Collaborative Research: Promoting Reasoning In Undergraduate Mathematics (PRIUM)

数学证明可以被认为是一种论证，它使用公认的逻辑规则来验证数学陈述中的主张。精通数学证明是数学专业本科生的核心期望之一，但也被认为是这些学生面临的关键挑战之一。为了解决这个问题，这个名为“促进本科生数学推理(PRIUM)”的项目将实施一个循环，评估学生的知识，计划和实施对这些发现的教学反应，评估学习，然后反思评估结果和进一步的课程修订。更具体地说，该项目将利用本科生数学教育(RUME)中关于学生学习和理解数学证明的大量研究成果，以便为侧重于数学证明的高年级本科生数学课程的教学和评估决策提供信息。这个项目的关键是数学教育者和研究数学家之间的合作，前者是研究学生学习的专家，后者是课程的讲师。在这个项目中，来自佐治亚州立大学(GSU)和北达科他州州立大学(NDSU)的研究人员将支持研究型数学家在两所大型州立大学实施基于教育研究的方法来教学和评估证明学习。通过访谈、调查、人工制品(例如，年度系评估报告)和小型会议上的讨论/演示，拟议的项目将解决以下研究问题：(1)数学家如何利用基于规则的模型来评估他们教学中的证明？(2)这种方法对学生对证明的理解有什么影响，从学生对证明的本地和全球概念的定性理解的程度上可见一斑？(3)数学家和数学教育工作者之间的合作如何影响教授对实施基于研究的数学教学和评估方法的态度？(4)什么变化，如果有的话，参加这个项目的数学系有没有在三年内建立起这个项目？

A mathematical proof can be thought of as an argument that uses accepted rules of logic to validate the claims in a mathematical statement. Becoming proficient at producing mathematically valid proofs is one of the central expectation for undergraduate mathematics majors, but has also been identified as one of the key challenges that these students face. Working toward addressing this problem, this project, "Promoting Reasoning In Undergraduate Mathematics (PRIUM)", will implement a cycle of assessing student knowledge, planning and implementing instructional responses to those findings, assessing learning, followed by reflection on assessment outcomes and further course revision. More specifically, the project will employ results from a strong body of research in undergraduate mathematics education (RUME) about student learning and understanding of mathematical proving in order to inform instructional and assessment decisions in upper-division undergraduate mathematics courses that focus on mathematical proofs. Key to this project is the collaboration between mathematics educators who are experts in the research about student learning and research mathematicians who are the instructors of the courses. Also key to this project is the emphasis on connecting education research and classroom practice.In this project, investigators from Georgia State University (GSU) and North Dakota State University (NDSU) will support research mathematicians in the implementation of education-research-based methods for teaching and assessing learning of proof at two large state universities. Using interviews, surveys, artifacts (e.g., annual department assessment reports), and discussions/presentations at mini-conferences, the proposed project will address the following research questions: (1) How do mathematicians make use of a RUME-based model for assessing proof in their instruction? (2) What impact does this approach have on student understanding of proof made evident by the extent to which students demonstrate a qualitative understanding of the local and global concepts of proofs? (3) How does this collaboration between mathematicians and mathematics educators impact professors' attitudes toward implementing research-based methods of mathematics teaching and assessment? (4) What changes, if any, have the participating mathematics departments instituted as a result of this project over a three-year period?