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Identifying Structure In Introductory Topology: Diagrams, Examples, And Gestures, Keith N. Gallagher

Graduate Theses, Dissertations, and Problem Reports

Despite the prevalence of research in calculus, linear algebra, abstract algebra, and analysis in undergraduate mathematics, the teaching and learning of general topology is a largely unexplored area of research. Although enrollment in courses like linear algebra is often higher than that of topology, the study of students’ learning and understanding of topology is of great significance to the Research in Undergraduate Mathematics Education (RUME) community. Courses in topology present many students with their first experience in axiomatic reasoning and explicit interactions with mathematical structure, itself.

I present a thorough case study of Stacey, an undergraduate taking a first course …