Soft Clustering of Physics Misconceptions Using a Mixed Membership Model

Students often possess multiple, conflicting misconceptions which may be activated and expressed in different contexts. In this paper, we use a mixed membership model to explore the patterns of misconceptions in introductory physics. Mixed membership models have been widely used for modeling observations that have partial membership in several latent groups. The latent groups in the current study are misconception patterns. This model allows us to examine whether students are likely to hold a few or many misconceptions, as well as which misconceptions are likely to co-exist. Physics knowledge was measured with the Force concepts inventory (FCI). We found three dominant response patterns, with different misconceptions prominent within each pattern.