In the Trends in Mathematics and Science Study (TIMSS) 2015, the educational systems from the Dutch speaking part of Belgium (Flanders), Germany, and Norway included scales capturing three dimensions of instructional quality (INQUA): classroom management, supportive climate, and cognitive activation. With the inclusion of these extra scales, a unique opportunity was created to investigate the various dimensions of INQUA and their relation to educational outcomes. In this study, multilevel structural equational modelling analyses are conducted to answer three research questions: (a) 'Do the items reliably measure the three dimensions of INQUA as classroom constructs? And if not, can we build reliable scales with the items, capturing the dimensions of INQUA as classroom constructs?' (b) 'To what extent can INQUA contribute to achievement?', and (c) 'To what extent can INQUA contribute to (social and ethnic) equity?'. Results indicate that INQUA might serve as a catalyst in increasing achievement in education systems. Furthermore, results indicate that INQUA does not relate to equity and consequently that all students benefit from the same educational practices. However, issues in the cross-cultural conceptualization and measurement of INQUA are raised, questioning the extent to which the three well-known dimensions of INQUA (a) are well-defined and might be sufficiently differentiated from each other, (b) sufficiently capture the diverse set of educational practices relating to students' educational outcomes, and (c) can be established across countries in a unified manner. The results of this study give direction to educational practitioners and policy makers in creating and providing effective learning environments.