Using module analysis for multiple choice responses: A new method applied to Force Concept Inventory data

We describe a methodology for carrying out a network analysis of Force Concept Inventory (FCI) responses that aims to identify communities of incorrect responses. This method first treats FCI responses as a bipartite, student X response, network. We then use Locally Adaptive Network Sparsification\citep{Foti2011} and InfoMap\citep{rosvall2009map} community detection algorithms to find modules of incorrect responses. This method is then used to analyze post-FCI data from one cohort of Danish university students. From this analysis, we find nine modules which we then interpret. The first three modules include: Impetus Force, More Force Yields More Results, and Force as Competition or Undistinguished Velocity and Acceleration. This approach to analysis of FCI results is an alternative to factor analysis and yields results that could be useful for modifying classroom activity. As a methodology, this is a first step and has a variety of potential uses particularly to help classroom instructors in using the FCI as a diagnostic instrument.