Structuring Equitable Participation in Undergraduate Mathematics Proof Classes

该项目旨在通过改善学生在基于证明的数学课堂上的体验来服务于国家利益。这些课程是由未来的高中数学教师和数学专业的学生学习的。基于证据的课程的独特内容和特点有可能加强数学专业学生的概念联系，包括为未来的中学教师提供与K-12数学的联系。然而，这些好处并不总是公平地惠及学生，以证据为基础的课程有时会成为学生未来STEM职业生涯的障碍。这一II级国际教育、科学及文化组织：EDU参与的学生学习跟踪项目将促进专业发展，并与这些课程的讲师合作，设计和实施小组工作任务，以支持更公平的学习体验。这种专业发展的创新将在于适应和实施小组工作原则，从从K-12水平发展到高级本科水平的复杂教学。该项目还将调查实施这种小组工作如何能够减少小组工作参与中的不平等现象。因此，这项工作的意义将包括发展知识和具体的教学策略，以支持将高等数学课堂转变为更具包容性的空间。该项目建立在坚实的研究基础上，证明复杂的教学原则和纳入有小组价值的任务可以导致更公平地参与数学课堂。利用这一研究基础作为催化剂，该项目将追求几个目标。第一个目标是设计、实施和学习研讨会，以支持以证据为基础的课程的讲师在他们的课程中实施有小组价值的任务。第二个目标是建立对小组工作的设计特征如何影响学生互动以及如何在数学课堂上更公平地参与的理解。另一个目标是在地方、地区和国家层面将项目成果和小组工作资源传播给数学科学系和其他STEM系，努力提高学生的学习、成功和公平的课堂参与。社会环境中存在的身份等级制度往往会影响学生的协作工作。也就是说，决定发声、提出问题或提出想法不一定是学生所知道的直接结果，而往往是他们如何看待自己在课堂上的地位以及他们认为导师和同龄人如何看待他们的相互作用。该项目将专注于有意利用学生不同优势的任务。通过恰当地开发和实施这些任务，教师可以帮助克服消极的地位效应，培养学生之间的积极相互依赖。虽然这些原则已经在K-12级别得到了很好的确立，但人们对它们在高等本科级别的潜力知之甚少。通过项目研究和评估，该项目旨在产生新的知识，以加强与循证课程和公平小组工作有关的文献和课堂实践。将从研讨会和后续课程中收集定性和定量数据，并将进行混合方法分析，以更好地理解如何制定和实施公平的有群体价值的任务，以及任务、指导和小组工作之间的总体关系。反过来，研究结果将使研究人员能够建立这样的小组工作如何在高等数学背景下发挥作用的理论。通过为以证据为基础的课堂中更公平的小组工作贡献任务和模式，该项目将成为课程开发人员、教师和专业实践社区的资源。将通过地方、区域和国家渠道进行传播，包括研讨会、会议报告和同行评议的出版物。NSF IUSE：EDU计划支持研究和开发项目，以提高所有学生的STEM教育的有效性。通过其参与的学生学习跟踪，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NSF的法定使命，并通过使用基金会的智力优势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’ experiences in proof-based mathematics classes. These courses are taken by future high school mathematics teachers and mathematics majors. The unique content and features of proof-based courses have the potential to strengthen conceptual connections for mathematics majors, including connections to K-12 mathematics for prospective secondary teachers. However, these benefits do not always fall equitably to students, and proof-based courses can sometimes serve as a barrier to students’ future STEM careers. This Level II IUSE:EDU Engaged Student Learning track project will facilitate professional development and collaboration with instructors of these courses to design and implement group-work tasks that may support more equitable learning experiences. The innovation of this professional development will lie in adapting and implementing group-work principles from complex instruction, developed at K-12 levels, to the advanced undergraduate level. The project will also investigate how implementing such group work can alleviate inequities in group-work participation. Thus, the significance of this work will include the development of knowledge and concrete instructional strategies that may support transformation of advanced mathematics classes into more inclusive spaces.This project builds on a substantial foundation of research illustrating that complex instruction principles and the incorporation of group-worthy tasks can lead to more equitable participation in mathematics classrooms. Using this research foundation as a catalyst, the project will pursue several goals. The first goal is to design, implement, and study workshops to support instructors of proof-based courses in implementing group-worthy tasks in their courses. A second goal is to build understanding of how design features of group work impact student interactions and can lead to more equitable participation in mathematics classrooms. An additional goal is to disseminate project outcomes and group-work resources at local, regional, and national levels to mathematical sciences departments and other STEM departments working to enhance student learning, success, and equitable classroom participation. Status hierarchies that exist in social settings often shape student collaborative work. That is, the decision to speak up, ask a question, or offer an idea is not necessarily a direct consequence of what the student knows, but often is an interplay with how they perceive their status in the class as well as how they think their instructor and their peers perceive them. The project will focus on tasks that intentionally make use of students’ diverse strengths. By properly developing and implementing these tasks, instructors can help override negative status effects and cultivate positive interdependence among students. While these principles have been well established at K-12 levels, little is known about their potential at the advanced undergraduate level. Through project research and evaluation, the project aims to generate new knowledge to enhance literature and classroom practice related to proof-based courses and equitable group work. Qualitative and quantitative data will be collected from the workshops and subsequent classes, and mixed methods analyses will be conducted to result in a better understanding of how to develop and implement equitable group-worthy tasks and of the overall relationships between tasks, instruction, and group work. In turn, the outcomes will enable the investigators to build theories on how such group work plays out in the advanced mathematics context. By contributing tasks and models for more equitable group work in proof-based classes, the project will serve as a resource for curriculum developers, instructors, and professional communities of practice. Dissemination will be through local, regional, and national outlets and will include workshops, conference presentations, and peer-reviewed publications. The NSF IUSE: EDU Program supports research and development projects to improve the effectiveness of STEM education for all students. Through its 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.