To Matrix, Network, or Hierarchy: That Is the Question

The authors present a structural analysis of three spatial diagrams-matrices, networks, and hierarchies-that specifies 10 properties on which these diagrammatic representations are hypothesized to differ: global structure, building block, number of sets, item/link constraints, item distinguishability, link type, absence of a relation, linking relations, path, and traversal. Each property has a "value" for each diagram, and these property values constitute the applicability conditions for the representations. Twenty-three college students (computer science majors and math educators) selected the type of diagram they thought would be most efficient for organizing the information in each of 18 short scenarios and verbally justified the reasons for their selections. The verbal protocols were coded with respect to the structural analysis. Both the representation selection and verbal justification data provided strong support for the structural analysis. Additionally, a factor analysis of students' justifications indicated that the organization of their knowledge is consistent with the structural analysis. Students' use of the structural properties to select appropriate representations and to justify those selections indicates that the structural analysis has psychological force.