Collaborative Research: Mental Abacus Education and Spatial Representations of Number

以空间形式学习数学如何影响儿童对数字的理解，以及支持这种理解的基本认知过程？拟议中的项目将通过调查“心算”的用户来探索这个问题，“心算”是世界各地儿童练习的心算系统。使用心算的孩子首先学习在物理设备上做算术，然后通过创造算盘的心理形象将这些计算内在化。通过在他们的脑海中移动珠子，孩子们以惊人的速度和准确性进行加法、减法、乘法和除法等计算。在三组实验中，我们将探索如何在算盘上可视化珠子做算术影响能力，如估计和比较数量，视觉注意力和工作记忆，以及儿童对早期数字概念的理解，如加法，位值和交换性。参与者将包括印度古吉拉特省的儿童，他们在算盘方面受过高度训练，以及美国的儿童和成人。我们的假设是，学习空间格式的数学不仅有助于早期理解数字，而且通过训练支持数字推理的潜在认知过程，为学习高等数学奠定了基础。

How does learning mathematics in a spatial format affect children's understanding of number, and the basic cognitive processes that support it? The proposed project will explore this question by investigating users of 'mental abacus' a system of mental arithmetic practiced by children throughout the world. Children who use mental abacus first learn to do arithmetic on a physical device, and then internalize these computations by creating a mental image of an abacus. By moving beads in their mental representation, children perform computations like addition, subtraction, multiplication, and division, all with astonishing speed and accuracy. In three sets of experiments, we will explore how visualizing beads on an abacus to do arithmetic affects abilities such as estimation and comparison of amount, visual attention and working memory, and children's understanding of early numerical concepts, such as addition, place value, and commutativity. Participants will include children in Gujarat Province, India, who are highly trained in abacus, as well as children and adults in the US. Our hypothesis is that learning to do math in a spatial format facilitates not only early understanding of number, but also lays the groundwork for learning advanced mathematics, by training the underlying cognitive processes that support numerical reasoning.