Reasoning about systems of physics equations

Many problems in introductory Physics require the student to enter a system of algebraic equations as the answer. Tutoring systems must be able to understand the student's submission before they can generate useful feedback. This paper presents an approach that accepts from the student a system of equations, describing the physics of the problem and checks to see if it is correct. When it is not, the student's equation set is analyzed vis-a-vis one or more correct sets of equations, known physics concepts, and algebraic transformations. During this analysis credit-blame assignment is performed to identify one of several types of errors including 1) algebraic errors, 2) one or more omitted physics concepts, 3) incorrect instances of a required physics concept, and 4) use of an inappropriate physics concept. Experimental data collected from an introductory physics class is summarized and discussed vis-a-vis other methods. Results indicate that the techniques applied are effective,at localizing most errors but that more work is needed to distinguish between algebraic and conceptual errors.