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

本项目将调查学生在本科期间对证明的理解发展情况。它将首先对本科生在不同学术环境下的证明概念进行广泛的分析，然后进行一项设计研究，以考察本科生在数学课程序列的早期阶段过渡到数学证明的社会和认知方面。学生通过数学证明的内化阶段，以及符号、视觉和话语心理工具在这一过程中的作用，将被研究。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，以确定能够支持数学证明学习的教学和课程策略，并将其移植到典型大学的其他数学课程中。教师资源将被用来重组早期课程的内容、教学方法和评估实践，以便以可行和有教育意义的方式整合数学证明的机会。通过这种合作所产生的教师专业发展也将被考察。定性和定量方法都将被用来追踪学生对数学证明的学习，以及拟议的创新对教师实践的影响。将开发一个全国性的研究合作项目，以共享和扩展关于K-16年级数学证明的新兴知识库。这种协作将被用来确定和进一步研究所需的领域，以建立一个贯穿小学、中学和三年级的数学证明的连贯和联系的故事。拟议的工作将在本科早期数学的数学证明的学习和教学方面开辟新的途径，这与数学和数学教育界的总体进步趋势产生了共鸣。

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.