This paper explores factors associated with effective external representation (ER) use. We describe an information-processing approach to the assessment of ER knowledge. We also present findings from a study that examined the effects of users' background knowledge of ERs upon performance and their preferences for particular information display forms across a range of database query types that differed in their representational specificity. A representationally specific task is one which can only be performed effectively with one type of representation (or a narrow range of representations). On highly representationally specific tasks, optimal ER selection is crucial. Both ER selection performance and reasoning performance are, in turn, predicted by an individual's prior knowledge of ERs. On representationally nonspecific tasks, participants performed well with any of several different ER types regardless of their level of prior ER knowledge. It is argued that ER effectiveness crucially depends upon a three-way interaction between user characteristics (e.g. prior knowledge), the cognitive properties of an ER, and task characteristics.