studies on conceptual representation include Brown (1986), Bassok and Holyoak (1989a, b), and Singley and Anderson (1989). Whether students will transfer across domains—such as distance formulas from physics to formally equivalent biological growth problems, for example—depends on whether they conceive of the growth as occurring continuously (successful transfer) or in discrete steps (unsuccessful transfer) (Bassok and Olseth, 1995).

Singley and Anderson (1989) argue that transfer between tasks is a function of the degree to which the tasks share cognitive elements. This hypothesis was also put forth very early in the development of research on transfer of identical elements, mentioned previously (Thorndike and Woodworth, 1901; Woodworth, 1938), but it was hard to test experimentally until there was a way to identify task components. In addition, modern theorists include cognitive representations and strategies as “elements” that vary across tasks (Singley and Anderson, 1989).

Singley and Anderson taught students several text editors, one after another, and sought to predict transfer, defined as the savings in time of learning a new editor when it was not taught first. They found that students learned subsequent text editors more rapidly and that the number of procedural elements shared by two text editors predicted the amount of this transfer. In fact, there was large transfer across editors that were very different in surface structures but that had common abstract structures. Singley and Anderson also found that similar principles govern transfer of mathematical competence across multiple domains when they considered transfer of declarative as well as procedural knowledge.

A study by Biederman and Shiffrar (1987) is a striking example of the benefits of abstract instruction. They studied a task that is typically difficult to learn in apprentice-like roles: how to examine day-old chicks to determine their sex. Biederman and Shiffrar found that twenty minutes of instruction on abstract principles helped the novices improve considerably (see also Anderson et al., 1996). Research studies generally provide strong support for the benefits of helping students represent their experiences at levels of abstraction that transcend the specificity of particular contexts and examples (National Research Council, 1994). Examples include algebra (Singley and Anderson, 1989), computer language tasks (Klahr and Carver, 1988), motor skills (e.g., dart throwing, Judd, 1908), analogical reasoning (Gick and Holyoak, 1983), and visual learning (e.g., sexing chicks, Biederman and Shiffrar, 1987).

Studies show that abstracted representations do not remain as isolated instances of events but become components of larger, related events, schemata (Holyoak, 1984; Novick and Holyoak, 1991). Knowledge representations are built up through many opportunities for observing similarities and differences across diverse events. Schemata are posited as particularly im-



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