Szkudlarek Emily, Zhang Haobai, DeWind Nicholas K, Brannon Elizabeth M
Department of Psychology, University of Pennsylvania, Philadelphia, PA, United States.
Front Hum Neurosci. 2022 Feb 25;16:752190. doi: 10.3389/fnhum.2022.752190. eCollection 2022.
Children bring intuitive arithmetic knowledge to the classroom before formal instruction in mathematics begins. For example, children can use their number sense to add, subtract, compare ratios, and even perform scaling operations that increase or decrease a set of dots by a factor of 2 or 4. However, it is currently unknown whether children can engage in a true division operation before formal mathematical instruction. Here we examined the ability of 6- to 9-year-old children and college students to perform symbolic and non-symbolic approximate division. Subjects were presented with non-symbolic (dot array) or symbolic (Arabic numeral) dividends ranging from 32 to 185, and non-symbolic divisors ranging from 2 to 8. Subjects compared their imagined quotient to a visible target quantity. Both children (Experiment 1 = 89, Experiment 2 = 42) and adults (Experiment 3 = 87) were successful at the approximate division tasks in both dots and numeral formats. This was true even among the subset of children that could not recognize the division symbol or solve simple division equations, suggesting intuitive division ability precedes formal division instruction. For both children and adults, the ability to divide non-symbolically mediated the relation between Approximate Number System (ANS) acuity and symbolic math performance, suggesting that the ability to calculate non-symbolically may be a mechanism of the relation between ANS acuity and symbolic math. Our findings highlight the intuitive arithmetic abilities children possess before formal math instruction.
在正式开始数学教学之前，儿童就已将直观的算术知识带入课堂。例如，儿童可以运用他们的数感进行加法、减法、比较比率，甚至进行缩放运算，即将一组点增加或减少2倍或4倍。然而，目前尚不清楚儿童在正式数学教学之前是否能够进行真正的除法运算。在此，我们研究了6至9岁儿童和大学生进行符号和非符号近似除法的能力。向受试者呈现范围从32到185的非符号（点阵）或符号（阿拉伯数字）被除数，以及范围从2到8的非符号除数。受试者将他们想象的商与一个可见的目标数量进行比较。儿童（实验1 = 89人，实验2 = 42人）和成年人（实验3 = 87人）在点阵和数字格式的近似除法任务中均取得成功。即使在那些不认识除号或无法解简单除法方程的儿童子集中也是如此，这表明直观除法能力先于正式的除法教学。对于儿童和成年人来说，非符号除法的能力介导了近似数字系统（ANS）敏锐度与符号数学表现之间的关系，这表明非符号计算能力可能是ANS敏锐度与符号数学之间关系的一种机制。我们的研究结果凸显了儿童在正式数学教学之前所具备的直观算术能力。
