In physics education, a number of studies have developed assessments of teachers' knowledge of student understanding (KSU) of specific physics concepts with modified versions of existing concept inventories, in which teachers were asked to predict the popular incorrect answers from students. The results provide useful but indirect information to…

In this paper, we describe student understanding of the "force concept" (basic concepts of Newtonian mechanics) by representing it as a vector-valued quantity, which we refer to as the "score-state vector," in a (30-dimensional) Force Concept Inventory (FCI) score space. We use a large ensemble of FCI results collected…

Concept inventories are widely used in physics education research, yet numerous studies show that concept inventories measure dramatically different learning gains in different demographic groups. Prior studies show that the performance gaps between demographic groups are already present in their preinstruction responses, suggesting that the…