Using centrality of concept maps as a measure of problem space states in computer-supported collaborative problem solving

Problem solving likely involves at least two broad stages, problem space representation and then problem solution (Newell and Simon, Human problem solving, 1972). The metric centrality that Freeman (Social Networks 1:215-239, 1978) implemented in social network analysis is offered here as a potential measure of both. This development research study applied centrality measures to reanalyze existing concept maps from a recent investigation (Engelmann and Hesse, Computer-Supported Collaborative Learning 5:299-319, 2010). Participants (N = 120) were randomly assigned to interdependent (i.e. hidden profiles) or non-interdependent conditions to work online in triads using CmapTools software to create a concept map in order to solve a problem scenario. The centrality values of these group-created concept maps agreed with the common relations count analysis used in that investigation and allowed for additional comparisons as well as analysis by multidimensional scaling. Specifically, the interdependent triad maps resembled the fully explicated problem space, while the non-interdependent triad maps mainly resembled the problem solution. The results demonstrate that centrality is a useful measure of knowledge structure contained in these team concept map artifacts that allows researchers to infer problem representation start and goal state transitions during problem solving.