Keith Gallagher Prospectus

Student Use of Visualization and Example Generation in Undergraduate Topology

Abstract: Research into undergraduate mathematics education has examined students’ learning and understanding of proof in contexts such as algebra and analysis. However, students’ approaches to proof in topology are underrepresented in the literature. This study investigates the ways in which students approach proofs in undergraduate topology. Specifically, this study looks at the ways in which students use and construct examples, counterexamples, and visual resources when proving or disproving topological conjectures. Preliminary data analysis show several emerging themes, including the construction of diagrams to serve as generic examples during orientation to novel concepts and the propensity of students to construct diagrams in response to the need for counterexamples. This talk will discuss the existing literature on proof, examples and counterexamples, and visualization in undergraduate mathematics education, and it will present the themes which have emerged from the data based on these preliminary analyses and discuss potential future trajectories for this study.

Date: 5/1/2018
Time: 10:00AM-11:00AM
Place: 315 Armstrong Hall

Everyone is invited to attend.

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