Context and structure: The nature of students' knowledge about three spatial diagram representations

The authors investigated whether college students possess abstract rules concerning the applicability conditions for three spatial diagrams that are important tools for thinking—matrices, networks, and hierarchies. A total of 127 students were asked to select which type of diagram would be best for organising the information in each of several short scenarios. The scenarios were written using three different story contexts: (a) neutral, presenting a real-life situation but not cueing a particular representation; (b) abstract, presenting only variable names and relations; and (c) incongruent, in which the context and informational structure cued different representations. The results indicated above-chance performance on the abstract scenarios, as well as comparable performance on the abstract and neutral context scenarios. In a follow-up study in which eight students thought out loud while selecting diagrams for the abstract scenarios, there were almost no references to concrete examples. The results of these studies suggest that students possess abstract rules concerning the applicability conditions for matrices, networks, and hierarchies.