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How People Learn: Brain, Mind, Experience, and School
perceive problem solving in physics as memorizing, recalling, and manipulating equations to get answers. When solving problems, experts in physics often pause to draw a simple qualitative diagram—they do not simply attempt to plug numbers into a formula. The diagram is often elaborated as the expert seeks to find a workable solution path (e.g., see Larkin et al., 1980; Larkin and Simon, 1987; Simon and Simon, 1978).
Differences in how physics experts and novices approach problems can also be seen when they are asked to sort problems, written on index cards, according to the approach that could be used to solve them (Chi et al., 1981). Experts’ problem piles are arranged on the basis of the principles that can be applied to solve the problems; novices’ piles are arranged on the basis of the problems’ surface attributes. For example, in the physics subfield of mechanics, an expert’s pile might consist of problems that can be solved by conservation of energy, while a novice’s pile might consist of problems that contain inclined planes; see Figure 2.4. Responding to the surface characteristics of problems is not very useful, since two problems that share the same objects and look very similar may actually be solved by entirely different approaches.
Some studies of experts and novices in physics have explored the organization of the knowledge structures that are available to these different groups of individuals (Chi et al., 1982); see Figure 2.5. In representing a schema for an incline plane, the novice’s schema contains primarily surface features of the incline plane. In contrast, the expert’s schema immediately connects the notion of an incline plane with the laws of physics and the conditions under which laws are applicable.
Pause times have also been used to infer the structure of expert knowledge in domains such as chess and physics. Physics experts appear to evoke sets of related equations, with the recall of one equation activating related equations that are retrieved rapidly (Larkin, 1979). Novices, in contrast, retrieve equations more equally spaced in time, suggesting a sequential search in memory. Experts appear to possess an efficient organization of knowledge with meaningful relations among related elements clustered into related units that are governed by underlying concepts and principles; see Box 2.3. Within this picture of expertise, “knowing more” means having more conceptual chunks in memory, more relations or features defining each chunk, more interrelations among the chunks, and efficient methods for retrieving related chunks and procedures for applying these informational units in problem-solving contexts (Chi et al., 1981).
Differences between how experts and nonexperts organize knowledge has also been demonstrated in such fields as history (Wineburg, 1991). A group of history experts and a group of gifted, high-achieving high school seniors enrolled in an advanced placement course in history were first given a test of facts about the American Revolution. The historians with back-