When concepts act concretely: Exploring the notion of conceptual concreteness in a novel mathematical domain

Abstract

The information we seek to communicate to learners is often conveyed by symbols, and the symbols we choose may directly affect cognition independently of the instructional strategies that we apply. The current series of experiments investigates this claim from an information-based account of concreteness. This account defines concreteness as the prior informational load – both perceptual and conceptual – carried by a symbol. The experiments examined this account in a complex mathematical domain. Each experiment followed a general theme in which participants were taught a set of abstract rules using various symbol sets and tested to ascertain the extent to which symbol choice affected learning, defined as the ability to successfully perform tasks using the same symbols used for initial training, and transfer, defined as the ability to successfully perform similar tasks using new symbols. In particular, these experiments evaluated whether the conceptual information associated with a symbol can have effects on learning and transfer that parallel those of perceptually concrete symbols. The results of Experiment 1 suggest that the conceptual information associated with Arabic numbers can indeed have effects that parallel those of perceptually concrete symbols. The results of Experiment 2 corroborate this finding and provide evidence that activation of prior addition schemas can modulate these effects. The data further suggest that learning with concrete symbols that are aligned with the to-be-learned content can impair learners’ appreciation for the deep structure of the task. The results of Experiment 3 showed that a brief intervention designed to imbue a symbol with irrelevant conceptual knowledge failed to have the same effects on learning and transfer as the overlearned prior knowledge associated with numbers.