•Cognitive activation is positively related to mathematics performance.•A positive disciplinary climate favours cognitive activation.•Teacher directed instruction is positively related to mathematics performance.•But high levels of directed instruction are negative for student performance. Modern educational theories emphasise effectiveness enhancing factors at the classroom level and differential effectiveness for sub-groups of students and across different learning contexts. Theoretical developments, however, are generally based on national evidence and have been criticised for lacking cross-cultural perspectives. This study used PISA 2012 data to examine how subject-specific teaching strategies related to mathematics performance of students across education systems whilst considering curvilinear associations and interactions with the socio-economic and instructional context. The results provide consistent evidence of a positive curvilinear relationship between cognitive activation strategies and mathematics performance. The association tends to be stronger in schools with a positive disciplinary climate and for students from advantaged socio-economic backgrounds, but not in every education system. Teacher-directed strategies are positively related to mathematics performance, but the association tends to become negative for high levels of teacher-directed instruction. Associations of student-oriented strategies with mathematics performance are inconsistent. The cross-national evidence contributes to the knowledge base of educational theory.