative direction. Gender by nation interactions were also found to be significant for both affective and cognitive math anxiety.