## 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 ...

## Logarithms: The Dark Sorcery

I used to hate logarithms. They were hopelessly confusing. Sort of like this: https://www.smbc-comics.com/comic/operations This is the third year now that IR...

## The Problem with Mathematical Notation

Mathematics is beautiful. Mathematical notation, meanwhile, is a horrid mess second only to English itself for its arbitrariness. For instance, basic arithmetic...

We tend to act as if multiplying is repeated addition. This misses a key, crucial difference between the two operations: WE CANNOT ADD UNLIKE THINGS. We can abs...

## The Math Meme That Would Not Die

Some version of this question keeps getting asked on the internet. What is $$8\div2(2+2)$$? Some background The strength of mathematical notation is at the inte...

## Deriving Euler’s Identity

Euler’s Identity has been called “the most beautiful equation” in mathematics. It neatly encapsulates five key values and three operators into...

## The Natural Base e: Thoughts on Teaching

In “Burn Math Class”, Jason Wilkes spends quite a few pages deriving the value of $$e$$. I did not notice him at any point mentioning compound inter...

## The Problem with Problems

I’m currently reading “Burn Math Class,” and it’s got me thinking about language. Yesterday, I saw an item about teaching students why c...

## Some Thoughts on Teaching Mathematics

This morning, I was reading the NCTM blog, and the subject was on students struggling with systems of linear inequalities. First, as background: I don’t h...

## Dividing and remainders

As a high school teacher, I struggle routinely with getting students to understand that $$x/0$$ is undefined. Students don’t seem to understand that divis...