Butterworth Brian
Institute of Cognitive Neuroscience, University College, London, UK.
J Child Psychol Psychiatry. 2005 Jan;46(1):3-18. doi: 10.1111/j.1469-7610.2004.00374.x.
Arithmetical skills are essential to the effective exercise of citizenship in a numerate society. How these skills are acquired, or fail to be acquired, is of great importance not only to individual children but to the organisation of formal education and its role in society.
The evidence on the normal and abnormal developmental progression of arithmetical abilities is reviewed; in particular, evidence for arithmetical ability arising from innate specific cognitive skills (innate numerosity) vs. general cognitive abilities (the Piagetian view) is compared.
These include evidence from infancy research, neuropsychological studies of developmental dyscalculia, neuroimaging and genetics. The development of arithmetical abilities can be described in terms of the idea of numerosity -- the number of objects in a set. Early arithmetic is usually thought of as the effects on numerosity of operations on sets such as set union. The child's concept of numerosity appears to be innate, as infants, even in the first week of life, seem to discriminate visual arrays on the basis of numerosity. Development can be seen in terms of an increasingly sophisticated understanding of numerosity and its implications, and in increasing skill in manipulating numerosities. The impairment in the capacity to learn arithmetic -- dyscalculia -- can be interpreted in many cases as a deficit in the concept in the child's concept of numerosity. The neuroanatomical bases of arithmetical development and other outstanding issues are discussed.
The evidence broadly supports the idea of an innate specific capacity for acquiring arithmetical skills, but the effects of the content of learning, and the timing of learning in the course of development, requires further investigation.
在一个具备数字素养的社会中，算术技能对于有效履行公民职责至关重要。这些技能是如何习得的，或者未能习得，不仅对个体儿童，而且对正规教育的组织及其在社会中的作用都极为重要。
回顾了关于算术能力正常和异常发展进程的证据；特别比较了源于先天特定认知技能（先天数字感）与一般认知能力（皮亚杰观点）的算术能力证据。
这些证据包括来自婴儿研究、发育性计算障碍的神经心理学研究、神经影像学和遗传学的证据。算术能力的发展可以用数字感的概念来描述——一组物体的数量。早期算术通常被认为是诸如集合合并等对集合运算对数字感的影响。儿童的数字感概念似乎是天生的，因为婴儿，甚至在出生后的第一周，似乎就能根据数字感区分视觉阵列。发展可以从对数字感及其含义的日益复杂的理解，以及在操作数字方面不断提高的技能来看待。学习算术能力的损害——计算障碍——在许多情况下可以被解释为儿童数字感概念的缺陷。讨论了算术发展的神经解剖学基础和其他突出问题。
证据广泛支持存在一种先天的获取算术技能的特定能力这一观点，但学习内容的影响以及发展过程中学习的时机，还需要进一步研究。
