Reeve Robert A, Gray Sarah A, Butterworth Brian L, Paul Jacob M
Melbourne School of Psychological Sciences, University of Melbourne, Melbourne, VIC, Australia.
Centre for Educational Neuroscience, University College London, London, United Kingdom.
Front Psychol. 2018 Aug 14;9:1498. doi: 10.3389/fpsyg.2018.01498. eCollection 2018.
We assessed the degree to which the variability in the time children took to solve single digit addition (SDA) problems longitudinally, predicted their ability to solve more complex mental addition problems. Beginning at 5 years, 164 children completed a 12-item SDA test on four occasions over 6 years. We also assessed their (1) digit span, visuospatial working memory, and non-verbal IQ, and (2) the speed with which they named single numbers and letters, as well the speed enumerating one to three dots as a measure of subitizing ability. Children completed a double-digit mental addition test at the end of the study. We conducted a latent profile analysis to determine if there were different SDA problem solving response time (PRT) variability patterns across the four test occasions, which yielded three distinct PRT variability patterns. In one pattern, labeled a typical acquisition pathway, mean PRTs were relatively low and PRT variability diminished over time. In a second pattern, label a delayed pathway, mean PRT and variability was high initially but diminished over time. In a third pattern, labeled a deficit pathway, mean PRT and variability remained relatively high throughout the study. We investigated the degree to which the three SDA PRT variability pathways were associated with (1) different cognitive ability measures, and (2) double-digit mental addition abilities. The deficit pathway differed from the typical and delayed pathway on the subitizing measure only, but not other measures; and the latter two pathways also differed from each other on the subitizing but not other measures. Double-digit mental addition problem solving success differed between each of the three pathways, and mean PRT variability differed between the typical and the delayed and deficit pathways. The latter two pathways did not differ from each other. The findings emphasize the value of examining individual differences in problem-solving PRT variability longitudinally as an index of math ability, and highlight the important of subitizing ability as a diagnostic index of math ability/difficulties.
我们纵向评估了儿童解决一位数加法（SDA）问题所需时间的变异性，对其解决更复杂心算加法问题能力的预测程度。从5岁开始，164名儿童在6年时间里分四次完成了一项包含12道题目的SDA测试。我们还评估了他们的（1）数字广度、视觉空间工作记忆和非言语智商，以及（2）他们说出单个数字和字母的速度，还有将一到三个点计数的速度，以此作为估算能力的衡量指标。在研究结束时，儿童完成了一项两位数心算测试。我们进行了潜在剖面分析，以确定在四次测试中是否存在不同的SDA问题解决反应时间（PRT）变异性模式，结果产生了三种不同的PRT变异性模式。在一种模式中，标记为典型习得途径，平均PRT相对较低，且PRT变异性随时间减少。在第二种模式中，标记为延迟途径，平均PRT和变异性最初较高，但随时间减少。在第三种模式中，标记为缺陷途径，整个研究过程中平均PRT和变异性一直相对较高。我们研究了这三种SDA PRT变异性途径与（1）不同认知能力指标，以及（2）两位数心算能力之间的关联程度。缺陷途径仅在估算指标上与典型途径和延迟途径不同，在其他指标上并无差异；而后两种途径在估算指标上也彼此不同，但在其他指标上无差异。三种途径中每一种的两位数心算问题解决成功率都有所不同，典型途径与延迟途径及缺陷途径之间的平均PRT变异性也不同。后两种途径彼此无差异。这些发现强调了纵向研究问题解决PRT变异性中的个体差异作为数学能力指标的价值，并突出了估算能力作为数学能力/困难诊断指标的重要性。
