available, make it possible to find solutions with little or no searching. For example, someone who knows the calculus finds the maximum of a function by applying a known algorithm (taking the derivative and setting it equal to zero). To continue the assessment analogy, strong methods are often measured by such tests as the SAT II. Paradoxically, although one of the hallmarks of expertise is access to a vast store of strong methods in a particular domain, both children and scientists fall back on their repertoire of weak methods when faced with truly novel problems (Klahr and Simon, 1999).

Schemas and the Organization of Knowledge

Although weak methods remain the last resort when one is faced with novel situations, people generally strive to interpret situations so that they can apply schemas—previously learned and somewhat specialized techniques (i.e., strong methods) for organizing knowledge in memory in ways that are useful for solving problems. Schemas help people interpret complex data by weaving them into sensible patterns. A schema may be as simple as “Thirty days hath September” or more complex, such as the structure of a chemical formula. Schemas help move the burden of thinking from working memory to long-term memory. They enable competent performers to recognize situations as instances of problems they already know how to solve; to represent such problems accurately, according to their meaning and underlying principles; and to know which strategies to use to solve them.

This idea has a very old history. In fact, the term schema was introduced more than 50 years ago to describe techniques people use to reconstruct stories from a few, partially remembered cues (Bartlett, 1932). The modern study of problem solving has carried this idea much further. Cheng and Holyoak’s (1985) study of schematic problem solving in logic is a good example. It is well known that people have a good deal of trouble with the implication relationship, often confusing “A implies B” with the biconditional relationship “A implies B, and B implies A” (Wason and Johnson-Laird, 1972). Cheng and Holyoak showed that people are quite capable of solving an implication problem if it is rephrased as a narrative schema that means something to them. An example is the “permission schema,” in which doing A implies that one has received permission to do B; to cite a specific case, “Drinking alcoholic beverages openly implies that one is of a legal age to do so.” Cheng and Holyoak pointed out that college students who have trouble dealing with abstract A implies B relationships have no trouble understanding implication when it is recast in the context of “permission to drink.”

The existence of problem-solving schemas has been demonstrated in a wide variety of contexts. For instance, Siegler and colleagues have shown

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