Understanding the complex relationships between teacher knowledge, teaching, and student learning is critical to systematically  improve mathematics education in the US. We, the TeKno research team, at the University of Arizona, in Tucson, Arizona, study these relationships through the systematic development of measures. 

The Capturing Teacher Knowledge (TeKno) Project explores the usefulness of a novel assessment approach to measuring teacher knowledge of teaching mathematics. The approach is based on teachers' ability to analyze instruction, which is an important teaching skill. Building on findings of research on expertise that show that expert and novice teachers view and interpret classroom instruction differently, the Classroom Video Analysis (CVA) approach uses video clips of authentic mathematics instruction to elicit teachers' usable teaching knowledge. 

To complete the CVA instrument teachers view a set of  short video clips online and analyze each clip in writing (teknoclips). Specifically, teachers are asked to discuss how the teacher and the student(s) in the video clips interact around the mathematical content. Teachers written responses to the video clips, which are treated as "samples of their teaching knowledge" are scored according to four rubrics. We hypothesized that teachers' written responses to the video clips not only depict their knowledge as it relates to the video clips but also whether they are able to use  that knowledge in the classroom.  In an initial study we were able to confirm this hypothesis.  We found that teachers' scored responses to a set of fraction video clips not only predicted teachers own quality of instruction, as measured through videotaped classroom lessons coded for instructional quality, but also their student learning on a fraction quiz from pre to post. Further investigations into the predictive validity of the CVA instrument are currently underway. We are also working on automated scoring techniques of the open-ended responses to make the assessment more practical to use. Initial efforts showed promising results. We are able to produce computer-generated total scores that correlate .80 or greater with rater assigned scores. 

If you are interested in using our CVA assessment, click here or click the Go to Teknoclips link in the side bar.  A total of 127 subtitled video clips on elementary and middle school mathematics are available to create customized assessments on our teknoclips web interface. In addition, we have reliable, ready to use CVA scales on four topics areas:  Fractions, Ratio & Proportions, Variables, Expressions, & Equations, and Numbers & Operations. The teknoclips web interface can also be used as a data collection tool for all activities that involve tasks and responses around videos. You can use your own video clips (.mpg3 or .mov) to create video vignettes and tasks for your teachers or students.

The Value-Added project develops measures of instructional quality to to be applied to videotaped classroom lessons and relates them to teacher value-added scores, different measures of teacher knowledge, and project-developed measures of student learning.  
The project has two main goals: It explores the validity of teacher value-added scores by comparing instructional quality of teachers with different value-added scores (VAEs), and it seeks to identify instructional strategies that promote student learning. The project also explores the stability of teacher value-added scores across different models and model specifications to better understand their psychometric properties, and to evaluate the suitability of value-added measures for use in formal teacher evaluation and accountability systems. Preliminary findings indicate that model specifications do impact teacher VAEs and that higher value-added scores are associated with some standard-based teaching strategies.