The Power of Big Ideas in Mathematics Education: Development and Pilot Testing of POWERSOURCE Assessments

The characteristics of expert knowledge—interconnectedness, understanding, and ability to transfer—are inextricably linked, a point that is critically important for educators and constitutes a major theme of this paper. In this paper we explore how an analysis of the architecture of expert knowledge can inform the development of assessments to help teachers move students toward greater expertise in mathematics, and we present examples of such assessments. We also review student responses and preliminary results from pilot tests of assessments administered in sixth-grade classes in a large urban school district. Our preliminary analyses suggest that an assessment strategy based on the structure of mathematical knowledge can reveal deficiencies in student understanding of and ability to apply fundamental concepts of pre-algebra, and has the potential to help teachers remediate those deficiencies.