Department of Psychology, University of Pennsylvania, Philadelphia, PA 19104, USA.
Department of Psychology, University of Pennsylvania, Philadelphia, PA 19104, USA.
J Exp Child Psychol. 2021 Jul;207:105116. doi: 10.1016/j.jecp.2021.105116. Epub 2021 Mar 5.
Prior work indicates that children have an untrained ability to approximately calculate using their approximate number system (ANS). For example, children can mentally double or halve a large array of discrete objects. Here, we asked whether children can perform a true multiplication operation, flexibly attending to both the multiplier and multiplicand, prior to formal multiplication instruction. We presented 5- to 8-year-olds with nonsymbolic multiplicands (dot arrays) or symbolic multiplicands (Arabic numerals) ranging from 2 to 12 and with nonsymbolic multipliers ranging from 2 to 8. Children compared each imagined product with a visible comparison quantity. Children performed with above-chance accuracy on both nonsymbolic and symbolic approximate multiplication, and their performance was dependent on the ratio between the imagined product and the comparison target. Children who could not solve any single-digit symbolic multiplication equations (e.g., 2 × 3) on a basic math test were nevertheless successful on both our approximate multiplication tasks, indicating that children have an intuitive sense of multiplication that emerges independent of formal instruction about symbolic multiplication. Nonsymbolic multiplication performance mediated the relation between children's Weber fraction and symbolic math abilities, suggesting a pathway by which the ANS contributes to children's emerging symbolic math competence. These findings may inform future educational interventions that allow children to use their basic arithmetic intuition as a scaffold to facilitate symbolic math learning.
先前的研究表明，儿童具有未经训练的能力，可以使用他们的近似数量系统（ANS）进行近似计算。例如，儿童可以在心理上双倍或减半大量离散的物体。在这里，我们在正式乘法教学之前，询问儿童是否可以灵活地关注乘数和被乘数，从而执行真正的乘法运算。我们向 5 至 8 岁的儿童呈现非符号乘数（点数组）或符号乘数（阿拉伯数字），范围从 2 到 12，以及非符号乘数，范围从 2 到 8。儿童将每个想象的产品与可见的比较数量进行比较。儿童在非符号和符号近似乘法上的表现都超过了机会水平，并且他们的表现取决于想象的产品和比较目标之间的比率。在基本数学测试中无法解决任何单个数字符号乘法问题（例如 2×3）的儿童，尽管如此，他们在我们的两个近似乘法任务中都取得了成功，这表明儿童具有独立于符号乘法教学的乘法直觉。非符号乘法表现中介了儿童韦伯分数和符号数学能力之间的关系，这表明 ANS 为儿童正在发展的符号数学能力提供了一种途径。这些发现可能会为未来的教育干预提供信息，这些干预措施允许儿童使用他们的基本算术直觉作为支架，促进符号数学学习。
