CAREER: Predictors and consequences of early understanding of mathematical equivalence

职业：早期理解数学等价的预测因素和后果

• 批准号: 1054467
• 负责人: Nicole McNeil
• 金额: $ 39.26万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-04-01 至 2017-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1054467&HistoricalAwards=false
• 关键词: CAREER; Predictors; consequences; early; understanding

The purpose of this project is to longitudinally investigate (K-Grade 6) a child's understanding of mathematical equivalence. This project will answer two major research questions: (1) What are the origins of individual differences in a child's early understanding of mathematical equivalence? And (2) What are the long-term consequences of having a poor understanding of mathematical equivalence? To answer the first research question, the PI will identify skills (early number sense, relational thinking, and cognitive flexibility) in kindergarten (Time 1 in the longitudinal design) that predict individual differences in understanding of mathematical equivalence in later grades, while controlling for gender, SES, and IQ. To answer the second research question, the PI will measure a child's understanding of mathematical equivalence at second grade (Time 2), and then she will use this measure to predict mathematics achievement at the third, fourth, fifth, and sixth grades. At the sixth grade, the PI will also measure algebra readiness. For answering research question 2, the PI will control for gender, IQ, and computational fluency. The development of algebraic thinking is a timely topic with national and international interests. This project takes a unique approach to explore ways to develop student algebraic thinking, especially the use of a longitudinal design. In addition, this project is exemplary for interdisciplinary work on integrating cognitive psychology and mathematics education. The findings from this project can have both theoretical and practical implications.

这个项目的目的是纵向调查（K级6）儿童的理解数学等价。 本研究将回答两个主要的研究问题：（1）儿童早期数学等价理解的个体差异的根源是什么？以及（2）对数学等价性理解不足的长期后果是什么？ 为了回答第一个研究问题，PI将确定幼儿园（纵向设计中的时间1）中的技能（早期数字感，关系思维和认知灵活性），这些技能可以预测以后年级对数学等价理解的个体差异，同时控制性别，SES和IQ。 为了回答第二个研究问题，PI将测量一个孩子在二年级（时间2）时对数学等价性的理解，然后她将用这个测量来预测三年级、四年级、五年级和六年级的数学成绩。 在六年级，PI还将衡量代数准备。 为了回答研究问题2，PI将控制性别、智商和计算流畅性。 代数思维的发展是一个及时的话题与国家和国际利益。 这个项目采取了一种独特的方法来探索如何发展学生的代数思维，特别是使用纵向设计。 此外，该项目是整合认知心理学和数学教育的跨学科工作的典范。 该项目的研究结果具有理论和实践意义。