Vanbinst Kiran, Ceulemans Eva, Ghesquière Pol, De Smedt Bert
Parenting and Special Education Research Unit, Faculty of Psychology and Educational Sciences, KU Leuven, B-3000 Leuven, Belgium.
Parenting and Special Education Research Unit, Faculty of Psychology and Educational Sciences, KU Leuven, B-3000 Leuven, Belgium.
J Exp Child Psychol. 2015 May;133:29-46. doi: 10.1016/j.jecp.2015.01.003. Epub 2015 Feb 27.
The current longitudinal study tried to capture profiles of individual differences in children's arithmetic fact development. We used a model-based clustering approach to delineate profiles of arithmetic fact development based on empirically derived differences in parameters of arithmetic fact mastery repeatedly assessed at the start of three subsequent school years: third, fourth, and fifth grades. This cluster analysis revealed three profiles in a random sample-slow and variable (n = 8), average (n = 24), and efficient (n = 20)-that were marked by differences in children's development in arithmetic fact mastery from third grade to fifth grade. These profiles did not differ in terms of age, sex, socioeconomic status, or intellectual ability. In addition, we explored whether these profiles varied in cognitive skills that have been associated with individual differences in single-digit arithmetic. The three profiles differed in nonsymbolic and symbolic numerical magnitude processing as well as phonological processing, but not in digit naming or working memory. After also controlling for cluster differences in general mathematics achievement and reading ability, only differences in symbolic numerical magnitude processing remained significant. Taken together, our longitudinal data reveal that symbolic numerical magnitude processing represents an important variable that contributes to individual variability in children's acquisition of arithmetic facts.
当前的纵向研究试图描绘儿童算术事实发展中个体差异的概况。我们使用基于模型的聚类方法，根据在随后三个学年（三年级、四年级和五年级）开始时反复评估的算术事实掌握参数的经验性差异，来描绘算术事实发展的概况。这项聚类分析在一个随机样本中揭示了三种概况——缓慢且不稳定型（n = 8）、平均型（n = 24）和高效型（n = 20）——其特点是儿童从三年级到五年级在算术事实掌握方面的发展存在差异。这些概况在年龄、性别、社会经济地位或智力能力方面并无差异。此外，我们探究了这些概况在与个位数算术个体差异相关的认知技能方面是否有所不同。这三种概况在非符号和符号数字大小处理以及语音处理方面存在差异，但在数字命名或工作记忆方面没有差异。在控制了一般数学成绩和阅读能力的聚类差异后，只有符号数字大小处理方面的差异仍然显著。综上所述，我们的纵向数据表明，符号数字大小处理是一个重要变量，它导致了儿童在算术事实习得方面的个体差异。
