A Longitudinal Study of the Development of Rational Number Knowledge in the Middle Grades

本文旨在对中学生有理数学习的发展轨迹进行为期3年的纵向研究。拟开展的工作目标包括：1.工作目标；1 .揭示学生对有理数和比例推理理解的发展规律和机制；2 .通过考察对有理数子构念的理解是如何并行地、互动地发展的，将目前零散的有理数研究整合成一个连贯的发展模型；随着时间的推移，深入了解课堂教学，特别是教师提问的技巧和任务，如何影响学生思考、表达和交流他们对有理数概念和运算的理解的能力；and4。生成可移动的有理数发展模型，这些模型可以被纳入教师在职前和在职人员的发展中，以促进未来的高质量教学实践。广泛影响：在项目的整个生命周期中，这项工作的开展将影响160名不同背景的初中生的生活。该项目的研究结果将对全国职前和在职教学产生影响。最后，本研究将纵向重构数学教育问题，并提供高质量的软件产品，以支持学生的学习。小组总结：智力优势：本研究旨在对中学生有理数学习的发展轨迹进行为期3年的纵向研究。该小组认为该项目的目标是非常值得的，纵向关注这个年龄组，对现有的有理数理解研究做出了独特的贡献。审稿人还热衷于对个别学生的知识和理解进行详细的建模，并将其与对课堂上的学习机会、话语和铭文的详细、丰富的上下文检查相结合，特别是在几年的多个教室中。研究团队实力雄厚，并提出了一个有组织的计划来完成拟议的研究。

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; and4. 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.