Abstract
Most research in explanation-based learning involves relaxing constraints on the entities in a situation, rather than generalizing the number of entities themselves. Nonetheless, many important concepts require generalizing number. This can be accomplished in an explanation-based fashion by generalizing the structure of the explanations. PHYSICS 101 is a mathematical reasoning system, offered as a psychologically plausible model, that performs explanation-based learning in mathematically oriented domains. Mathematically based domains are an area where the strengths of explanation-based learning are particularly appropriate, because explanation-based learning supports the construction of large concepts by analyzing how smaller concepts can be pieced together to solve a specific problem. Combining “small” concepts to form “larger” ones is the basis of progress in mathematical domains. Obstacles are variables that preclude the direct evaluation of the unknown. Canceling these variables allows the determination of the value of the unknown. One important feature of analyzing variable cancellations is that the generalization of number is motivated.
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