## Coloring Vertices

The other day, I came across this problem on Twitter: How many distinct ways are there to color the vertices of a cube, such that exactly four are one color and...

## On Cognitive Load Theory and Story Problems

I’m currently reading “Sweller’s Cognitive Load Theory in Action” by Oliver Lovell, specifically the section on reducing extraneous load...

## What is a fraction?

The other day, I saw a tweet joking that while calculus teachers insist that $$\frac{dy}{dx}$$ is not a fraction, the LaTeX is \frac{dy}{dx}. That reminded me o...

One thing I realized while writing and editing the previous article is the depth of the mismatch between notation for addition and multiplication (on the one ha...

## The Basic Operators

By the time most students graduate from high school in the United States, they have seen the following operators*: Addition, subtraction, negation, multiplicati...

## What is Subtraction? (Reflective draft)

Conceptually, subtraction and addition of negatives are two very different processes. Subtraction involves an undoing of addition: It is an inverse function. Ad...

## Logs, Roots, and Fractions

How notation gets in the way of understanding The other day I tweeted this: Objectively, I realize that $$\sqrt2$$, $$\log6$$, and $$\frac57$$ are all specific ...

## The Logarithmic Rules

In this item, I will show how the basic logarithmic rules, including the Change of Base formula, follow from this equivalency: \[\log_b m = n \Leftrightarrow b^...

## Thoughts on Memorization (Facebook repost)

There are two basic forms of “memorization”: (a) Rote, through the repetition of the specifically, often decontextualized, data and (b) Habituation,...

## How Notation Obscures Patterns

This is another stab for me at what continues to prove to be a complicated topic: How our mess of mathematical notation obfuscates key patterns. This is also a ...