A Longitudinal Exploration of Relations Between Fractions and Algebra Knowledge: An Interdisciplinary Approach
Effective Years: 2023-2028
This project aims to improve understanding of the relationships between students’ knowledge of fractions and their knowledge of algebra. Success in algebra is an important determinant of life outcomes, from high school graduation to college access and career and economic prospects. Unfortunately, a broad swath of research has documented the struggles students face learning algebra. Findings from both psychology and mathematics education research suggest that enhancing students’ fraction learning may be one route to improving algebra learning. Researchers from both fields have found that fractions and algebra competence are closely related, but the basis of this relationship remains unclear. This project will design measures that efficiently capture the breadth and depth of students’ fractions and algebra knowledge and investigate relations between fractions and algebra knowledge over a three-year period, from grades 7 to 9. By investigating how students’ understanding develops over time, this study will identify critical time points at which instruction might prove especially fruitful.
The project will take place in two phases. Phase 1 is a measurement project in which participants in grades 7-9 will engage in within-subjects assessments of algebra knowledge and fractions knowledge using assessments adapted from prior research. A subset of students will also be interviewed to gain greater insight into their problem-solving approaches. Key covariates, including children’s mathematics anxiety, whole number skills, and general cognitive skills, will be measured in order to isolate the relations between fractions and algebra knowledge. This allows for empirical examination of the factor structure of the fractions and algebra domains and for development of efficient instruments with optimal coverage of the constructs. Phase 2 will use the refined measures to follow a new sample of children longitudinally over three school years (grades 7–9). Cross-lagged panel models will be used to simultaneously examine effects of fractions knowledge on algebra knowledge and vice versa, while also considering the role of covariates. Results will yield information about the developmental relations between fractions and algebra knowledge. Data will be collected online in both phases.
This project is supported by NSF's EDU Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field. Investments are made in critical areas that are essential, broad and enduring: STEM learning and STEM learning environments, broadening participation in STEM, and STEM workforce development.
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.