RUI/ROLE: Invigorating The Early Undergraduate Mathematics Experience: Understanding Linkages Between Social and Cognitive Aspects of Students’ Transition To Mathematical

RUI/角色：激发早期本科数学体验：理解学生社会和认知方面之间的联系

• 批准号: 0337703
• 负责人: Maria Blanton
• 金额: --
• 依托单位: University of Massachusetts, Dartmouth
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-12-15 至 2008-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0337703&HistoricalAwards=false
• 关键词: RUI; ROLE; Invigorating; Early; Undergraduate

This project will investigate the development of students' understanding of proof during the undergraduate experience. It will include first a broad analysis of undergraduate students' conceptions of proof in diverse academic settings followed by a design study to examine social and cognitive aspects of undergraduate students' transition to mathematical proof during the early part of their mathematics course sequence. The stages of internalization of mathematical proof through which students progress, as well as the role of symbolic, visual, and discursive psychological tools in this process will be examined. As part of this work, a series of classroom-grounded case studies will be developed to identify pedagogical and curricular strategies that can support the learning of mathematical proof and that can be transported into other mathematics programs in typical universities. Faculty resources will be drawn upon to restructure content, pedagogy, and assessment practices in early coursework so that opportunities for mathematical proof are integrated in ways that are viable and instructive. The faculty professional development that occurs through this collaboration will also be examined. Both qualitative and quantitative methodologies will be used to trace student learning of mathematical proof and the effect of the proposed innovations on faculty practice. A national research collaborative will be developed to share and expand on an emerging knowledge base about mathematical proof across grades K-16. This collaborative will be used to identify and pursue further areas of research needed to build a coherent and connected story of mathematical proof across elementary, secondary, and tertiary grade levels. The proposed work will open new avenues in the learning and teaching of mathematical proof in early undergraduate mathematics, which resonate with overall progressive trends in the mathematics and mathematics education community.

这个项目将调查学生在本科期间对证明的理解的发展。 它将首先对本科生在不同学术环境中的证明概念进行广泛分析，然后进行设计研究，以检查本科生在数学课程序列的早期阶段向数学证明过渡的社会和认知方面。 学生通过数学证明的内化阶段的进展，以及符号，视觉和话语心理工具在这一过程中的作用将被检查。作为这项工作的一部分，将开发一系列以课堂为基础的案例研究，以确定可以支持数学证明学习的教学和课程策略，并可以将其转移到典型大学的其他数学课程中。 教师资源将被用来重组内容，教学法，并在早期课程的评估实践，使数学证明的机会是可行的和有指导意义的方式集成。 通过这种合作发生的教师专业发展也将进行检查。定性和定量的方法将被用来跟踪学生学习的数学证明和教师实践的建议创新的效果。 将开发一个国家研究协作，以分享和扩展关于K-16年级数学证明的新兴知识库。 这项合作将用于确定和追求进一步的研究领域，需要建立一个连贯和连接的故事，数学证明跨越小学，中学和大学年级水平。 拟议的工作将开辟新的途径，在学习和教学的数学证明在早期的本科数学，这与整体的进步趋势，在数学和数学教育界的共鸣。