Theoretical and methodological challenges in measuring instructional quality in mathematics education using classroom observations

In this article, we analyze theoretical as well as methodological challenges in measuring instructional quality in mathematics classrooms by examining standardized observational instruments. At the beginning, we describe the results of a systematic literature review for determining subject-specific aspects measured in recent lesson studies in mathematics education. The main results are that there is little or no consistency in the conceptualization and nomination of subject-specific aspects. We therefore structured these different aspects along two perspectives, a mathematical perspective on mathematics educational quality of instruction as well as a pedagogical perspective. Furthermore, referring to the usage of these observational instruments in the field, in this paper we inquire into methodological challenges in measuring instructional quality in mathematics classrooms, e.g., the optimal number of raters and lessons to be observed. The results are twofold: on the one hand, there are recent studies that provide a useful answer to these questions. On the other hand, these results appear to be specific to the given data. Therefore, this problem seems to be unsolved so far. © 2016, FIZ Karlsruhe.