Addressing Cognitive and Instructional Challenges in Introductory Proofs Courses: A Gateway to Advanced STEM Studies

该项目旨在通过提高学生的逻辑推理能力、批判性思维能力和解决复杂问题的能力，为国家利益服务。它将确定入门证明课程的教学策略，使学生能够分析和解决高级STEM环境中的重要问题。在证明课程中表现不佳通常会成为学生成功学习课程的障碍，并可能阻止他们成为或留在STEM专业。在弗吉尼亚理工学院和州立大学（弗吉尼亚理工大学）开展的IUSE参与式学生学习1级项目旨在增加和多样化从事STEM职业的学生群体。这将是一个两阶段的项目，第一阶段将包括一个循环的方法来调查学生的推理，并设计和研究基于研究的教学任务，以唤起和解决基础思想的教学和学习中的挑战。第一阶段的努力将对弗吉尼亚理工大学的每个数学专业产生直接影响，包括准备教中学数学的职前教师。在第二阶段，项目成果将被传播并用于支持全国范围内的入门证明讲师，因为他们优化教学，促进学生发展强大的逻辑推理、批判性思维，并在STEM领域取得全面成功。该项目将追求几个基本目标。第一个目标是为参加证明入门课程的学生提供发展推理技能的机会，并结合在高级STEM设置中灵活解决问题所必需的逻辑结构。第二个目标是通过调查研究成果，为知识库做出贡献并填补文献空白：(1)学生如何在证明课程中经历认识论障碍；(2)课程教师如何面对这些学生的障碍；(3)如何使这些教师能够围绕认识论挑战进行教学和学习互动，为学生提供认识、探索和克服这些困难的机会。第三个目标是（通过国家研讨会和其他场所）传播研究成果、资源和可复制和可持续的课程模式，以促进教师、院系和机构的学生成功，以提高学生的学习、解决问题的能力，并在入门证明课程和其他课程中取得成功。项目团队将采用循环方法，通过调查学生的推理，设计和修改基于研究的教学任务，以唤起学生对与基本思想（如逻辑暗示、量词和证明技术）相关的认知挑战的体验。研究和任务设计将借鉴行动-客体理论，该理论源于皮亚杰（1970）的遗传认识论和杜宾斯基（1991）的扩展。NSF IUSE: EHR计划支持研究和开发项目，以提高所有学生STEM教育的有效性。通过参与学生学习轨道，该计划支持有前途的实践和工具的创建，探索和实施。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project aims to serve the national interest by improving students’ abilities to reason logically, think critically, and solve complex problems. It will identify instructional strategies for introductory proofs courses that empower students to analyze and solve important problems in advanced STEM settings. Poor performance in proofs courses often serves as a barrier for students’ successful course progression and can prevent them from becoming or remaining as STEM majors. This IUSE Engaged Student Learning Level 1 project at Virginia Polytechnic Institute and State University (Virginia Tech) is designed to increase and diversify the pool of students pursuing STEM careers. This will be a two-phase project for which phase 1 will include a cyclical approach to investigate student reasoning and to design and study research-based instructional tasks that evoke and address challenges in the teaching and learning of foundational ideas. Efforts from phase 1 will have an immediate impact on every Virginia Tech mathematics major, including pre-service teachers preparing to teach secondary mathematics. In phase 2, project outcomes will be disseminated and used to support introductory proofs instructors nation-wide as they optimize instruction for facilitating students’ development of robust logical reasoning, critical thinking, and overall success in the STEM arena.The project will pursue several underlying goals. The first goal is to provide students taking an introduction to proofs course with opportunities to develop reasoning skills and to incorporate the logical structures that are essential for flexibly solving problems in advanced STEM settings. The second goal is to contribute to the knowledge base and fill gaps in the literature through research findings by investigating: (1) how students experience epistemological obstacles in proofs courses; (2) how course instructors experience these student obstacles; and (3) how to enable these instructors to employ teaching and learning interactions surrounding the epistemological challenges that provide the students with opportunities to realize, explore, and overcome these difficulties. The third goal is to disseminate (through national workshops and other venues) research findings, resources, and a replicable and sustainable course model that promotes student success to instructors, departments, and institutions working to enhance student learning, problem solving abilities, and success in introductory proofs courses and beyond. The project team will take a cyclical approach by investigating student reasoning and designing and modifying research-based instructional tasks for evoking student experience of the cognitive challenges associated with foundational ideas such as logical implication, quantifiers, and proof techniques. Research and task design will draw on action-object theory, which derives from Piaget’s (1970) genetic epistemology and Dubinski’s (1991) extensions. The NSF IUSE: EHR Program supports research and development projects to improve the effectiveness of STEM education for all students. Through the Engaged Student Learning track, the program supports the creation, exploration, and implementation of promising practices and tools.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.