CAREER: Predictors and consequences of early understanding of mathematical equivalence

这个项目的目的是纵向调查（k - 6年级）儿童对数学等效的理解。本项目将回答两个主要的研究问题：(1)儿童早期对数学等值理解的个体差异的来源是什么？(2)对数学等价理解不佳的长期后果是什么？为了回答第一个研究问题，PI将识别幼儿园（纵向设计中的时间1）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效性理解的个体差异，同时控制性别，社会经济地位和智商。为了回答第二个研究问题，PI将测量孩子在二年级（时间2）对数学等效的理解，然后她将使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也将衡量代数的准备程度。对于回答研究问题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具有国家和国际利益的及时话题。该项目采用独特的方法来探索培养学生代数思维的方法，特别是纵向设计的使用。此外，该项目是将认知心理学与数学教育相结合的跨学科工作的典范。这个项目的研究结果具有理论和实践意义。

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.