Extending the Classroom Video Analysis Into a Content-Focused, Common Core–Aligned Measure of Mathematics Knowledge for Teaching

• In Event: Developing and Validating Indicators for Teachers' Science and Mathematics Content Knowledge for Teaching

Abstract

Being able to measure the mathematics knowledge for teaching that teachers can access and apply in the classroom is critical for understanding how it develops and how teachers use it in the process of teaching (Ball & Bass, 2000; Ball, Thames, & Phelps, 2008; Hill et al., 2004). The Classroom Video Analysis (CVA) instrument, which is based on teachers’ ability to analyze teaching events, is designed to capture usable knowledge (Author, 2010; Author, 2012). Under this approach, teachers view a set of video clips of authentic mathematics instruction and provide written analyses of what they see, which are scored to obtain measures of their usable knowledge. Prior studies have shown that teachers’ scores on the CVA positively related to their scores on the Mathematics Knowledge for Teaching (MKT) instrument (Author, 2014b) and for an in-depth study on fractions predicted instructional quality and student learning (Author, 2010; 2012).

In this study, we further extended the CVA approach and developed a new set of 24 content-specific, video-based fraction items that are aligned with the Common Core Standards (CCSS, 2010), to create a classroom-focused measure of teachers’ usable mathematics knowledge for teaching. Using 13 existing CVA fraction clips, we developed four new content-focused analysis prompts along with multiple-choice and rating scale items. We explored item and scale functioning of our new items and their relationship to the original CVA measure and the MKT (Hill et al., 2004).

Analyzing responses to a subset of 12 new items from 104 mathematics teachers (grades 3-6), internal consistency was estimated at .55, which we expect to increase when all 24 items are analyzed. We also learned that the new analysis prompts worked well across different video clips, which is important for scale-up. Of the seven closed-ended items, three showed acceptable psychometric properties. Finally, we found that teachers’ scores on the new items statistically significantly related to their scores on the original CVA and the MKT measures, which teachers’ had also completed as part of this study, at roughly the same magnitude (r = .50** and r = .52**, respectively). The correlation between the original CVA and the MKT was slightly lower (r = .38**). The preliminary results suggest that the knowledge teachers use to answer the new items is similar to the knowledge teachers draw on for the original CVA and the MKT. To better understand whether and how much of the shared variance between the pairs of variables is explained by the remaining variable, we computed partial correlations. The pattern of partial correlations is consistent with the idea that the observed relationship between the new items and the MKT reflects the focus on the mathematics of both measures, while the relationship between the new items and the original CVA reflects the fact that both instruments measure usable knowledge. Although results obtained at this point have to be considered preliminary, they provide some indication of promise for our newly developed items.

Authors

• Nicole B. Kersting, The University of Arizona

• Mei-Kuang Chen, The University of Arizona

• Guadalupe Lozano, The University of Arizona

• Saeideh Heshmati, The University of Arizona

• Kathleen Jablon Stoehr, Santa Clara University

• James W. Stigler, University of California - Los Angeles