Observable mathematical teaching expertise among upper elementary teachers: connections to student experiences and professional learning

Researchers examining elementary teachers’ mathematical teaching expertise—that is, teachers’ knowledge both of mathematics and of how to effectively teach mathematics—have linked such expertise to student outcomes. But, given the increasing use of classroom observations for teacher evaluation in the USA, this study considers whether and how upper elementary teachers’ mathematical teaching expertise is observable in everyday classroom observations. Using classroom observation data collected with the widely used CLASS observation instrument, this study examines relationships among observation data, student outcome data, and data on opportunities for professional learning from 298 upper elementary teachers in four urban school districts in the USA. Using principal components analysis, this study isolates an observable dimension of mathematical teaching expertise. Regression analyses then identify statistically significant relationships among observed mathematical teaching expertise and multiple student outcomes, including mathematics learning and self-efficacy, as well as teacher professional learning through collaboration with mathematics coaches. Our findings inform strategies for observing mathematical teaching expertise, strengthening the practices of upper elementary teachers, and improving student experiences in the upper elementary grades.