Understanding Mathematics Classroom Instruction Through Students and Teachers

High quality instruction is necessary for students of all ages to develop a deep understanding of mathematics. Value-added models, a common approach used to describe teachers and classroom practices, are defined by the student standardized achievement gains teachers elicit. They may, however, fail to account for the complexity of mathematics instruction as it actually occurs in the classroom. To truly understand both a teacher’s impact on his/her students and how best to improve student learning, a richer picture of the classroom experience than can be provided from test scores is required. This dissertation considers broader conceptualizations of classroom practices to understand effective mathematics instruction. The first study aims to characterize instructional practices in terms of patterns of practices and examines the correlations among teachers’ ratings of instructional practices across the four time points of observed instruction. Findings from this study indicate that observed instructional practices are highly variable during the academic year. The second study uses patterns obtained in the first study and relates them to classroom level achievement gains using both a domain-general and a domain-specific observation protocol. Findings from this study suggest that a domain-general observation protocol is better at explaining variance in classroom-level achievement gains. The third study tests whether student perceptions of the classroom environment are a mechanism to explain the association between observed instructional practices. I find that different aspects of observed instruction related to different aspects of student perceptions and that these perceptions explained the association between observed instruction and student outcomes. Despite the identification of certain best practices in mathematics instruction, researchers and policymakers fail to understand how several aspects of mathematics instruction work together to yield gains in student achievement. Combining instructional practices and situating them within a classroom context allows researchers, practitioners, and policymakers to gain a better understanding of the complex phenomena surrounding classroom instruction