UC San Diego

Students in the U.S. demonstrate a pattern of knowing mathematics as procedures rather than as a discipline of principled reasoning. International studies trace this pattern to cultural regularities within classroom mathematics instruction. Current researchers seeking to understand the expression of mathematics instruction explore dyadic, and sometimes mediational, relationships between teachers' mathematical knowledge for teaching, their beliefs about teaching and learning mathematics, their social interactions, and their interpretations of curricular materials. However, most prior studies have not taken the school, district, or policy context into account as a mediating factor. Using a situative perspective, this study incorporates these factors into a comprehensive exploration of what plays into teachers' mathematics instruction. This study used a combination of quantitative and qualitative methods to gather information about the factors influencing mathematics instruction of seven upper elementary grade teachers in a single school district. It used validated surveys and assessments to measure teachers' knowledge for teaching mathematics and beliefs about teaching and learning mathematics. Observational data were also analyzed using pre-established rubrics to characterize the mathematical quality of teachers' instruction. Additionally, teacher interviews were conducted to uncover teachers' interpretations of policies and triangulate knowledge and beliefs data. The data were analyzed quantitatively and qualitatively using within and cross-case approaches. Analysis of the data revealed that the mathematical quality of the teachers' instruction was determined by dynamic interaction between each teacher's beliefs, knowledge, policy interpretation, and context- specific factors. Teachers' mathematical knowledge for teaching was related to their mathematical explanations and responses to student math productions during instruction. However, the study also found that curricular materials, teachers' interactions with their colleagues, and local policies played a critical role in mediating instructional quality. Knowledge, beliefs, and interpretation of curriculum and accountability policies interacted differently depending on the teachers' social and institutional contexts. Implications for practice are discussed