Exploring the Construct Validity of the Classroom Video Analysis Instrument as a Measure of Usable Teaching Knowledge in Mathematics

• In Event: Further Exploration of the Classroom Video Analysis Approach for Measuring Usable Teaching Knowledge in Mathematics

Abstract

The Classroom Video Analysis (CVA) approach is designed to measure Usable Teaching Knowledge in Mathematics. We focused explicitly on knowledge use (i.e., the knowledge teachers are able to access and use in the classroom) because it is this usable knowledge that is most likely to affect instruction and student learning. In this paper we examine the construct validity of the CVA.
We defined Usable Mathematics Teaching Knowledge building on findings from studies in cognitive science and expertise (How People Learn, 2000). We hypothesized that to become usable teacher knowledge needs to be “conditionalized”, which means that information that identifies the instructional contexts in which the knowledge can be applied is stored, and that different kinds of knowledge need to be connected, forming subroutines of integrated knowledge that are activated when the instructional context arises. This conceptualization of usable knowledge has two strengths: We can describe differences among teachers’ usable knowledge. Teachers with more conditionalized and integrated knowledge have greater usable knowledge. We specified a model for the development of usable knowledge that can be empirically tested.
Based on this construct definition we reasoned that usable teaching knowledge can be thought of a single dimension representing the amount of integrated knowledge teachers have. To elicit usable knowledge, we showed teachers video clips of authentic classroom instruction and asked them to analyze the teaching episodes in writing.
We score teachers’ responses according to four rubrics. We rate the degree to which responses analyze the mathematical content and student thinking, include suggestions for improvement, and the overall depth of the analysis. Although each rubric score means something specific (Kersting et al., 2010), across rubrics a score of “0” indicates that a teacher does not have a particular knowledge or that the knowledge is not yet conditionalized, a score of “1” means that the knowledge is conditionalized but not yet integrated, and a score of “2” implies that knowledge is not only conditionalized but also integrated.
To test whether usable knowledge is a unidimensional construct we factor analyzed data from three CVA scales, each on a different topic. We dichotomized our rubric scores in two different ways. We combined “0s” and “1s” and kept the “2”s to obtain a measure of integrated knowledge and we combined the “1s” and “2s” and kept the “0s” to obtain a measure of conditionalized knowledge. We fit 1-factor and 4-factor correlated models to each set of dichotomized scores.
Model fit and comparison information revealed that for all three topic areas the 1-factor model represented the best data model fit when we analyzed the scores that reflected integrated knowledge providing empirical evidence for the validity of our construct. The 4-factor model fit best when we analyzed the scores that reflect different kinds of conditionalized knowledge, highlighting the importance of knowledge integration for the usable teaching knowledge construct.
The stability of our results across three different CVA scales provides convincing evidence for the construct validity of the CVA and has important implications for studying usable teaching knowledge and its development.

Author

• Nicole B. Kersting, The University of Arizona