Marty’s Viral Pizza Load
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 ...
Category: Mathematics
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 ...
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 ...