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Two experiments were conducted to investigate the nature of the intuitive problem representation used in evaluating mathematical strategies. The first experiment tested between two representations: a representation composed of principles and an integrated representation. Subjects judged the correctness of unseen math strategies based only on the answers they produced for a set of temperature mixture problems. The distance of the given answers from the correct answers and whether the answers violated one of the principles of temperature mixture were manipulated. The results supported the principle representation hypothesis. In the second experiment we manipulated subjects' understanding of an acid mixture task with a brief paragraph of instruction on one of the principles. Subjects then completed an estimation task intended to measure their understanding of the problem domain. The evaluation task from the first experiment was then presented, but with acid mixture instead of temperature mixture. The results showed that intuitive understanding of the domain mediates the effect of instruction on evaluating problems. Additionally, the results supported the hypothesis that subjects perform a mapping process between their intuitive understanding and math strategies.

Characterizing the intuitive representation in problem solving: Evidence from evaluating mathematical strategies