Colloquium
 

September 13, 2022 

Refreshments will be served at 10:30 AM in 301 Gordon Palmer Hall, and the presentation will begin at 11:00 AM in 346 Gordon Palmer Hall 

Dr. Hortensia Soto
Department of Mathematics at  

Colorado State University  

Hortensia is a professor in the department of mathematics at Colorado State University. Her research centers on the teaching and learning of undergraduate mathematics where she adopts an embodied cognition perspective. Hortensia has mentored young women and promoted mathematics via summer outreach programs. She has facilitated professional development for K-16 teachers in Nebraska, Colorado, and California. She is a recipient of the MAA Deborah and Franklin Tepper Haimo Award for Distinguished College of University Teaching of Mathematics. 
 

Hortensia is a working member of the MAA. She served as the Associate Treasurer, the Associate Secretary, as an editor of the MAA Instructional Practices Guide, and currently serves as MAA President-Elect. She enjoys hiking, practicing yoga, meditating, reading, and most of all spending time with her son Miguel.  

Title: The Geometry of the Cauchy-Riemann Equations: A Marriage of Embodied, Symbolic, and Formal Interpretations  

Abstract:  

In this case study we explored how a mathematician weaved embodied, symbolic, and formal interpretations as he taught the Cauchy-Riemann equations. Instead of teaching using the standard definition-theorem-proof model, the mathematician devoted time to embedding inscriptions and metaphors, which he brought to life with representational gestures. He also grounded abstract symbolism with pointing gestures. Furthermore, when he introduced formal notation, he navigated to a blend of embodied explanations where he reiterated the geometry behind the formal mathematics. Our results suggest that intentional teaching such as that displayed by the mathematician can help paint a picture of a mathematicians’ internal understanding of an abstract mathematical topic. We also offer implications for teaching and research based on our findings.