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Describing and measuring instructional quality of mathematics lessons is a common goal amongst mathematics education researchers. Such work takes several forms such as classifying and coding instructional moves and student activity or providing high-level rubric-based scores in relation to categories. In this work, we share an innovative mixed methods approach to analyzing lesson data that includes both a time-based classification of instruction and an overall scoring component. Using the Math Habits framework, our project team analyzed a set of 97 fourth-eighth grade mathematics lessons including overall scores. From this qualitative analysis, we developed quantitative models to predict overall scores and better understand the ways that individual codes do or do not contribute to overall lesson score characterizations. 

Abstract In this paper, we network five frameworks (cognitive demand, lesson cohesion, cognitive engagement, collective argumentation, and student contribution) for an analytic approach that allows us to present a more holistic picture of classrooms which engage students in justifying. We network these frameworks around the edges of the instructional triangle as a means to coordinate them to illustrate the observable relationships among teacher, students(s), and content. We illustrate the potential of integrating these frameworks via analysis of two lessons that, while sharing surface level similarities, are profoundly different when considering the complexities of a classroom focused on justifying. We found that this integrated comparison across all dimensions (rather than focusing on just one or two) was a useful way to compare lessons with respect to a classroom culture that is characterized by students engaging in justifying. 

Centering class discussions around student mathematical thinking has been identified as one of the critical components of teaching that engages students in justifying and generalizing. This report shares analysis from a larger project aimed at describing and quantifying student and teacher components of productive classrooms at a fine-grain level. We share results from this analysis of 39 mathematics lessons with a focus working with public records of students’ mathematical thinking.