Noticing in Mathematics: A Video-Annotation Curriculum to Enhance Instructors' Understanding of Student Thinking in Proof-Transition Courses

该项目旨在通过提高教学团队对大学证明入门课程中学生数学思维的理解，为国家利益服务。很大比例的本科生没有通过证明转换课程。内容难度的显著增加以及从计算数学到基于证明的数学的过渡是决定学生是否在STEM领域学习和职业的因素。这个问题对代表性不足群体的学生影响尤为严重。为了应对这些挑战，本项目将调查视频注释课程的有效性，该课程旨在支持本科证明转换课程中响应性和公平的数学教学。该项目将为六个教学团队提供《抽象代数入门》课程的专业发展。教学小组将由一名课程讲师、两名研究生助教和四名本科生学习助理组成。该项目的目的是加强教学实践，以提高学生在大学数学专业课程中的成功。该项目借鉴了广泛的K-12数学教育研究，以教师注意为中心设计了一个创新的专业发展课程。注意需要关注学生在课堂上的数学思维和定位，有策略地和适当地回应，提高学习和归属感。本研究将提供有关注意建构如何适应高等教育环境的新发现。通过基于设计的研究方法，该项目的跨学科团队将参与三个阶段的研究：探索性、早期实施和有效性研究。通过多次修订，团队将设计并严格测试课程对学生学习和教学团队知识、注意能力和教学质量的影响。加州大学欧文分校（University of California-Irvine）是一所为拉美裔学生服务的机构，将专门测试该课程对拉美裔学生的效果。此外，该课程将免费提供给其他机构，包括那些在STEM课程中代表性不足的群体中提供大量学生的机构。研究结果将通过出版物和会议报告进行分享。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 instructional teams’ understanding of student mathematical thinking in introductory college proof courses. Large percentages of undergraduates fail proof-transition courses. The notable increase in content difficulty and transition from computational to proof-based mathematics are factors in determining whether students pursue studies and careers in STEM. This issue affects students from underrepresented groups disproportionately. To address these challenges, this project will investigate the effectiveness of a video-annotation curriculum designed to support responsive and equitable mathematics instruction in undergraduate proof-transition courses. The project will provide professional development for six instructional teams for an Introduction to Abstract Algebra course. The instructional teams will consist of a course instructor, two graduate teaching assistants, and four undergraduate learning assistants. The project’s aim is to enhance instructional practices to increase student success in college courses for mathematics majors.This project draws on extensive K-12 mathematics education research to ground its design of an innovative professional development curriculum centered on teacher noticing. Noticing entails attending to student mathematical thinking and positioning in the classroom, responding strategically and appropriately, and improving both learning and sense of belonging. This project will provide novel and important findings about adaptation of the noticing construct to the higher education setting. Through a design-based research approach, the project’s interdisciplinary team will engage in three phases of research: exploratory, early implementation, and efficacy study. Through multiple cycles of revisions the team will design and rigorously test the curriculum for its impact on student learning and instructional teams’ knowledge, noticing competencies, and instructional quality. The University of California-Irvine, a Hispanic-Serving Institution, will test the efficacy of the curriculum specifically on Latinx students. Additionally, the curriculum will be made freely available to other institutions, including those serving large percentages of students from groups underrepresented in their participation in STEM courses of study. Findings will be shared via publications and conference presentations. 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.