Checking for Dimensional Correctness in Physics Equations

C. W. Liew and D. E. Smith

One of the key components of an Intelligent Tutoring System (ITS) is the mechanism for reasoning about the student’s input. The impact of this component extends far beyond the presentation of the lesson material to the success of the system itself. It affects how precisely the system can pinpoint student errors and thus the subsequent help that the system provides. This paper describes an example of a class of physics problems whose answers are most naturally represented as systems of algebraic equations. Analyzing such input requires not only an understanding of algebra but also knowledge of physics concepts. This paper describes a technique for determining the dimensional consistency of algebraic equations in physics using constraint propagation. Unlike other methods, it does not depend on the user defining the dimensions of each variable. Instead, it uses a knowledge base of well known physics variables combined with constraint propagation to determine both the dimensions of values (variables and constants) and also the dimensional consistency of an equation. The technique has been successfully tested on answers obtained from a class of college level introductory physics students.

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