Structuring Equitable Participation in Undergraduate Mathematics Proof Classes

该项目旨在通过提高学生在基于证明的数学课堂上的体验来服务于国家利益。这些课程面向未来的高中数学教师和数学专业的学生。基于证据的课程的独特内容和特点有可能加强数学专业的概念联系，包括未来中学教师与K-12数学的联系。然而，这些好处并不总是公平地落到学生身上，基于证据的课程有时会成为学生未来STEM职业的障碍。这个IUSE:EDU参与学生学习跟踪项目将促进专业发展和与这些课程教师的合作，以设计和实施可能支持更公平的学习体验的小组工作任务。这一专业发展的创新在于适应和实施小组工作原则，从K-12阶段的复杂教学发展到高级本科阶段。该项目还将调查实施这种小组工作如何能够减轻小组工作参与方面的不平等。因此，这项工作的意义将包括知识的发展和具体的教学策略，这些策略可能支持将高等数学课堂转变为更具包容性的空间。该项目建立在大量研究的基础之上，这些研究表明，复杂的教学原则和有小组价值的任务的结合可以使数学课堂的参与更加公平。利用这个研究基金作为催化剂，该项目将追求几个目标。第一个目标是设计、实施和研究研讨会，以支持基于证明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的理解，并导致数学课堂上更公平的参与。另一个目标是将地方、区域和国家层面的项目成果和小组工作资源传播给数学科学部门和其他STEM部门，以提高学生的学习、成功和公平的课堂参与。社会环境中存在的地位等级经常影响学生的协作工作。也就是说，决定发言，提出问题或提出想法不一定是学生所知道的直接结果，但通常是与他们如何看待自己在课堂上的地位以及他们认为他们的导师和同龄人如何看待他们的相互作用。该项目将侧重于有意利用学生不同优势的任务。通过适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存关系。虽然这些原则已经在K-12阶段得到了很好的确立，但它们在高等本科阶段的潜力却鲜为人知。通过项目研究和评估，该项目旨在产生新的知识，以加强与实证课程和公平小组工作相关的文献和课堂实践。将从讲习班和随后的班级收集定性和定量数据，并将进行混合方法分析，以便更好地了解如何制定和执行公平的小组任务，以及任务、教学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关于这种小组工作如何在高等数学环境中发挥作用的理论。通过在基于证据的课堂中为更公平的小组工作提供任务和模型，该项目将成为课程开发人员、教师和专业实践社区的资源。传播将通过地方、区域和国家渠道进行，并将包括讲习班、会议报告和同行评议出版物。NSF IUSE: EDU项目支持研究和开发项目，以提高所有学生STEM教育的有效性。通过其参与学生学习轨道，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’ 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.