Collaborative Research: Origins of Recursive Mathematical Knowledge in Childhood

合作研究：童年递归数学知识的起源

基本信息

批准号：
1749518
负责人：
David Barner
金额：
$ 28.77万
依托单位：
University of California-San Diego
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-08-01 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1749518&HistoricalAwards=false
关键词：
Collaborative Research Origins Recursive Mathematical

项目摘要

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.

该项目将调查 3 至 7 岁的儿童如何学习计数规则。该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授给儿童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，并将在授予博士学位的加州大学圣地亚哥分校和斯基德莫尔学院之间建立合作桥梁，斯基德莫尔学院将研究作为本科生培训的一部分进行。这将促进两个校区的新形式培训，涵盖心理学、认知科学、语言学和教育领域。研究人员将研究不同语言之间不同的词汇计数表的结构如何影响儿童学习核心数学概念的方式。为了实现这一目标，研究人员将评估儿童的数数能力，并评估儿童在不数数时生成数字序列中下一个数字的能力。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孩子们推断出数字是无限的。最后，研究人员将使用类似的方法来检查学习数字是无限的是否会导致孩子们推断其他领域（例如空间和时间）也是无限的。因此，研究人员将确定学习具体的计数规则系统如何引导孩子们了解永远无法直接体验的抽象实体（例如无穷大）。该项目使用简单的行为方法，解决了数学教育的核心属性，对数学教育实践具有重要影响。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。

项目成果

期刊论文数量（3）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Starting small: exploring the origins of successor function knowledge

从小事做起：探索后继函数知识的起源

DOI：
10.1111/desc.13091
发表时间：
2021
期刊：
Developmental Science
影响因子：
3.7
作者：
Schneider, Rose M.;Pankonin, Ashlie;Schachner, Adena;Barner, David
通讯作者：
Barner, David

Counting to Infinity: Does Learning the Syntax of the Count List Predict Knowledge That Numbers Are Infinite?

数到无穷大：学习计数列表的语法是否可以预测数字是无穷大的知识？

DOI：
10.1111/cogs.12875
发表时间：
2020
期刊：
Cognitive Science
影响因子：
2.5
作者：
Chu, Junyi;Cheung, Pierina;Schneider, Rose M.;Sullivan, Jessica;Barner, David
通讯作者：
Barner, David

Do children use language structure to discover the recursive rules of counting?