Learning in Mathematically-Based Domains: Understanding and Generalizing Obstacle Cancellations

Mathematical reasoning provides the basis for problem solving and learning in many complex domains. A model for applying explanation-based learning in mathematically-based domains is presented, and an implemented learning system is described. In explanation-based learning, a specific problem’s solution is generalized into a form that can be later used to solve conceptually similar problems. The presented system’s mathematical reasoning processes are guided by the manner in which variables are cancelled in specific problem solutions. Analyzing the cancellation of obstacles – variables that preclude the direct evaluation of the problem’s unknown – leads to the generalization of the specific solution. Two important general issues in explanation-based learning are also addressed. Namely, generalizing the number of entities in a situation and acquiring efficiently-applicable concepts.

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