  The ability to categorize problems based upon underlying principles, rather
than surface features or contexts, is considered one of several proxy
predictors of expertise in problem solving. With inspiration from the classic
study by Chi, Feltovich, and Glaser, we assess the distribution of expertise
among introductory physics students by asking three introductory physics
classes, each with more than a hundred students, to categorize mechanics
problems based upon similarity of solution. We compare their categorization
with those of physics graduate students and faculty members. To evaluate the
effect of problem context on students' ability to categorize, two sets of
problems were developed for categorization. Some problems in one set included
those available from the prior study by Chi et al. We find a large overlap
between calculus-based introductory students and graduate students with regard
to their categorizations that were assessed as "good." Our findings, which
contrast with those of Chi et al., suggest that there is a wide distribution of
expertise in mechanics among introductory and graduate students. Although the
categorization task is conceptual, introductory students in the calculus-based
course performed better than those in the algebra-based course. Qualitative
trends in categorization of problems are similar between the non-Chi problems
and problems available from the Chi study used in our study although the Chi
problems used are more difficult on average.
