The objective of this assessment study is to create and validate an instrument that can be used in our research to evaluate an innovative online instructional unit for teacher professional development (TPD) that uses video from the Robert B. Davis Institute for Learning's video collection. The assessment may be used or adapted for other instructional contexts in which the goals are to assess teachers' mathematics knowledge, mathematics knowledge for teaching, adaptive expertise, and awareness of complexity in children's mathematical reasoning and argumentation as demonstrated in videos of children engaged in problem solving. The mathematical content of this assessment is combinatorics problem solving.
This instrument was modeled on the assessment approaches we have evolved over several years of experience with online instruction and assessment. The assessment approach thus particularly appropriate for online professional development courses.
The study that developed this assessment obtained input from experts in mathematics education and educational psychology. The assessment was administered to students who participated in the experimental unit within the context of a larger course, and also to a comparison group of students in other sections of the same course who did not participate in the experimental unit. The data are being analyzed to gain insight regarding the impact of participating in the unit. We will conduct comparative quantitative and qualitative analyses between the groups to further understand how the unit influences teacher understanding of student reasoning. Some interesting contrasts are afforded by our data, including a comparison of pre-service elementary and middle school teachers with little mathematics training who participated in the experimental online intervention, with pre-service teachers who did not participate in the intervention but who majored in mathematics. The data are still being analyzed and initial findings are soon to follow!