CAREER: Predictors and consequences of early understanding of mathematical equivalence

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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.