This is a proposal for a 3-year longitudinal study of developmental trajectories in middle school students' learning about rational numbers. The goals of the proposed work include: 1. Uncovering patterns and mechanisms of development in students' understanding of rational numbers and proportional reasoning; 2. Integrating the current piecemeal body of research on rational number into a coherent developmental model by examining how understanding of rational number sub-constructs evolve concurrently and interactively; 3. Developing insight into the ways in which classroom instruction, especially teacher questioning techniques and tasks, impact students' ability to think about, represent, and communicate their understanding of rational number concepts and operations as it develops over time; and 4. Generating transportable models of rational number development that can be factored into teacher pre- and in-service staff development to promote quality instructional practices in the future.
Broad Impact: The conduct of the work will affect the lives of 160 middle grade students of diverse backgrounds throughout the life of the project. The results of the project will influence pre-service and in-service teaching nationally. Finally, the study will reframe math education issues longitudinally and deliver high quality software products I support of student learning.
Panel Summary:
Intellectual Merit: This is a proposal for a 3-year longitudinal study of developmental trajectories in middle school students' learning about rational numbers. The panel believes the aims of the project to be very worthwhile, with the longitudinal focus on this age group making a unique contribution to existing research on the understanding of rational numbers. Reviewers were also enthusiastic about detailed modeling of individual students' knowledge and understanding being combined with detailed, rich, contextual examination of learning opportunities, discourse, and inscriptions in classrooms, especially in multiple classrooms over several years. The research team is strong and presents an organized plan for accomplishing the proposed research.
