Measuring dynamical interdependence in small-group collaborations

This paper addresses dynamical interdependence among the actions of group members. I assume that the actions of each member can be represented as nodes of a dynamical network and then collect the nodes into disjoint subsets (components) representing the individual group members. Interdependence among group members’ actions can then be defined with reference to a K-partite network, in which the partitions correspond to the group member components. Independence among group members’ actions can be defined with reference to a network in which the group member components are disconnected from one another. The degree to which the interactions of actual groups correspond to either of these theoretical network structures can be characterized using modified versions of existing network statistics. Taking this approach, I propose a number of network-based measures of dynamical interdependence, discuss the interpretation of the proposed measures, and consider how to assess their reliability and validity. These ideas are illustrated using an example in which dyads collaborated via online chat to complete a grade 12 level mathematics assessment.