Dixon J A, Moore C F
University of Wisconsin, Madison, USA.
Mem Cognit. 1997 May;25(3):395-412. doi: 10.3758/bf03211295.
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.
进行了两项实验来研究在评估数学策略时所使用的直观问题表征的本质。第一个实验在两种表征之间进行了测试：一种由原理组成的表征和一种综合表征。受试者仅根据他们对一组温度混合问题给出的答案来判断未见过的数学策略的正确性。给定答案与正确答案的距离以及答案是否违反了温度混合的原理之一被加以操控。结果支持了原理表征假说。在第二个实验中，我们通过一段关于其中一个原理的简短说明来操控受试者对酸混合任务的理解。受试者随后完成了一项旨在测量他们对问题领域理解的估计任务。接着呈现了第一个实验中的评估任务，但使用的是酸混合而非温度混合。结果表明，对该领域的直观理解介导了说明对问题评估的影响。此外，结果支持了这样的假说，即受试者在其直观理解和数学策略之间执行一个映射过程。
