Abstract
Investigations related to expertise in problem solving and ability to transfer learning from one context to another are important for developing strategies to help students perform more expert-like tasks. Here we analyze written responses to a pair of non-intuitive isomorphic problems given to introductory physics students and discussions with a subset of students about them. Students were asked to explain their reasoning for their written responses. We call the paired problems isomorphic because they require the same physics principle to solve them. However, the initial conditions are different and the frictional force is responsible for increasing the linear speed of an object in one of the problems while it is responsible for decreasing the linear speed in the other problem. We categorize student responses and evaluate student performance within the context of their evolving expertise. We compare and contrast the patterns of student categorization for the two isomorphic problems. We discuss why certain incorrect responses were better than others and shed light on the evolution of students' expertise. We compare the performance of students who worked on both isomorphic problems with those who worked only on one of the problems to understand whether students recognized their underlying similarity and whether isomorphic pairs gave students additional insight in solving each problem.
Highlights
Developing expertise in problem solving constitutes a major goal of most physics courses.[1,2,3,4,5] Problem solving can be defined as any purposeful activity where one is presented with a novel situation and devises and performs a sequence of steps to achieve a set goal.[6]
The initial linear speed was nonzero in the pool ball problem but not in the other. Students who solved both problems in the rotational and rolling motion IPP sometimes used different knowledge resources because the initial conditions are very different for the two problems
The fact that the linear velocity of the pool ball must decrease in order to make it roll made the “higher means lower vf” idea almost twice as prevalent as in the spinning wheel problem, where the linear speed must increase for the rolling condition to hold
Summary
Developing expertise in problem solving constitutes a major goal of most physics courses.[1,2,3,4,5] Problem solving can be defined as any purposeful activity where one is presented with a novel situation and devises and performs a sequence of steps to achieve a set goal.[6] Both knowledge and experience are required to solve the problem efficiently and effectively. Genuine problem solving is not algorithmic; it is heuristic. The range of potential solution trajectories that different people may follow to achieve the goal can be called the problem space.[1] For each problem, the problem space is very large and based upon one’s expertise; people may traverse very different paths in this space which can analogically be visualized as a mazelike structure
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