The ability to categorize problems based upon underlying principles, ratherthan surface features or contexts, is considered one of several proxypredictors of expertise in problem solving. With inspiration from the classicstudy by Chi, Feltovich, and Glaser, we assess the distribution of expertiseamong introductory physics students by asking three introductory physicsclasses, each with more than a hundred students, to categorize mechanicsproblems based upon similarity of solution. We compare their categorizationwith those of physics graduate students and faculty members. To evaluate theeffect of problem context on students' ability to categorize, two sets ofproblems were developed for categorization. Some problems in one set includedthose available from the prior study by Chi et al. We find a large overlapbetween calculus-based introductory students and graduate students with regardto their categorizations that were assessed as "good." Our findings, whichcontrast with those of Chi et al., suggest that there is a wide distribution ofexpertise in mechanics among introductory and graduate students. Although thecategorization task is conceptual, introductory students in the calculus-basedcourse performed better than those in the algebra-based course. Qualitativetrends in categorization of problems are similar between the non-Chi problemsand problems available from the Chi study used in our study although the Chiproblems used are more difficult on average.
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