The approximate number system and its relation to early math achievement: evidence from the preschool years.
The approximate number system and its relation to early math achievement: evidence from the preschool years.
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DOI：
10.1016/j.jecp.2012.09.015
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发表时间：
2013-03
影响因子：
2.6
通讯作者：
Lourenco SF
中科院分区：
文献类型：
--
作者：
Bonny JW;Lourenco SF
人类依赖于两个主要的量化系统-一个是非符号的，涉及近似数字表示（称为近似数字系统或ANS），另一个是符号的，允许精确计算数字。尽管ANS在整个发育过程中普遍存在，但最近对青少年和学龄儿童的研究指出，这些表征的精确度存在个体差异，重要的是，即使在控制了智力的一般方面之后，这些表征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享的ANS与人类特有的形式数学系统有着特定的接口。然而，其他研究结果指向一个不那么简单的画面，留下了关于这两个系统之间关系的性质和个体发生起源的悬而未决的问题。通过对学龄前儿童的测试，我们发现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，数学成绩较低的孩子比数学成绩较高的孩子的ANS精度和数学能力之间的相关性更强。总之，我们的研究结果表明，早期发展的ANS和数学之间的联系可能是根本不连续的。这种非线性的可能机制进行了讨论。
Humans rely on two main systems of quantification - one is non-symbolic and involves approximate number representations (known as the approximate number system or ANS), 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, which, 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 non-linear. 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 non-linearity are discussed.
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