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

We describe Module Analysis for Multiple Choice Responses (MAMCR), a new methodology for carrying out network analysis on responses to multiple choice assessments. This method is used to identify modules of non-normative responses which can then be interpreted as an alternative to factor analysis. MAMCR allows us to identify conceptual modules that are present in student responses that are more specific than the broad categorization of questions that is possible with factor analysis and to incorporate non-normative responses. Thus, this method may prove to have greater utility in helping to modify instruction. In MAMCR the responses to a multiple choice assessment are first treated as a bipartite, student X response, network which is then projected into a response X response network. We then use data reduction and community detection techniques to identify modules of non-normative responses. To illustrate the utility of the method we have analyzed one cohort of postinstruction Force Concept Inventory (FCI) responses. From this analysis, we find nine modules which we then interpret. The first three modules include the following: Impetus Force, More Force Yields More Results, and Force as Competition or Undistinguished Velocity and Acceleration. This method has a variety of potential uses particularly to help classroom instructors in using multiple choice assessments as diagnostic instruments beyond the Force Concept Inventory.