Department of Psychology, Emory University, Atlanta, GA 30322, USA.
Proc Natl Acad Sci U S A. 2012 Nov 13;109(46):18737-42. doi: 10.1073/pnas.1207212109. Epub 2012 Oct 22.
Humans and nonhuman animals share the capacity to estimate, without counting, the number of objects in a set by relying on an approximate number system (ANS). Only humans, however, learn the concepts and operations of symbolic mathematics. Despite vast differences between these two systems of quantification, neural and behavioral findings suggest functional connections. Another line of research suggests that the ANS is part of a larger, more general system of magnitude representation. Reports of cognitive interactions and common neural coding for number and other magnitudes such as spatial extent led us to ask whether, and how, nonnumerical magnitude interfaces with mathematical competence. On two magnitude comparison tasks, college students estimated (without counting or explicit calculation) which of two arrays was greater in number or cumulative area. They also completed a battery of standardized math tests. Individual differences in both number and cumulative area precision (measured by accuracy on the magnitude comparison tasks) correlated with interindividual variability in math competence, particularly advanced arithmetic and geometry, even after accounting for general aspects of intelligence. Moreover, analyses revealed that whereas number precision contributed unique variance to advanced arithmetic, cumulative area precision contributed unique variance to geometry. Taken together, these results provide evidence for shared and unique contributions of nonsymbolic number and cumulative area representations to formally taught mathematics. More broadly, they suggest that uniquely human branches of mathematics interface with an evolutionarily primitive general magnitude system, which includes partially overlapping representations of numerical and nonnumerical magnitude.
人类和非人类动物都具有通过近似数量系统（ANS）估算一组物体数量的能力，而无需进行计数。然而，只有人类才会学习符号数学的概念和运算。尽管这两种量化系统之间存在巨大差异，但神经和行为学研究结果表明它们之间存在功能联系。另一项研究表明，ANS 是更大、更通用的数量表示系统的一部分。关于认知交互和数量以及其他数量（如空间范围）的共同神经编码的报告，促使我们提出这样的问题：非数值数量是否以及如何与数学能力相互作用。在两项数量比较任务中，大学生在不进行计数或明确计算的情况下估计两个数组中哪个数量或累计面积更大。他们还完成了一系列标准化的数学测试。数量和累计面积精度（通过在数量比较任务中的准确性来衡量）的个体差异与数学能力的个体间变异性相关，尤其是高级算术和几何，即使在考虑到一般智力方面之后也是如此。此外，分析表明，虽然数量精度对高级算术有独特的贡献，但累计面积精度对几何有独特的贡献。总的来说，这些结果为非符号数量和累计面积表示对正式教授的数学的共同和独特贡献提供了证据。更广泛地说，它们表明，人类特有的数学分支与进化上原始的通用数量系统相互作用，其中包括数字和非数字数量的部分重叠表示。
