This is making its internet rounds again: These days, I see it in math teacher forums clucking about our colleagues. There is often a microaggressive wink-wink ...

## Arithmetic and Operations

This is a “what-if” document. It’s not intended as a serious suggestion for how we should write mathematical notation or for replacing current...

## 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 ...

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 ...