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This study explores the relationship between teacher knowledge and student learning in the area of mathematics by developing and evaluating an innovative approach to assessing teacher knowledge. This approach is based on teachers’ analyses of classroom video clips. Teachers watched 13 video clips of classroom instruction and then provided written comments on the interactions of the teacher, students, and content. The quality of teachers’ analyses, coded using an objective rubric, are shown to be reliable and valid, relating both to another widely used measure of teacher knowledge and to teachers’ own students’ learning (from pre- to posttest).

Responding to the scarcity of suitable measures of teacher knowledge, this article reports on a novel assessment approach to measuring teacher knowledge of teaching mathematics. The new approach uses teachers' ability to analyze teaching as a proxy for their teaching knowledge. Video clips of classroom instruction, which respondents were asked to analyze in writing, were used as item prompts. Teacher responses were scored along four dimensions: mathematical content, student thinking, alternative teaching strategies, and overall quality of interpretation. A prototype assessment was developed and its reliability and validity were examined. Respondents' scores were found to be reliable. Positive, moderate correlations between teachers' scores on the video-analysis assessment, a criterion measure of mathematical content knowledge for teaching, and expert ratings provide initial evidence for the criterion-related validity of the video-analysis assessment. Results suggest that teachers' ability to analyze teaching might be reflective of their teaching knowledge.

A growth-mindset intervention teaches the belief that intellectual abilities can be developed. Where does the intervention work best? Prior research examined school-level moderators using data from the National Study of Learning Mindsets (NSLM), which delivered a short growth-mindset intervention during the first year of high school. In the present research, we used data from the NSLM to examine moderation by teachers’ mindsets and answer a new question: Can students independently implement their growth mindsets in virtually any classroom culture, or must students’ growth mindsets be supported by their teacher’s own growth mindsets (i.e., the mindset-plus-supportive-context hypothesis)? The present analysis (9,167 student records matched with 223 math teachers) supported the latter hypothesis. This result stood up to potentially confounding teacher factors and to a conservative Bayesian analysis. Thus, sustaining growth-mindset effects may require contextual supports that allow the proffered beliefs to take root and flourish.

Elementary school teachers’ math anxiety has been found to play a role in their students’ math achievement. The current study addresses the role of teacher math anxiety on ninth-grade students’ math achievement and the mediating factors underlying this relationship. Using data from the National Mindset Study, we find that higher teacher math anxiety is associated with lower math achievement. This relationship is partially mediated by the students’ perception that their teacher believes not everyone can be good at math and is not explainable by teachers’ usable knowledge to teach mathematics. In subsequent analyses, we find that higher teacher math anxiety relates to a reduction in process-oriented (as opposed to ability-oriented) teaching practices, which in turn predict students’ perception of teacher mindset. We argue that math anxious teachers and their use of particular teaching strategies have the potential to shape students’ math achievement and their perceptions of what their teacher believes about math.