Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore, MD 21218, USA.
Proc Natl Acad Sci U S A. 2012 Jul 10;109(28):11116-20. doi: 10.1073/pnas.1200196109. Epub 2012 Jun 25.
It has been difficult to determine how cognitive systems change over the grand time scale of an entire life, as few cognitive systems are well enough understood; observable in infants, adolescents, and adults; and simple enough to measure to empower comparisons across vastly different ages. Here we address this challenge with data from more than 10,000 participants ranging from 11 to 85 years of age and investigate the precision of basic numerical intuitions and their relation to students' performance in school mathematics across the lifespan. We all share a foundational number sense that has been observed in adults, infants, and nonhuman animals, and that, in humans, is generated by neurons in the intraparietal sulcus. Individual differences in the precision of this evolutionarily ancient number sense may impact school mathematics performance in children; however, we know little of its role beyond childhood. Here we find that population trends suggest that the precision of one's number sense improves throughout the school-age years, peaking quite late at ∼30 y. Despite this gradual developmental improvement, we find very large individual differences in number sense precision among people of the same age, and these differences relate to school mathematical performance throughout adolescence and the adult years. The large individual differences and prolonged development of number sense, paired with its consistent and specific link to mathematics ability across the age span, hold promise for the impact of educational interventions that target the number sense.
确定认知系统在整个生命周期的宏大时间尺度上是如何变化的一直很困难，因为很少有认知系统被很好地理解；可以在婴儿、青少年和成年人中观察到；并且足够简单，可以进行测量，以便在非常不同的年龄段进行比较。在这里，我们使用来自 11 至 85 岁的 10000 多名参与者的数据来应对这一挑战，并研究基本数值直觉的精确性及其与学生在整个生命周期中学校数学表现的关系。我们都有一个基础的数感，这个数感在成年人、婴儿和非人类动物中都有观察到，而且在人类中，是由顶内沟的神经元产生的。这种进化古老的数感的精确性个体差异可能会影响儿童的学校数学表现；然而，我们对其在儿童期之外的作用知之甚少。在这里，我们发现人口趋势表明，人们的数感精确性在整个学龄期都在提高，在 30 岁左右达到顶峰。尽管有这种逐渐的发展提高，但我们发现，具有相同年龄的人的数感精确性存在很大的个体差异，而且这些差异与整个青春期和成年期的学校数学表现有关。数感的个体差异很大，发展时间很长，而且与整个年龄段的数学能力有着一致而具体的联系，这对数感的教育干预措施可能产生影响。
