Assessing Student Expertise in Introductory Physics with Isomorphic Problems. I. Performance on Nonintuitive Problem Pair from Introductory Physics.

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.