Dan McGee

Friday evening invited speaker.

A Teaching Focus on Commonalities across Representations

A guiding principle throughout my career as an educator is that concepts are best understood by seeing the commonality across situations, formulas, tables, and graphs. Pursuing this goal has led me in various directions. A slope between 2 points in 3D was not included in Multivariable Calculus curriculum but it is a fundamental representation that is needed to understanding partial and directional derivatives. So, I found that I needed to create curriculum supplements that include a 3D slope in various representations. Finding that students struggle to visualize 3D concepts on a page or screen, I created a 3D “kit” that allows students to experience 3D points, curves, surfaces and volumes in their natural dimension. To facilitate multirepresentational understanding, I shifted from a lecture format to an activity-based classroom. And created numerous activities designed to be completed as part of our classroom discussion. In this presentation, I’ll discuss this journey, the materials I’ve created, what I’ve learned and how it has impacted my mathematics instruction from Precalculus to Multivariable Calculus.

Dr. Daniel McGee graduated from Georgia Tech and began his career in engineering. However, after working several years teaching middle and high school math in Botswana as a Peace Corps volunteer, he knew math education was destined to be a part of his life. He enrolled in the Doctoral Program in Applied Mathematics at the University of Arizona, and upon receiving his degree, spent almost two decades in Puerto Rico where he studied the impact of metarepresentational approaches to teaching undergraduate mathematics. In 2013, he came to Kentucky to serve as the Executive Director of the Kentucky Center for Mathematics. He spent 6 years in this role where he focused on continuity across grades in the p–16 mathematics learning experience. In 2019, he returned to the classroom as a mathematics professor at NKU where he continues his exploration of student understanding of postsecondary mathematics across multiple contexts.