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Abstract
Learning abstract concepts through concrete examples may promote learning at the cost of inhibiting transfer. The present study investigated one approach to solving this problem: systematically varying superficial features of the examples. Participants learned to solve problems involving a mathematical concept by studying either superficially similar or varied examples. In Experiment 1, less knowledgeable participants learned better from similar examples, while more knowledgeable participants learned better from varied examples. In Experiment 2, prior to learning how to solve the problems, some participants received a pretraining aimed at increasing attention to the structural relations underlying the target concept. These participants, like the more knowledgeable participants in Experiment 1, learned better from varied examples. Thus, the utility of varied examples depends on prior knowledge and, in particular, ability to attend to relevant structure. Increasing this ability can prepare learners to learn more effectively from varied examples.
Notes
Concept representations are sometimes referred to as “schemas,” and the process of deriving them from multiple examples as “schema abstraction” (Bernardo, Citation2001; Elio & Anderson, Citation1981, Citation1984; Gick & Holyoak, Citation1983; Reed, Citation1989). The term “concept representation” is preferred to schema here to avoid confusion with our somewhat different use of the term schema to describe our experimental stimuli. See note 4.
Of course, studying examples of different concepts may draw attention to features that distinguish concepts, instead of or in addition to commonalities within each concept (Birnbaum, Kornell, Bjork, & Bjork, Citation2012; Chang, Citation2006; Goldstone, Citation1996; Kang & Pashler, Citation2012; Rosch & Mervis, Citation1975; Taylor & Rohrer, Citation2010; Vanderstoep & Seifert, Citation1993). Furthermore, studying both examples and nonexamples of a concept may highlight criterial features that determine whether or not the concept applies rather than highlighting commonalities among examples more generally (Chang, Citation2006; Gick & Paterson, Citation1992; Große & Renkl, Citation2007; Namy & Clepper, Citation2010). However, because the present study is concerned mainly with effects of variation among examples of a single concept, we focus on extraction of commonalities rather than detection of distinctive or criterial features.
The common perception that a province will be chosen for each child, so that the provinces fill the role of options and the children that of selections, is incorrect because it rules out the possibility of individual children receiving multiple provinces, which is expressly allowed, and allows the possibility of some provinces remaining unassigned, which is expressly ruled out.
Past research has often employed the term “schema” to refer to relational concepts such as SWR. In the present study, the term schema is reserved for specific versions of abstract concepts defined by specific constraints on the types of elements that may fill their structural roles.