Faculty-led Inquiry into Reflective and Scholarly Teaching (FIRST)
Date of this Version
2019
Document Type
Portfolio
Citation
Zupan, Alex. "Course Portfolio for Math 872: Topology II" (2019). UNL Faculty Portfolios, 139. https://digitalcommons.unl.edu/prtunl/139
Abstract
In this course portfolio, I explore tactics for engaging a group of beginning mathematics graduate students taking the second semester of the first-year sequence in topology. Course objectives include computing algebraic invariants of topological spaces, understanding the Galois correspondence between covering spaces and fundamental groups, and using a range of invariants to distinguish spaces. My main instructional tools include a series of three "Activities" tailored to each student, a project involving computing invariants with the program SnapPy and using homology of covering spaces to distinguish 3-dimensional knots, and individual student board work during class periods. The activities served as benchmarks to gauge student understanding of key concepts; the first functioned as a pretest, the second was completed mid-semester, and the third served as a posttest. I have used the activities to analyze the progression of student understanding over the course of the semester, and in addition, I have examined student performance on midterm exams in order to determine the extent to which individual board work impacted learning. The portfolio also contains a number of examples of student work including the activities, projects, board work, and exam responses.