Subgoal identification and error analysis in problem solving

Quantitative problem solving is the major ingredient of core pre-engineering physics courses. The analysis of problem-solving behaviors in these courses can provide an important source of information not only about how students approach problems in general, but how their performance might be enhanced through the development and assessment of instructional innovations. We have focused on the electromagnetics portion of our introductory physics sequence. This course has a failure rate exceeding 30%. Thus, any system for enhancing problem solving in this difficult course will significantly impact many students. A principal barrier to successful problem solving is lack of generalization, i.e. the ability to transfer knowledge and skills from one problem to another and to recognize classes of problems. The common tendency is to treat each problem as a separate entity to be approached by rigid application of memorized formulae, or simply by trial and error. Seemingly small changes in requirements or conditions can be met with bafflement. We have approached problem solving in two interlocked ways. One is the systematic analysis and classification of errors that students make when attempting standard problems in quizzes and exams. The second consists of breaking problems down into a sequence of subgoals. The results show that students often improperly identify both the correct operational equations and the appropriate subgoals required for solution. Our analysis is used to teach students more effective problem-solving strategies with a computerized tutorial.