In this chapter, we review two approaches for understanding these national differences in math abilities. The first approach attempts to link cross-national differences in educational input to cross-national differences in test scores. A tacit assumption of this approach is that children's performance on tests of mathematics is a direct effect of input. The second approach attempts to link cross-national differences in educational input to cross-national differences in test scores by means of indirect effects through more basic cognitive abilities. The assumption of this approach is that the specific educational inputs that differ among nations do not make much difference unless they have an effect on basic cognitive abilities that improve learning for all students. We argue that this approach has two related virtues. Because it is mechanistic, it greatly constrains the search for potential causes. Also, because it is mechanistic, it offers a clearer path to closing the learning gap. We then examine our theory in light of existing cross-national research on math-related cognitive abilities and preview results of a study (under review) that tested our idea. [This is a chapter in: Berch, D. B., Geary, D. C., & Koepke, K. M. (Eds.) "Mathematical Cognition and Learning Book Series (Vol. 4)" (p99-130). Cambridge, MA: Academic Press.]