## In (Partial) Defense of Butterflies

Teaching students how to add fractions can be a real struggle. A big part of this is that we tend to get conceptually complicated about what fractions are. And ...

## What’s the Deal with Logarithms?

I’m going to talk about logs here. I have more to say later, but this is a basic intro sketch. First I’m going to talk about the stuff of elementary school. Whe...

## A Hodgepodge of Inconsistencies

Mathematical terminology and notation through a linguistic lens Introduction The first time I attended graduate school was for Linguistics. My first year, I tau...

## Keeping, Changing, Flipping

Consider the following task: $1.\quad \text{Simplify the expression }\frac{3}{4}\div\frac{2}{5}.$ It is very common for students to struggle with this sort of...

## Reflections on Inverse Function Notation

I was thinking about inverse function notation, and that got me thinking about function notation, and that got me thinking about operations and how meh our nota...

## Math Education and One True Wayism

This is a common criticism of Common Core (CCSS): It offers these strange new methods that students must use. Except… only the first part of that is true. CCSS ...

## Reframing the Quadratic Formula

When I was in school, I was taught the Quadratic Formula. I was taught that it was the most efficient, more reliable way to find the roots of a quadratic functi...

## Proof: The rationality of the y-intercept

Theorem: Given a quadratic function with rational roots, the $$y$$-intercept is rational if and only if the stretch is rational. Proof: If $$f$$ is a quadratic ...

## Functions and Domains: The Other Shoe

I have taught high school mathematics for nearly a decade. I have a BS in Mathematics. The Algebra II curriculum, which I largely built for my school, is based ...

## Rate of Change and the Power Rule

I’ll keep this one short. Also, it’s on calculus, for whatever that’s worth. The Power Rule for Differentiation says that the derivative of a monomial $$ax^b$$ ...