This paper considers various approaches to classroom observation that combine generic and mathematics content-specific dimensions of instructional quality. Using results from previous research in which three research teams each analysed the same three mathematics lessons (from fourth-grade mathematics classrooms in the USA) using different frameworks, we compare features of the frameworks and assess the extent to which these lead to convergent, divergent or complementary assessments of instructional quality. These findings inform reflections on how a synthesis of existing conceptualisations of instructional quality captures shared aspects of different frameworks but may be differentially useful than individual frameworks depending upon the purposes of observations. Specifically, single frameworks may be particularly useful within specific contexts and for professional development and accountability, but a synthesis of frameworks can foster more coherent cross-cultural understandings of instructional quality. We argue that establishing international networks of scholars can facilitate collaborations aiming to investigate and understand instructional quality.