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

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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.