Benefits of Variation Increase with Preparation

Benefits of Variation Increase with Preparation David W. Braithwaite (baixiwei@gmail.com) Department of Psychology, Indiana University, 1101 E. 10th Street Bloomington, IN 47405 USA Robert L. Goldstone (rgoldsto@indiana.edu) Department of Psychology, Indiana University, 1101 E. 10th Street Bloomington, IN 47405 USA An additional consideration more specific to abstract con- cepts is that similarity between examples can lead to over- specified concept representations, while variation can avoid this pitfall. Similar examples are likely to share superficial features in addition to their common, constitutive structure. Learners may then incorporate these superficial features as part of the learned concept, limiting their ability to extend the concept to novel instances that do not share the same features, a phenomenon known as conservative generalization (Medin & Ross, 1989). Varied examples, by contrast, are likely to share few or no superficial features. Concepts learned from such examples would include only the relevant underlying structure and, therefore, would generalize more easily to novel cases. Indeed, several studies have found that abstract concepts learned from varied rather than similar examples are more easily extended to novel instances (Chen & Mo, 2004; Day, Goldstone, & Hills, 2010). However, variation among examples also has potential drawbacks. Too much variation might prevent learners from discerning what the examples have in common with each other, preventing them from learning the underlying concept at all. By contrast, if the examples are similar – that is, share some surface features in addition to underlying structure – then correspondences between their surface features may be easy for learners to notice. These correspondences can serve as scaffolding, allowing learners to notice their shared under- lying structure, a phenomenon known as progressive align- ment (Kotovsky & Gentner, 1996). Consistent with this view, some studies have found that abstract concepts are ac- quired more easily if similar, rather than varied, examples are presented initially (Elio & Anderson, 1984; Kotovsky & Gentner, 1996). These results dovetail with studies on per- ceptual category learning that have shown slower category learning from varied, relative to similar, examples (Hahn et al., 2005). Thus, varied and similar examples may each offer potential benefits for abstract concept learning. The relative strengths of their benefits may depend on an additional factor: learners’ predisposition, and ability, to attend to the structural relations present in the examples. On the one hand, learners who at- tend to structural relations might easily ignore superficial commonalities between examples. On this account, attention to relations would reduce the risk of conservative generaliza- tion, a potential drawback of similar examples, and would thereby increase the relative benefits of similar examples. On the other hand, learners who can easily attend to structural Abstract Abstract concepts are characterized by their underlying struc- ture rather than superficial features. Variation in the examples used to teach abstract concepts can draw attention towards shared structure and away from superficial detail, but too much variation can inhibit learning. The present study tested the pos- sibility that increasing attention to underlying structural rela- tions could alleviate the latter difficulty and thereby increase the benefits of varied examples. Participants were trained with either varied or similar examples of a mathematical concept, and were then tested on their ability to apply the concept to new cases. Before training, some participants received pretraining aimed at increasing attention to the structural relations under- lying the concept. The relative advantage of varied over simi- lar examples was increased among participants who received the pretraining. Thus, preparation that promotes attention to the relations underlying abstract concepts can increase the ben- efits of learning from varied examples. Keywords: variation; concept learning; conservative general- ization; progressive alignment; prior knowledge; mathematics. Background Abstract concepts – that is, concepts characterized by un- derlying structure rather than by surface similarities among their members – are pervasive in human thought and lan- guage (Gentner & Kurtz, 2005). Such concepts play a partic- ularly prominent role in formal education. Examples include functions in mathematics, forces in physics, supply and de- mand in economics, and natural selection in biology. The power of such concepts comes from their ability to capture deep commonalities across superficially dissimilar situations. Thus, a key goal for instruction is to enable learners to extend such concepts to a wide range of instances, which may differ substantially from studied examples. Evidence suggests that learning concepts from highly var- ied examples can help to achieve this goal. Most directly, variation in studied examples increases the chance that a novel instance will resemble a studied example. Also, expo- sure to varied examples can increase the range of variation associated with the concept. Both of these considerations suggest that learning from varied, relative to similar, exam- ples would allow concepts to be extended to a wider range of novel instances, a prediction confirmed by numerous studies of category learning (Hahn, Bailey, & Elvin, 2005; Posner & Keele, 1968).