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

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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.