This article discusses the cognitive differences between reasoning with self-constructed external representations (ERs) and reasoning with presented representations (e.g. textbook diagrams). Examples of ERs produced by subjects solving reasoning problems are provided. It is argued that effective reasoning with ERs involves a three-way interaction between (a) the cognitive and semantic properties of the representation; (b) the match between the demands of the task and the type of information read-off afforded by the representation and (c) the effects of within-subject factors (e.g. prior knowledge, cognitive style). It is suggested that providing direct instruction in the use of ERs could usefully address each factor
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