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 why the analysis of rational functions can feel so overwhelming to beginners [...]

Inspired by Annie Perkins and her post "For Those Hesitant to Protest" and prodded by a friend to share the following more widely, I offer here the following passage which was my contribution our family's Christmas letter to family and friends this year. While I do enjoy math a great deal, what I truly love is being [...]

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 is oblivious to or overwhelmed by the concept. (For one [...]

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 of quadratic equations in Algebra 1 and 2, and have [...]