# Education

## 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…

## Introducing the Spry

Some time ago, the discussion on π being the incorrect number for calculations in trigonometry, in favor of τ (2π), led me to muse about creating a unit to replace the degree, called the wedge and being equal to nearly two degrees (100W…

## Reflections on Fractions

I was reading an article on fractions, waiting for students to show up for after-school tutoring. One of them asked me what I was reading, so I told him. He groaned. I asked him what his least favorite topic in…

Education

An adult friend is getting tested to see if she has a formal neurological problem that would account for her struggles with mathematics. She asked how it could be that she might make it all the way through public education…

Education

## Slide rules and calculators

Several of my math teacher colleagues are of the opinion that calculators have destroyed math sense. I am not convinced that this is directly true: Calculators are a tool, nothing more. A few months ago, I saw a video by…

## Pyramids and Squares

I have been spending my free time the last few days on the task of working backwards through three proofs in a 19th century French language mathematics journal. This started with a simple question in the G+ Mathematics community, posted…

## The Pizza Party

In this post, I’d like to reflect on story problems and the purpose of mathematics education. Consider this problem: Every week, Julie invites some friends over for pizza. Last week, she had four friends over and they ate one whole…

## “Two Kinds” of Zero: Same But Not The Same?

I recently got into a protracted discussion in which the other person insisted that the fact that the character 0 is used in place value notation is merely a place holder is evidence that zero is not a number, but…