Gilmore Camilla K, McCarthy Shannon E, Spelke Elizabeth S
Learning Sciences Research Institute, University of Nottingham, Wollaton Road, Nottingham NG8 1BB, UK.
Nature. 2007 May 31;447(7144):589-91. doi: 10.1038/nature05850.
Symbolic arithmetic is fundamental to science, technology and economics, but its acquisition by children typically requires years of effort, instruction and drill. When adults perform mental arithmetic, they activate nonsymbolic, approximate number representations, and their performance suffers if this nonsymbolic system is impaired. Nonsymbolic number representations also allow adults, children, and even infants to add or subtract pairs of dot arrays and to compare the resulting sum or difference to a third array, provided that only approximate accuracy is required. Here we report that young children, who have mastered verbal counting and are on the threshold of arithmetic instruction, can build on their nonsymbolic number system to perform symbolic addition and subtraction. Children across a broad socio-economic spectrum solved symbolic problems involving approximate addition or subtraction of large numbers, both in a laboratory test and in a school setting. Aspects of symbolic arithmetic therefore lie within the reach of children who have learned no algorithms for manipulating numerical symbols. Our findings help to delimit the sources of children's difficulties learning symbolic arithmetic, and they suggest ways to enhance children's engagement with formal mathematics.
符号算术对于科学、技术和经济至关重要，但儿童掌握它通常需要数年的努力、指导和练习。成年人进行心算时，会激活非符号化的近似数字表征，如果这个非符号化系统受损，他们的表现就会受到影响。非符号化数字表征还使成年人、儿童甚至婴儿能够对点阵对进行加法或减法运算，并将得到的和或差与第三个点阵进行比较，前提是只需要近似精度。我们在此报告，已经掌握了口头计数且即将接受算术指导的幼儿，可以在其非符号化数字系统的基础上进行符号加法和减法运算。来自广泛社会经济背景的儿童在实验室测试和学校环境中都解决了涉及大数近似加法或减法的符号问题。因此，对于尚未学习过操作数字符号算法的儿童来说，符号算术的某些方面是可以掌握的。我们的研究结果有助于界定儿童学习符号算术困难的根源，并提出增强儿童对形式数学参与度的方法。
