Department of Psychology, Emory University, Atlanta, GA 30322, USA.
J Exp Child Psychol. 2013 Mar;114(3):375-88. doi: 10.1016/j.jecp.2012.09.015. Epub 2012 Nov 30.
Humans rely on two main systems of quantification; one is nonsymbolic and involves approximate number representations (known as the approximate number system or ANS), and the other is symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across development, recent studies with adolescents and school-aged children point to individual differences in the precision of these representations that, importantly, have been shown to relate to symbolic math competence even after controlling for general aspects of intelligence. Such findings suggest that the ANS, which humans share with nonhuman animals, interfaces specifically with a uniquely human system of formal mathematics. Other findings, however, point to a less straightforward picture, leaving open questions about the nature and ontogenetic origins of the relation between these two systems. Testing children across the preschool period, we found that ANS precision correlated with early math achievement but, critically, that this relation was nonlinear. More specifically, the correlation between ANS precision and math competence was stronger for children with lower math scores than for children with higher math scores. Taken together, our findings suggest that early-developing connections between the ANS and mathematics may be fundamentally discontinuous. Possible mechanisms underlying such nonlinearity are discussed.
人类依赖于两个主要的量化系统；一个是非符号的，涉及近似数量的表示（称为近似数量系统或 ANS），另一个是符号的，可以进行数量的精确计算。尽管 ANS 在整个发展过程中都很普遍，但最近对青少年和学龄儿童的研究表明，这些表示的精确性存在个体差异，重要的是，即使在控制了一般智力因素后，这些差异也与符号数学能力有关。这些发现表明，人类与非人类动物共有的 ANS 与正式数学的独特人类系统具体相关。然而，其他发现表明情况并非如此简单，这使得这两个系统之间的关系的性质和发生起源存在疑问。我们对整个学前阶段的儿童进行测试，发现 ANS 精度与早期数学成绩相关，但关键是，这种关系是非线性的。更具体地说，对于数学成绩较低的儿童，其 ANS 精度与数学能力之间的相关性比数学成绩较高的儿童更强。总之，我们的发现表明，ANS 和数学之间早期发展的联系可能是根本不连续的。讨论了这种非线性的潜在机制。
