The relation between problem categorization and problem solving among experts and novices

Abstract

These investigations were conducted to examine the relationship between problem-solving ability and the criteria used to decide that two classical mechanics problems would be solved similarly. We began by comparing experts and novices on a similarity judgment task and found that the experts predominantly relied on the problems' deep structures in deciding on similarity of solution, although the presence of surface-feature similarity had a clear adverse effect on performance. The novices relied predominantly on surface features, but were capable of using the problems' deep structures under certain conditions. In a second experiment, we compared groups of novices, at the same level of experience, who tended to employ different types of reasoning in making similarity judgments. Compared to novices who relied predominantly on surface features, novices who made greater use of principles tended to categorize problems similarly to how experts categorized them, as well as score higher in problem solving. These results suggest that principles play a fundamental role in the organization of conceptual and procedural knowledge for good problem solvers at all levels.

Conceptual problem solving in high school physics

“…[25] but modified to be grade appropriate. Students must select one of two problems that would be solved most like a third "model" problem.…”

“…By selecting appropriate principle(s) or concept(s) (e.g., work-energy theorem or conservation of energy), and specifying initial conditions and problem context (e.g., whether or not frictional forces were present, whether a body possessed kinetic and/or potential energies in some initial state), conceptual qualitative analyses of problems could be performed, which in turn resulted in one or more equations that the tool generated to fit the specific analysis performed. Compared to students who experienced a more traditional control treatment, students who used the analysis tool were better able to categorize problems according to the underlying principle [25] and to solve problems.…”

Development of a mechanics reasoning inventory

“…It is not obvious, however, what form such an assessment should take (see, e.g., [1,2,3]). One of the earliest findings of physics education research is that experts are adept at classifying physics problems by the principles that will most readily lead to a solution, while novices fixate on surface features of problems which have little bearing on the solution [4,5]. The favored instrument in this early research was the classification of a large number of problems into groups based on similarity of solution.…”

Leader Experience and the Identification of Challenges in a Stability and Support Operation

“…In the expert-novice literature, this sophisticated understanding is referred to as knowledge structure (Hardiman et al, 1989), representation of knowledge (Glaser & Chi, 1988), mental models (Hanisch, Kramer, & Hulin, 1991), or schema (Chi, Feltovich, & Glaser, 1981;Davies, 1994;Olsen, 2004). These schema allow experts to perceive large patterns, better understand the nature of a problem, set parameters for problem solving, clearly visualize potential solutions to a problem, comprehend constraints and contingencies associated with potential solutions, and make good decisions (Cellier et al, 1997, Glaser & Chi, 1988Lord & Hall, 2005;Shanteau, 1992).…”

“…While experts use principles and abstract concepts to group information, novices group by actual objects or features of a problem. For example, Hardiman, Dufresne, and Mestre (1989) conducted a study in which experts and novices performed a categorization task of 32 physics problems. Subjects were asked to compare 24 problems to eight model problems, which represented certain physics principles that would be used to solve the problem.…”