were changed, or this part?” (Cognition and Technology Group at Vanderbilt, 1997). A third way is to generalize the case so that learners are asked to create a solution that applies not simply to a single problem, but to a whole class of related problems. For example, instead of planning a single boat trip, students might run a trip planning company that has to advise people on travel times for different regions of the country. Learners are asked to adopt the goal of learning to “work smart” by creating mathematical models that characterize a variety of travel problems and using these models to create tools, ranging from simple tables and graphs to computer programs. Under these conditions, transfer to novel problems is enhanced (e.g., Bransford et al., 1998).

Problem Representations

Transfer is also enhanced by instruction that helps students represent problems at higher levels of abstraction. For example, students who create a specific business plan for a complex problem may not initially realize that their plan works well for “fixed-cost” situations but not for others. Helping students represent their solution strategies at a more general level can help them increase the probability of positive transfer and decrease the degree to which a previous solution strategy is used inappropriately (negative transfer).

Advantages of abstract problem representations have been studied in the context of algebra word problems involving mixtures. Some students were trained with pictures of the mixtures and other students were trained with abstract tabular representations that highlighted the underlying mathematical relationships (Singley and Anderson, 1989). Students who were trained on specific task components without being provided with the principles underlying the problems could do the specific tasks well, but they could not apply their learning to new problems. By contrast, the students who received abstract training showed transfer to new problems that involved analogous mathematical relations. Research has also shown that developing a suite of representations enables learners to think flexibly about complex domains (Spiro et al., 1991).

Relationships Between Learning and Transfer Conditions

Transfer is always a function of relationships between what is learned and what is tested. Many theorists argue that the amount of transfer will be a function of the overlap between the original domain of learning and the novel one. Measuring overlap requires a theory of how knowledge is represented and conceptually mapped across domains. Examples of research



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