Faulkenberry Thomas J, Pierce Benton H
Department of Psychology and Special Education, Texas A&M University - Commerce, TX 75429-3011, USA.
Exp Psychol. 2011;58(6):480-9. doi: 10.1027/1618-3169/a000116.
In this study, we investigated the mental representations used in a fraction comparison task. Adults were asked to quickly and accurately pick the larger of two fractions presented on a computer screen and provide trial-by-trial reports of the types of strategies they used. We found that adults used a variety of strategies to compare fractions, ranging among just knowing the answer, using holistic knowledge of fractions to determine the answer, and using component-based procedures such as cross multiplication. Across all strategy types, regression analyses identified that reaction times were significantly predicted by numerical distance between fractions, indicating that the participants used a magnitude-based representation to compare the fraction magnitudes. In addition, a variant of the problem-size effect (e.g., Ashcraft, 1992) appeared, whereby reaction times were significantly predicted by the average cross product of the two fractions. This effect was primarily found for component-based strategies, indicating a role for strategy choice in the formation of mental representations of fractions.
在本研究中，我们调查了分数比较任务中使用的心理表征。要求成年人快速准确地从电脑屏幕上呈现的两个分数中挑选出较大的那个，并逐次报告他们所使用策略的类型。我们发现，成年人使用了多种策略来比较分数，包括仅仅知道答案、利用分数的整体知识来确定答案，以及使用基于成分的程序（如交叉相乘）。在所有策略类型中，回归分析表明，分数之间的数值距离能够显著预测反应时间，这表明参与者使用基于大小的表征来比较分数大小。此外，出现了问题大小效应的一种变体（例如，阿什克拉夫特，1992），即两个分数的平均交叉积能够显著预测反应时间。这种效应主要在基于成分的策略中发现，表明策略选择在分数心理表征的形成中发挥了作用。
