What makes a math metaphor land and what makes it crash? In this talk, I reflect on my journey as a mathematics educator through the lens of one of teaching’s most powerful and perilous tools: the conceptual metaphor. We begin at the University of Illinois at Urbana-Champaign, where, as a graduate teaching assistant, I deployed some genuinely tortured metaphors with the full confidence only inexperience can provide. We then move to the University of Arizona, where as a postdoc I discovered the subtler danger of mixed metaphors, where individually reasonable analogies placed side by side can quietly undermine each other and students’ developing understanding. And finally, we arrive at Auburn University, where I stumbled upon a metaphor that actually worked beautifully, and found myself compelled to understand why.

Along the way, I will draw lightly on cognitive theories of mathematics learning to ask: what is a metaphor really doing for a learner? What happens when the wrong one takes root? The talk will include penguins, binoculars, a poorly drawn summary of The Terminator, and a live encounter with the surprisingly rich metaphorical life of the equals sign. I will also invite the audience to consider a new and thought-provoking question: in an age of large language models that can generate metaphors fluently and instantly, what does that reveal about what makes a math metaphor genuinely good?

This talk is equal parts a confession, an investigation, and a love letter to the craft of teaching. P.S. As a lifelong Swiftie, I could not resist naming this talk after a certain album. But I promise that the parallel is more than cosmetic.

Introduction

Jeneva Clark