Centre for Neuroscience in Education, Faculty of Education, University of Cambridge, UK.
Behav Brain Funct. 2010 Feb 18;6:13. doi: 10.1186/1744-9081-6-13.
The development of an evolutionarily grounded analogue magnitude representation linked to the parietal lobes is frequently thought to be a major factor in the arithmetic development of humans. We investigated the relationship between counting and the development of magnitude representation in children, assessing also children's knowledge of number symbols, their arithmetic fact retrieval, their verbal skills, and their numerical and verbal short-term memory.
The magnitude representation was tested by a non-symbolic magnitude comparison task. We have perfected previous experimental designs measuring magnitude discrimination skills in 65 children kindergarten (4-7-year-olds) by controlling for several variables which were not controlled for in previous similar research. We also used a large number of trials which allowed for running a full factorial ANOVA including all relevant factors. Tests of verbal counting, of short term memory, of number knowledge, of problem solving abilities and of verbal fluency were administered and correlated with performance in the magnitude comparison task.
Verbal counting knowledge and performance on simple arithmetic tests did not correlate with non-symbolic magnitude comparison at any age. Older children performed successfully on the number comparison task, showing behavioural patterns consistent with an analogue magnitude representation. In contrast, 4-year-olds were unable to discriminate number independently of task-irrelevant perceptual variables. Sensitivity to irrelevant perceptual features of the magnitude discrimination task was also affected by age, and correlated with memory, suggesting that more general cognitive abilities may play a role in performance in magnitude comparison tasks.
We conclude that young children are not able to discriminate numerical magnitudes when co-varying physical magnitudes are methodically pitted against number. We propose, along with others, that a rather domain general magnitude representation provides the later basis for a specialized representation of numerical magnitudes. For this representational specialization, the acquisition of the concept of abstract numbers, together with the development of other cognitive abilities, is indispensable.
与顶叶相关的进化基础模拟数量表示的发展通常被认为是人类算术发展的主要因素。我们研究了儿童计数与数量表示发展之间的关系，同时评估了儿童对数字符号的认识、他们的算术事实检索、他们的言语技能以及他们的数字和言语短期记忆。
通过非符号数量比较任务来测试数量表示。我们通过控制以前的类似研究中未控制的几个变量，改进了以前测量 65 名幼儿园儿童（4-7 岁）数量辨别技能的实验设计。我们还使用了大量的试验，允许进行包括所有相关因素的全因子方差分析。进行了言语计数、短期记忆、数字知识、解决问题能力和言语流畅性的测试，并与数量比较任务的表现相关联。
言语计数知识和简单算术测试的表现与任何年龄的非符号数量比较都没有相关性。年龄较大的儿童在数字比较任务中表现出色，表现出与模拟数量表示一致的行为模式。相比之下，4 岁儿童无法独立于任务无关的感知变量来区分数字。对数量辨别任务的无关感知特征的敏感性也受到年龄的影响，并与记忆相关，这表明更一般的认知能力可能在数量比较任务的表现中发挥作用。
我们得出的结论是，当系统地将物理数量与数字进行对比时，年幼的儿童无法辨别数字大小。我们与其他人一起提出，一个相当普遍的数量表示为后来专门表示数字数量提供了基础。对于这种表示的专业化，抽象数字概念的获取以及其他认知能力的发展是不可或缺的。
