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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Inverse Functions a la Emily Alman

In her blog post, My Backwards Approach to Inverse Functions, Emily Alman makes an observation that is absolutely vital 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…


Inverse Functions a la Emily Alman

In her blog post, My Backwards Approach to Inverse Functions, Emily Alman makes an observation that is absolutely vital 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…


Inverse Functions a la Emily Alman

In her blog post, My Backwards Approach to Inverse Functions, Emily Alman makes an observation that is absolutely vital 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…


Inverse Functions a la Emily Alman

I love the comic that Emily Alman created as an introduction to inverse functions. I used it as homework in my precalculus class before we talked about inverse functions. (To make sure everyone was familiar with the cultural context of the comic, we did the Read more…


Lesson Ideas & Resources


End behavior of polynomials

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…


End behavior of polynomials

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…


End behavior of polynomials

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…