"If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries." - Carl Friedrich Gauss
February 20, 2017
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…
July 24, 2016
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…
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…
February 8, 2013
This worksheet is made up of a collection of graphs of polynomial and rational functions, challenging students to observe key features and come up with an equation for each. solutions
January 26, 2013
These are the functions that I think precalculus students ought to come to know very very well. Early in the year, I spend five minutes of class having students fill out as much of the first page as they can and then I collect them (but 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…