Bridging Borders in Graduate Mathematics Education: A Case Study of Preliminary and Advanced Coursework

• In Event: Analyzing Mathematical Experiences in Higher Education: Undergraduate and Graduate Perspectives

Abstract

This qualitative case study examines differences in teaching practices between preliminary and advanced graduate mathematics courses at a research-intensive university. Drawing on interviews and classroom observations, the study explores how course goals, assessment, and faculty roles shift across stages of doctoral education. Using communities of practice and border theory, findings show that preliminary courses emphasize coverage and exam preparation, reinforcing institutional boundaries. Advanced courses, by contrast, promote autonomy, exploration, and mentorship, supporting students’ transition into disciplinary participation. These shifts reflect a broader movement from demonstrating knowledge to contributing it. The study highlights opportunities for instructors to adopt more inclusive, developmental practices even within the constraints of graduate mathematics education.

Author

• Peter Karanevich, University of Colorado - Boulder