# Mathematics

It is the habit among mathematics teachers, particularly at the elementary level, to present multiplication as repeated addition. The inimitable Keith Devlin, among others, has ranted about this, but it’s easy enough to see the temptation. When dealing with integers, multiplication…

## Ratios vs Fractions

Several middle school math teachers have told me that there’s an important distinction between fractions and ratios that students don’t get. When I ask them what it is, the teachers can’t tell me; “it’s complicated”, they say. I’ve been troubled…

## White and Blue Elephants

First, a riddle… Q. How do you shoot a white elephant? A. With a white elephant gun. Q. How do you shoot a blue elephant? A. Paint him white, then shoot him with a white elephant gun. Back to Units…

## Zip and Abby

There are a lot of trite websites and apps available for teaching elementary education concepts. And then there are the occasional gems. Zip and Abby, from The Learning Chest, is one of the true gems. The goal of Zip and…

## Pizza Math

This gem is timely to my thinking about ratios and units:   It seems to have situated itself broadly enough across the Internet that I don’t know if it’s real or a fabrication, but it seems plausible enough. There are,…

## Division vs. Ratio

I’ve noticed that the teachers of fractions tend to make a strong distinction between division and ratios, but I haven’t entirely understood why. In my mind, ratios and division are intimately related, even inextricably so. However, my reflections on the…

## Philosophical Natterings: Abstraction

Background One of the thoughts I find myself returning to frequently is this: There is the belief shared among high school mathematics teachers that the struggle students have with algebra is that it’s the first time they’re exposed to abstraction….

## Tangents and the Pythagorean Theorem

A common exercise that’s used to reinforce the concept that the tangent of a circle is perpendicular to its radius involves finding the radius of a circle given two measurements which are related to the tangent and the diameter secant:…

## Spelling and Math

Last night, as part of our learning-play, I asked my five-year-old son how to spell “night”. He told me “nitk”. That got me thinking about math education. English spelling is notorious for its quirks and oddities. In the case of…

The lesser known of two math memes currently wandering around the Internet involves an interesting equation: $\sqrt{2\frac{2}{3}} = 2\sqrt{\frac{2}{3}}$ This has spawned at least three discussions I’ve seen so far: What other values is this equation true for? Is this…