Usable knowledge for teaching mathematics: Further exploration of the Classroom Video Analysis (CVA) Instrument.

In this article we report further explorations of the classroom video analysis instrument (CVA), a measure of usable teacher knowledge based on scoring teachers’ written analyses of classroom video clips. Like other researchers, our work thus far has attempted to identify and measure separable components of teacher knowledge. In this study we take a different approach, viewing teacher knowledge as a system in which different knowledge components are flexibly brought to bear on specific teaching situations. We explore this idea through a series of exploratory factor analyses of teachers clip level scores across three different CVA scales (fractions, ratio and proportions, and variables, expressions, and equations), finding that a single dominant dimension explained from 55 to 63 % of variance in the scores. We interpret these results as consistent with a view that usable teacher knowledge requires both individual knowledge components, and an overarching ability to access and apply those components that are most relevant to a particular teaching episode.