"If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries." - Carl Friedrich Gauss
January 9, 2016
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…
March 19, 2015
Over the past few years of teaching precalculus regularly, I’ve experimented with a variety of approaches to rational functions in an attempt to find one that will result in students discovering and eventually truly understanding how the equation of a rational function determines its graph. I have never felt very Read more…
April 3, 2013
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…
January 26, 2013
In her blog post, My Backwards Approach to Inverse Functions, Emily Alman makes an observation that is, I think, vitally important for math teachers to understand: “One problem with algebra is that there is often a disconnect between the meaning/understanding and the computations/doing. We try our darndest to Read more…
Here is a PowerPoint I use when introducing end-behavior of polynomial functions. For each slide everyone raises arms or lowers arms to indicate the end-behavior of the polynomial. The left arm indicates what happens to \(y\) as \(x\rightarrow -\infty \) and the right arm indicates what Read more…
December 6, 2012
We’ve just had a good week-plus of precalculus lessons built around a story, inspired by Daniel Willingham’s tweet and the article by Julie DeNeen about which he tweeted. [embedit snippet=”willingham-tweet”] The tweet came at an opportune time. It was Thanksgiving break, I was away from Read more…
