Productive struggle is crucial to students' mathematics learning. However, it has proven difficult for teachers to sustain struggle when it is productive or make it so when it is not. Studies show that teachers may offer students support when their struggles are productive or even refrain from offering support when students' struggles are…

We report a novel survey that narrows the gap between information about teachers' knowledge of fraction arithmetic provided, on the one hand, by measures practical to administer at scale and, on the other, by close analysis of moment-to-moment cognition. In particular, the survey measured components that would support reasoning directly with…

Interpreting findings from the numerous research studies that identify meta-variables linked with attitudes toward mathematics and their connections to achievement is complicated by the lack of theoretical clarity around the construct of attitudes. This mixed-methods multiple-case phenomenological study expands the body of research that describes…