Continuous Reflection

"If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries." - Carl Friedrich Gauss

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Tag: Desmos

A function defined by an integral

My daughter shared a lovely problem she had encountered in her calculus class: I was inspired to make a Desmos animation: FTC (Evaluation part)


Intercepts and Asymptotes and Holes, Oh My!

I’ve been teaching for 27 years. This morning during a discussion of rational functions in a precalculus class, I had one of those why-didn’t-I-think-of this-years-ago moments, when I found myself drawing a Venn diagram on the board in response to massive confusion about holes. My hypothesis about Read more…


Making Sense of Exponential Models

Exponential growth is a topic that deserves especially thoughtful treatment as part of a high school education because a person who has thought deeply about this ubiquitous phenomenon pays attention to and conceptualizes certain critical issues in, for example, science, economics, and social science, in a fundamentally different way than one who Read more…


Quadratic Functions with Desmos Activity Builder

I thoroughly enjoyed using an activity I created using Desmos Activity Builder over the course of the past couple of days with my precalculus students to help them think in new ways about quadratic functions. These are intelligent people who have graphed plenty of parabolas and solved plenty Read more…


Lines behaving oddly: Discovering log rules

I introduced log rules in a novel way in my precalculus class today. As a bit of important background, the idea of logs was not new to these students. We’d done extensive work with logs back in the fall when we were focused on learning Read more…

puzzle