Numerical Intuition Training as a Potential Tool to Improve Children's Math Skills

儿童早期数学学习为多种科学、技术、工程和数学（STEM）兴趣和职业提供了基础。然而，孩子们在学校和家里的早期数学经历差别很大。这个项目探讨了孩子们在学习形式数学之前所拥有的数字直觉是否可以被利用来提高数学成绩。两项研究将检验儿童非正式数值直觉和形式数学之间的联系。第一项研究包括学龄前儿童进行加减法运算。第二项研究包括小学高年级的孩子，对比率的理解以及这与分数的关系。数学教学中的一个重要问题是如何将定量推理的直观方面与使用数学符号来表示数字和运算联系起来。本项目由美国国家科学基金会EHR核心研究（ECR）项目支持。ECR项目强调在该领域产生基础知识的基础STEM教育研究。该项目的总体目标是评估非符号数学运算的训练是否有助于等效符号运算的性能。已有研究表明，原始数感是符号数学的基础。第一项研究考察了学龄前儿童的加法和减法。向孩子们展示了如何在不精确的加法和减法近似中组合点数组，以评估这是否提高了符号加法和减法的性能。第二个研究考察了二年级和四年级学生的比例推理。本研究探讨了非符号、近似比率推理的训练是否有助于比率的符号操作，以及这与儿童分数知识的关系。这两项研究都采用了一种实验设计，将儿童随机分配到训练条件中，并包括对数学知识（包括数字的符号和非符号表示）和执行功能的测试前和测试后评估。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Early mathematics learning for children provides the foundation for multiple Science, Technology, Engineering and Mathematics (STEM) interests and careers. However, early math experiences in school and at home differ dramatically among children. This project explores whether the numerical intuition that children possess before they learn formal mathematics can be harnessed to improve math performance. Two studies will examine the connections between children's informal numerical intuition and formal mathematics. The first study includes pre-school children performing addition and subtraction. The second study includes upper elementary children, the understanding of ratios and how this relates to fractions. An important question for mathematics teaching and learning is how to connect intuitive aspects of quantitative reasoning with the use of math symbols to represent numbers and operations. This project is supported by NSF's EHR Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field.The broad goal of the project is to assess whether training with non-symbolic mathematical operations facilitates performance on the equivalent symbolic operations. Prior research suggests that primitive number sense is foundational for symbolic mathematics. The first study examines addition and subtraction in pre-school children. Children are shown how to combine dot arrays in an imprecise approximation of addition and subtraction to assess whether this improves symbolic addition and subtraction performance. The second study examines ratio reasoning in second and fourth grade students. This study investigates whether training with non-symbolic, approximate ratio reasoning facilitates symbolic manipulation of ratios and how this relates to children's knowledge of fractions. Both studies use an experimental design with randomized assignment of children to training conditions and include pre-test and post-test assessments of mathematical knowledge (including symbolic and non-symbolic representations of number) and executive function.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.