Symbolic arithmetic knowledge without instruction
Symbolic arithmetic knowledge without instruction
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DOI：
10.1038/nature05850
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发表时间：
2007-05-31
期刊：
影响因子：
64.8
通讯作者：
Spelke, Elizabeth S.
中科院分区：
文献类型：
--
作者：
Gilmore, Camilla K.;McCarthy, Shannon E.;Spelke, Elizabeth S.
符号算术是科学，技术和经济学的基础，但儿童的习得通常需要多年的努力，指导和训练（1，2）。当成年人进行心算时，他们会激活非符号的近似数字表征（3，4），如果这种非符号系统受损，他们的表现就会受到影响（5）。非符号数字表示也允许成人，儿童，甚至婴儿添加或减去点阵列对，并将所得的总和或差异与第三个阵列进行比较，前提是只需要近似的精度（6-10）。在这里，我们报告说，幼儿，谁掌握了口头计数和算术指令的门槛，可以建立在他们的非符号数字系统执行符号加法和减法（11-15）。在实验室测试和学校环境中，来自不同社会经济阶层的儿童都能解决涉及大数近似加减的符号问题。因此，符号算术的各个方面都在那些没有学会处理数字符号的算法的孩子们的范围之内。我们的研究结果有助于界定儿童学习符号算术困难的来源，并提出了提高儿童参与正规数学的方法。
Symbolic arithmetic is fundamental to science, technology and economics, but its acquisition by children typically requires years of effort, instruction and drill(1,2). When adults perform mental arithmetic, they activate nonsymbolic, approximate number representations(3,4), and their performance suffers if this nonsymbolic system is impaired(5). 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(6-10). 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(11-15). 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.