Pathways to Conceptual Knowledge of Decimals

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Mathematics proficiency is essential for success in STEM fields, but remains a challenge for many US students, particularly proficiency in understanding decimals and decimal arithmetic. The project aims to test whether optimizing practice problems can improve students’ competency with and understanding of decimals. Currently, students receive certain types of practice problems more frequently than other types of practice problems, an occurrence that may limit as well as interfere with students’ development a robust understanding of decimals. This project investigates whether providing balanced distributions of practice problems with immediate feedback can improve students’ knowledge of decimals and decimal arithmetic in middle school.The project includes three short-term intervention studies with 6th and 7th grade students. Study 1 will focus on decimal arithmetic and test whether completing balanced practice problems with immediate feedback will improve students’ procedural knowledge. The researchers will compare the effectiveness of balanced decimal arithmetic practice problems with immediate feedback, unbalanced practice problems that reflect typical practice problems presented in textbooks, and business-as-usual activities. Study 2 will focus on decimal magnitude knowledge and test whether procedural knowledge developed from balanced practice with immediate feedback will further improve conceptual knowledge, and whether additional scaffolding is needed. The researchers will compare effects of balanced practice with accuracy feedback, balanced practice with accuracy feedback and conceptual prompts, and balanced practice with no feedback. Study 3 will combine the interventions from Studies 1 and 2 to examine whether boosting students’ conceptual knowledge of decimal magnitudes leads to greater benefits from a subsequent decimal arithmetic intervention involving balanced practice problems with immediate feedback. Together, these studies will provide insight into the cognitive processes involved in developing decimal knowledge through balanced practice problem distributions. Further, the findings promise to set the foundation for large-scale school-based interventions aimed at improving children’s mathematical outcomes via an easily malleable factor in instructional materials – distributions of practice problems.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.