## 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...

## Converting Between Bases

I was working through the November problems for NCTM’s Mathematics Teacher. There’s a problem on converting between bases, which led to me developin...

## Is Zero a Factor of Zero?

Generally speaking, if $$a \times b = c$$, then $$a$$ and $$b$$ are factors of $$c$$. This concept appears at the secondary level in two contexts: The factors o...

## Number values and multiple representations

One of the questions my mind keeps returning to is: What is a number? I don’t mean this in a high-level set theory way. I’m not talking about aleph-...

## Speaking English vs Speaking Math

One of the challenges that I see with students learning mathematics is their confusion with what qualifies as the content of mathematics and the language of mat...

## Three and a half methods for finding square roots

The easiest way to find a square root in this technological age is to use a calculator. That’s a fine method if what you want to do is simply calculate a ...

## De Gua and the Pythagoreans

The Pythagorean Theorem states that, given a right triangle, the areas of squares placed along the two legs will have the same area as a square placed on the hy...

## Pascal, Pacioli, Probability, and Problem-Based Learning

I’m currently reading Howard Eves’s Great Moments in Mathematics After 1650 (1983, Mathematical Association of America), a chronological collection ...

## The Fourth Dimension (Thoughts)

I’ve had two recent thoughts about the fourth dimension. The first relates to Euler’s Formula, which says that the difference between the sum of the...