Recent decades have seen a rapid acceleration in global participation in formal education, due to worldwide initiatives aimed to provide school access to all children. Research in high income countries has shown that school quality indicators have a significant, positive impact on numeracy and literacy--skills required to participate in the increasingly globalized economy. Schools vary enormously in kind, resources, and teacher training around the world, however, and the validity of using diverse school quality measures in populations with diverse educational profiles remains unclear. First, we assessed whether children's numeracy and literacy performance across populations improves with age, as evidence of general school-related learning effects. Next, we examined whether several school quality measures related to classroom experience and composition, and to educational resources, were correlated with one another. Finally, we examined whether they were associated with children's (4-12-year-olds, N = 889) numeracy and literacy performance in 10 culturally and geographically diverse populations which vary in historical engagement with formal schooling. Across populations, age was a strong positive predictor of academic achievement. Measures related to classroom experience and composition were correlated with one another, as were measures of access to educational resources and classroom experience and composition. The number of teachers per class and access to writing materials were key predictors of numeracy and literacy, while the number of students per classroom, often linked to academic achievement, was not. We discuss these results in the context of maximising children's learning environments and highlight study limitations to motivate future research.