Mental Representations in Fraction Comparison Holistic Versus Component-Based Strategies
Mental Representations in Fraction Comparison Holistic Versus Component-Based Strategies
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DOI：
10.1027/1618-3169/a000116
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发表时间：
2011-01-01
影响因子：
1.3
通讯作者：
Pierce, Benton H.
中科院分区：
文献类型：
--
作者：
Faulkenberry, Thomas J.;Pierce, Benton H.
在本研究中，我们考察了分数比较任务中使用的心理表征。成年人被要求快速准确地从电脑屏幕上显示的两个分数中较大的一个中选出一个，并提供他们所使用的策略类型的逐项试验报告。我们发现，成年人使用各种策略来比较分数，包括只知道答案，使用分数的整体知识来确定答案，以及使用基于分量的程序，如交叉乘法。在所有策略类型中，回归分析发现，反应时间显著地通过分数之间的数字距离进行预测，这表明参与者使用基于数量的表示来比较分数数量。此外，出现了问题大小效应的一个变种(例如，阿什克拉夫特，1992)，其中反应时间显著地通过两个组分的平均叉积来预测。这种效应主要在基于成分的策略中被发现，这表明策略选择在分数心理表征的形成中起着作用。
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.