This research examines the process of learning problem solving with minimal requirements for a priori knowledge and teacher involvement. Experience indicates that knowledge about the problem solving task can be used to improve problem solving performance. This research addresses the issues of what knowledge is useful, how it is applied during problem solving, and how it can be acquired. For each operator used in the problem solving domain, knowledge is incrementally learned concerning why it is

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... useful, when it is applicable, and what transformation it performs. The method of experimental goal regression is introduced for improving the learning rate by approximating the results of analytic learning. The ideas are formalized in an algorithm for learning and problem solving and demonstrated with examples from the domains of simultaneous linear equations and symbolic integration. Overview of the learning system PET can be viewed as a learning apprentice system, which Mitchell, Mahadevan, and Steinberg (1985) have defined as: