In a secondary analysis of the data base of the IEA second mathematics study, the association of school and instructional characteristics with mathematics achievement within and across 17 countries at the school and student level was investigated. The results indicate consistent positive associations of the factors ‘high expectations of pupils' progress’ and ‘opportunity to learn’ with achievement. Other factors, known from the literature on school and instructional effectiveness, showed more moderate and less consistent effects. The results of this study further indicate that, in each country, considerably more variance in pupils' mathematics achievement lies between classes than between schools when school and class are treated as independent variance components. It was established that specific variables defined at the class level explain more variance than specific variables defined at the school leve