Integrating Rational Number Sense

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This award was provided as part of NSF's Social, Behavioral and Economic Sciences Postdoctoral Research Fellowships (SPRF) program. The goal of the SPRF program is to prepare promising, early career doctoral-level scientists for scientific careers in academia, industry or private sector, and government. SPRF awards involve two years of training under the sponsorship of established scientists and encourage Postdoctoral Fellows to perform independent research. NSF seeks to promote the participation of scientists from all segments of the scientific community, including those from underrepresented groups, in its research programs and activities; the postdoctoral period is considered to be an important level of professional development in attaining this goal. Each Postdoctoral Fellow must address important scientific questions that advance their respective disciplinary fields. Under the sponsorship of Dr. Robert Siegler at Teachers College, Columbia University and Dr. Clarissa Thompson at Kent State University this postdoctoral fellowship award supports an early career scientist investigating children’s understanding of the relations among rational number notations (fractions, decimals, and percentages). Earlier work has shown that rational numbers, particularly fractions, are important for algebra, which in turn, is predictive of life outcomes. Unfortunately, children’s rational number understanding is quite poor. The ultimate goal of the proposed research is to understand children’s conceptions of our number system and to identify methods for improvement. This work may have important implications for curriculum and instruction across elementary and middle school. The current project builds on Siegler, Thompson, and Schneider’s (2011) Integrated Theory of Numerical Development, which argues that fractions are central to numerical development. Here, we focus on children’s understanding of the relations among fractions, decimals, and percentages, what we call, integrated number sense. Very little is known about children’s cross-notation understandings. Initial findings (Schiller, 2020) suggest that integrated number sense is a critical skill that is largely ignored by curriculum and research. Specifically, integrated number sense, as measured by magnitude comparison across notations, uniquely predicted math achievement beyond fraction magnitude representations. Additionally, integrated number sense predicted fraction arithmetic estimation, whereas fraction magnitude representation did not. However, students demonstrate little cross-notation understanding. For example, students are biased towards perceiving percentages as larger than fractions and decimals (e.g., higher accuracy for comparing 40% vs. 1/4 than 2/5 vs. 25%). The proposed project aims to develop instruction to build integrated number sense by: 1) investigating integrated number sense in much greater detail and the role it plays in other math outcomes, 2) examining use of the mental number line by investigating strategic use of magnitude within and across notations, 3) testing whether it is more effective to use an isolated or integrated approach to build this cross-notation abstraction of the mental number line.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.