DeWolf Melissa, Son Ji Y, Bassok Miriam, Holyoak Keith J
Department of Psychology, University of California, Los Angeles.
Department of Psychology, California State University, Los Angeles.
Cogn Sci. 2017 Nov;41(8):2053-2088. doi: 10.1111/cogs.12468. Epub 2017 Jan 17.
Why might it be (at least sometimes) beneficial for adults to process fractions componentially? Recent research has shown that college-educated adults can capitalize on the bipartite structure of the fraction notation, performing more successfully with fractions than with decimals in relational tasks, notably analogical reasoning. This study examined patterns of relational priming for problems with fractions in a task that required arithmetic computations. College students were asked to judge whether or not multiplication equations involving fractions were correct. Some equations served as structurally inverse primes for the equation that immediately followed it (e.g., 4 × 3/4 = 3 followed by 3 × 8/6 = 4). Students with relatively high math ability showed relational priming (speeded solution times to the second of two successive relationally related fraction equations) both with and without high perceptual similarity (Experiment 2). Students with relatively low math ability also showed priming, but only when the structurally inverse equation pairs were supported by high perceptual similarity between numbers (e.g., 4 × 3/4 = 3 followed by 3 × 4/3 = 4). Several additional experiments established boundary conditions on relational priming with fractions. These findings are interpreted in terms of componential processing of fractions in a relational multiplication context that takes advantage of their inherent connections to a multiplicative schema for whole numbers.
为何成年人对分数进行成分加工（至少在某些时候）可能是有益的呢？最近的研究表明，受过大学教育的成年人能够利用分数表示法的二分结构，在关系任务（尤其是类比推理）中，处理分数比处理小数更为成功。本研究在一项需要算术计算的任务中，考察了分数问题的关系启动模式。大学生被要求判断涉及分数的乘法等式是否正确。一些等式作为紧随其后的等式的结构逆启动项（例如，4×3/4 = 3 后面跟着 3×8/6 = 4）。数学能力相对较高的学生在有和没有高度感知相似性的情况下，都表现出关系启动（对两个连续的关系相关分数等式中的第二个等式，求解时间加快）（实验2）。数学能力相对较低的学生也表现出启动效应，但只有当结构逆等式对在数字间具有高度感知相似性时才会如此（例如，4×3/4 = 3 后面跟着 3×4/3 = 4）。另外几个实验确定了分数关系启动的边界条件。这些发现是根据在关系乘法情境中对分数的成分加工来解释的，这种加工利用了分数与整数乘法模式的内在联系。
