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 successful. Too many students get confused somewhere along the way, come to [...]

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 about a variety of fundamental functions. At that time, we [...]

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 bridge the gap between the two, but I find that [...]

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 as and the right arm indicates what happens to as . view full post »