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The present paper offers an exploration of the role achievement values play in the generation of mathematical achievement as measured in school grades and test scores. Based on a comparative study of 1665 German, Israeli, and Canadian 14-year-olds two hypotheses are tested. First, it is assumed that achievement value preferences have a dual role in the generation of high academic performance. On the one hand, they are assumed to facilitate a high achievement-related self-esteem, which itself is a strong covariate of good academic performance. On the other hand, they are expected to sensitize for achievement pressure from parents, which in turn increases anxiety, and henceforth lowers the achievement-related self-esteem. Secondly, it is assumed that one will find cross-cultural variation in the strength of the two postulated effects. The "positive" role of achievement values is assumed to be stronger in cultures with a more positive view on achievement (Canada, Israel), whereas the "negative" role is assumed to be stronger in cultures with a less positive view on achievement (Germany). Hypotheses were tested in a structural equation modeling frame, and are essentially confirmed. Effect sizes are, however, low, and confirmation pertains almost exclusively to grades, not to test scores as measures of mathematical abilities. [ABSTRACT FROM AUTHOR]