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

本文是一项为期三年的关于中学生有理数学习发展轨迹的纵向研究。 建议的工作目标包括：1。揭示学生对有理数和比例推理理解的发展模式和机制;2.通过研究有理数子结构的理解如何同时和交互地发展，将当前有理数研究的零碎部分整合到一个连贯的发展模型中;3.发展洞察力的方式，课堂教学，特别是教师提问技术和任务，影响学生的能力，思考，代表，并传达他们的理解有理数概念和运算，因为它随着时间的推移发展;和4。生成可移植的有理数发展模型，可以考虑到教师的职前和在职人员的发展，以促进质量的教学实践在future.Broad影响：这项工作的进行将影响整个项目的生命中不同背景的160名中年级学生的生活。 该项目的结果将影响全国的职前和在职教学。 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：这是一项为期3年的关于中学生学习有理数的发展轨迹的纵向研究。专家组认为，该项目的目标是非常值得的，对这一年龄组的纵向关注对理解有理数的现有研究做出了独特的贡献。评审员也热衷于对个别学生的知识和理解进行详细建模，并结合对课堂学习机会、话语和题词的详细、丰富、上下文的检查，特别是在多个教室中。研究团队是强大的，并提出了一个有组织的计划，以完成拟议的研究。

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.