Problem solving in schools and beyond: Transitions from the naive to the neophyte to the master

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Abstract
The naive learner's knowledge may be characterized in terms of rules and higher‐order rules that are not adequate individually for solving desired problems, but which by proper combination can be made so. The neophyte's knowledge is likened to knowing explicit rules for solving particular classes of problems. The master's, by way of contrast, corresponds to knowing rules consisting of more efficient procedures which operate on relatively complex structures. Processes of transition from naive to neophyte and from neophyte to master are shown to be explicable in terms of interactions among appropriate higher and lower‐order rules governed by a single universal control mechanism. Incidental comparisions arc made to other cognitive theories.