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 ...
Category: Mathematics
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 \(ax^b\) ...