# Language

## Factorials and the meaning of “is”

In a YouTube video, James Grime of NumberPhile makes the claim that the meaning of the factorial is $n! = \prod_{i=1}^n i$ for n > 0, and proceeds to explain why 0! = 1 using a recursive proof. This echoes…

## Numerators and denominators

I remember as a child studying fractions, being told that the top was called the numerator and that the bottom was called the denominator, for reasons that were not made clear to me at the time. In retrospect, it’s possible…

## Negative numbers squared

Background Mathematical conventions represent the linguistic aspect of mathematics. One of the strengths of modern mathematics is the way in which we can represent some fairly complex ideas in a shortened, rigorous symbol set. However, as a result of these…

## Let’s Make a Deal

The Problem In the misnomered “Monty Hall” problem, the rules are set out as follows: You as the contestant are faced with the choice of three doors, behind exactly one of which is money or something else of significant value….

## Number terms

An interesting question on the G+ Mathematics community I co-moderate asked about the difference between “numbers” and “numerals”. We wound up discussing this at a party I was hosting (which shows the sort of nerds we are), and this post…

## Expressions as Names

One basic concept in mathematics that I see students struggle with, and with which I struggled myself, is the notion of expressions. However, when we remove the mathematical component, we can see that expressions behave much like a concept that…

## The Prefix Dia-

A good teacher is always aware that there are things they can learn. One of the ways in which I encourage students to connect mathematics to other topics is by showing how words and morphemes used in mathematics are used…

## Trick question memes

From time to time, a mathematical question of some sort will make its rounds on Facebook and other social media platforms. For instance, the one making the rounds most recently in my portion of the blogosphere was: \[5 + 5…

## Introduction and purpose

As of this summer, the summer of 2012, I am qualified to teach mathematics at the high school level in the state of Michigan. I am expecting to be doing so full-time this fall. I am also qualified to teach English,…