We revisited the Chi categorization study three decades later at the same institution (University of Pittsburgh) in the “ecological” classroom environment with several hundred introductory physics students. We asked introductory students in the calculus-based and algebra-based physics courses to categorize 25 introductory mechanics problems based upon similarity of solution. Two versions of the problem sets were used in the study, with one version developed later including the seven problems that can be inferred from the Chi study. The later version was
developed because version I (that did not include Chi problems) showed significant deviation from the dichotomy of introductory physics students as “novices” and physics graduate students as “experts”. We find that students’ ability to categorize problems depends upon the nature of the questions asked but the overall qualitative trends were not strongly dependent on the version of the problem set given to the students. It is not possible to compare our data directly with that in the Chi study because most of their questions are no longer available. Although no direct comparison is possible, in both versions of the problem sets we used, the percentage of introductory physics students who chose categories such as “ramp” and “pulley” was significantly lower than the percentages reported in the Chi study.
Moreover, the categorization performed by the calculus-based introductory physics students was significantly better than that performed by the algebra-based introductory physics students. Also, there was a large overlap between the categorization performed by calculus-based introductory physics students and the graduate students in physics that were assessed “good”. This large overlap in the performance of the two groups suggests that, unlike the characterization in the Chi study, there is indeed a wide distribution of expertise as assessed by the categorization task in both groups and it is not appropriate to classify all introductory physics students as “novices” and all physics graduate students as “experts”. We also find that the categorization performed by physics faculty members was significantly better than that performed by the graduate students. We note that, in the Chi study, the comparison was between the categorization performed by 8 introductory physics students (labeled novices) and 8 physics graduate students (labeled experts).
While there is a large overlap between the calculus-based introductory students and graduate students in terms of the percentage of categorization that was assessed as “good”, there
are different reasons for each group for the overlap. Unlike the introductory students, the category names of the physics graduate students never included “ramps” or “pulleys.” In this sense, graduate students were more sophisticated than the introductory students in choosing their categories. The categorization by the graduate students was often not assessed “good” for other reasons. Some examples of this are if they only placed a problem in a secondary category (e.g. “centripetal force”), placed a problem that involved two physics principles in only one principle category, misplaced a problem (e.g. placed a problem related to “impulse and momentum” concepts in an energy-related category), or placed problems in a category such as “velocity” instead of grouping problems based upon the physics principles. However, we note that, on an average, the graduate students were more likely than an introductory physics student to place a problem involving two physics principles correctly in both categories.
In the future, it will be useful to investigate how the introductory students’ and graduate students’ categorization will differ if they were given the names of the categories they could choose from (which would include both poor categories such as ramps and pulleys and good categories based upon the laws of physics) but were told that they need not use all of them and could even come up with their own categories. Future investigation will also explore the similarities and differences in introductory students’ and graduate students’ responses if they were asked to solve the problems or at least outline the solution procedure rather than only being asked to do the categorization. While our interviews with the introductory physics students asked them to outline the solution procedure, it will be revealing to carry out similar interviews with graduate students. We hypothesize that the graduate students will perform better at outlining the solution procedure for the problems the than the calculus-based introductory students, but the
amount of overlap between the two groups will be useful to analyze with regard to student development within a curriculum.
Finally, we postulate that inclusion of categorization tasks in instruction can enhance learning. The categorization task focuses on higher-order thinking skills and asks students to evaluate the similarity of solution despite the fact that the problems placed in the same category may have very different surface features (Schoenfeld 1985, Schoenfeld 1989, Schoenfeld 1992, Schoenfeld and Herman 1982, Bransford and Schwarz 1999, Newell 1990, National Research Council 1999a and 1999b, Simon and Kaplan 1989, Anderson 1999). Such activity rewards conceptual analysis and planning stages of quantitative problem solving and discourages the plug-and-chug approach. Without guidance, students often jump into implementing a problem solution without thinking whether a particular principle is applicable. A categorization task can be used as a tool to help students learn effective problem solving and organize their knowledge hierarchically because such a task can guide students to focus on the similarity of problems based upon the underlying principles rather than focusing on the specific contexts (Hardiman et al. 1989, Dufresne et al. 1992). One instructional strategy for incorporating a categorization task is to give such a task to small groups of introductory physics students with different levels of expertise. One could ask students to categorize problems based upon similarity of solution, and then discuss and debate why different problems should be placed in the same group without asking them to solve the problems explicitly. Then, there can be a class discussion about why some categorizations are better than others and students can be given a follow-up categorization task individually to ensure individual accountability.