Incorporating Non-Euclidean Geometry Into Your GeT Course: Sparking Students’ Imaginations and Building Their Understanding of Geometric Concepts
Summary:
The GeT Student Learning Objectives (SLOs) assert that non-Euclidean geometry is an essential component of a GeT course. We recognize that GeT instructors may have different levels of knowledge of and experience with non-Euclidean geometry, and that the subject can be daunting. In this seminar, we discuss concrete ways for instructors to incorporate non-Euclidean geometry into their GeT courses. We focus on three different non-Euclidean geometries: taxicab, hyperbolic, and spherical geometry, each offering both different affordances and potential pitfalls. We offer ways to get started with non-Euclidean models for instructors who haven’t used them at all in the past, including stand-alone activities that could be included in an existing course without requiring significant changes in the overall course structure. However, non-Euclidean models also support the other SLOs in multiple ways, and we argue that infusing them throughout a GeT course supports a deeper understanding of geometry. As time permits, we will also offer suggestions of ways that an instructor could move in that direction with deeper dives into these models.
Registration Closed
Duration: 60 minutes
Format: Online seminar via Zoom web meeting software with questions and discussion. Detailed instructions for joining the seminar will be emailed to registered participants.
Presenters:
Nathaniel Miller is a Professor of Mathematical Sciences at the University of Northern Colorado. He led the online faculty working group that produced the GeT SLOs, and is one of the co-editors of the book The GeT Course: Resources and Objectives for Geometry Courses for Teachers. He is one of the co-facilitators of the upcoming Summer 2025 MAA Open Math Workshop “Big ideas for your College Geometry Course: Leveraging the GeT Student Learning Objectives.”
Dr. Tabitha T. Y. Mingus is an associate professor in collegiate mathematics education in the Mathematics Department at Western Michigan University. She earned her master’s in mathematics from Central Michigan University and Ph.D. in Educational Mathematics from the University of Northern Colorado, where she worked collaboratively with the mathematics faculty to create and implement student-focused pedagogy in linear algebra, discrete mathematics, and abstract algebra. At WMU, this work expanded to include the geometry for teachers’ courses and calculus 1. Her research examines the impact a student-focused pedagogy has on student retention, progression, understanding of mathematical concepts, and acquisition of proof skills. Much of this work also includes incorporating mathematical action technology to help students explore mathematical concepts and develop problem-solving and proof-writing skills. She also enjoys playing her violin, gardening, crocheting/knitting, making wildflower jelly, and sitting on her deck watching her two dogs and six ducks wander the woods.
Steve Szydlik is a professor of mathematics at the University of Wisconsin Oshkosh. He earned his M.A. and PhD. in mathematics from the University of Wisconsin, where he studied hyperplane arrangements under Dr. Peter Orlik. Over the course of his career, he has published research in both mathematics and mathematics education, and he especially enjoys finding connections between diverse areas of mathematics. He and his wife Jennifer (a math educator) recently completed a sabbatical where they interviewed Wisconsin high school teachers about their experiences during and after the COVID-19 pandemic. Steve taught a GeT course during his first year at UWO, and it quickly became his favorite course. His part of the seminar talk arises out of his experiences teaching that course.