Effects of Instruction on Students Holding Various Non-Newtonian Misconceptions

We analyzed individual wrong responses from 34k administrations of the FCI using our bayesian implementation of a multidimensional item response theory followed by transformations in the vectorspace of all responses (1). We discovered ~17 coherent, non-orthogonal student misconceptions and misunderstandings, including some not previously found in the PER literature, e.g. "objects with force perpendicular to their path go straight" and "air resists motion and pushes downwards". We can find the amount of each misconception held by a small class, allowing us to find the diminishment of each misconception after instruction for each pretest score (1-30) from our whole data set. We see examples where instruction leaves low-skill, high-skill, and all-skill students unimproved; the all-skill misconception being "impetus force for linear motion". Insights into what misconceptions students have and who benefits more or less from instruction can help instructors focus their lessons to make learning more effective and equitable.