Collaborative Research: Origins of Recursive Mathematical Knowledge in Childhood

这个项目将调查3至7岁的儿童如何学习计数规则。这个项目的主要目标是研究不同语言中计数的语言结构如何影响儿童学习递归和无穷大等核心数学概念的能力。因此，这项工作将对理解教给孩子的符号系统结构如何影响他们学习核心STEM概念的能力产生广泛的影响。该项目将促进跨学科研究，并将在加州大学圣地亚哥分校（一所授予博士学位的大学）和斯基德莫尔学院（在那里进行研究是本科生培训的一部分）之间建立一座合作桥梁。这将促进两个校区的新形式的培训，涵盖心理学，认知科学，语言学和教育学。研究人员将研究语言计数列表的结构-不同的语言-如何影响儿童学习核心数学概念。为了实现这一目标，研究人员将评估儿童的计数能力，并评估儿童在不计数时产生下一个数字序列的能力。这两项评估将使研究人员能够确定儿童是否获得了递归+1规则（“后继函数”）。研究人员将测试学习这种递归规则是否会导致儿童推断数字是无限的。最后，使用类似的方法，研究人员将研究学习数字是无限的是否可能导致儿童推断其他领域，如空间和时间，也是无限的。因此，研究人员将确定学习一个具体的计数规则系统如何引导儿童学习永远无法直接体验的抽象实体（如无穷大）。使用简单的行为方法，该项目解决了数学教育的一个核心属性，对数学教育实践具有重要意义。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project will investigate how children between the ages of 3 and 7 years learn about the rules that govern counting. The main goal of this project is to examine how the verbal structure of counting in different languages affects children's ability to learn core math concepts like recursion and infinity. Therefore, the work will have a broad impact on understanding how the structure of symbolic systems taught to children affect their ability to learn core STEM concepts. The project will foster interdisciplinary research, and will create a collaborative bridge between the University of California-San Diego, a PhD granting university, and Skidmore College, where research is conducted as part of undergraduate training. This will promote new forms of training on both campuses, spanning Psychology, Cognitive Science, Linguistics, and Education.Researchers will examine how the structure of the verbal count list - which differs across languages - affects how children learn core mathematical concepts. To accomplish this, researchers will assess how high children can count, and assess the ability of children to generate the next number in a sequence of numbers when not counting. These two assessments will allow the researchers to determine whether children have acquired a recursive +1 rule (the "successor function"). Researchers will test whether learning this recursive rule leads children to infer that numbers are infinite. Finally, using similar methods, the researchers will examine whether learning that numbers are infinite might lead children to infer that other domains, like space and time, are also infinite. Therefore, the researchers will determine how learning a concrete system of counting rules might lead children to learn about abstract entities (such as infinity) that can never be directly experienced. Using simple behavioral methods, the project addresses a central property of mathematics education with important implications for educational practices in mathematics.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.