BOX 3.3 Throwing Darts

In one of the most famous early studies comparing the effects of “learning a procedure” with “learning with understanding,” two groups of children practiced throwing darts at a target underwater (Scholckow and Judd, described in Judd, 1908; see a conceptual replication by Hendrickson and Schroeder, 1941). One group received an explanation of refraction of light, which causes the apparent location of the target to be deceptive. The other group only practiced dart throwing, without the explanation. Both groups did equally well on the practice task, which involved a target 12 inches under water. But the group that had been instructed about the abstract principle did much better when they had to transfer to a situation in which the target was under only 4 inches of water. Because they understood what they were doing, the group that had received instruction about the refraction of light could adjust their behavior to the new task.

trated with an example from biology that involved learning about the physical properties of veins and arteries. We noted that the ability to remember properties of veins and arteries (e.g., that arteries are thicker than veins, more elastic, and carry blood from the heart) is not the same as understanding why they have particular properties. The ability to understand becomes important for transfer problems, such as: “Imagine trying to design an artificial artery. Would it have to be elastic? Why or why not?” Students who only memorize facts have little basis for approaching this kind of problem-solving task (Bransford and Stein, 1993; Bransford et al., 1983). The act of organizing facts about veins and arteries around more general principles such as “how structure is related to function” is consistent with the knowledge organization of experts discussed in Chapter 2.

Time to Learn

It is important to be realistic about the amount of time it takes to learn complex subject matter. It has been estimated that world-class chess masters require from 50,000 to 100,000 hours of practice to reach that level of expertise; they rely on a knowledge base containing some 50,000 familiar chess patterns to guide their selection of moves (Chase and Simon, 1973; Simon and Chase, 1973). Much of this time involves the development of pattern recognition skills that support the fluent identification of meaningful patterns of information plus knowledge of their implications for future outcomes (see Chapter 2). In all domains of learning, the development of

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