Does teacher quality differ within and between countries, and how are measures of teacher quality related to instructional alignment and instructional time in mathematics? Fourth-grade classroom data from the IEA's Trends in Mathematics and Science Study (TIMSS) 2015 revealed that although measures of teacher quality were only weakly related to one another, countries with more variation along one dimension (for example, experience) also have high variation along other dimensions (such as education, or readiness to teach math topics). Measures of teacher quality were not strong or consistent predictors of instructional alignment or time, suggesting that primary school teachers' preparation to teach mathematics may have limited influence on classroom opportunity to learn. Crucially, in many countries, disadvantaged students have (by some measures) higher quality teachers. Teacher collaboration and school expectations of instructional behavior merit further research, and the influence of principals and other teachers may have strong impact on educational outcomes. Policymakers should focus their efforts on improving their systems of teacher preparation.