How much of what happens in mathematics classrooms is mathematics?

There’s an epic little book called ‘A Mathematician’s Lament’ that I’m certain crossed my path over a decade ago. I suspect I skipped over a few pages but wasn’t ready for it. Or wasn’t in the right headspace.?

However, after crossing my path again recently, ‘Lament’ floored me. I was gobsmacked, stunned, blown away by its simple message.?

Like any great book (Lament is a mini-book at best!), Lament made me see the obvious, an ‘obvious’ that had never previously been obvious.

I’m penning this article for one reason - to have more people read A Mathematician’s Lament. (Perhaps some holiday reading?)

BTW,?A Mathematician's Lament?is a short, 25-page book written in 2002 by Paul Lockhart, originally an American research mathematician and subsequently a mathematics teacher.

I have no intention of elaborating on Lockhart’s message. Instead, I’ll paste a few teasers below to entice you to give this thought-provoking piece your full attention, hopefully soon.?

But make sure you have the headspace. No one chews through a $75 Lobster Bisque at a 5-star restaurant as if it were an Olympic race. Similarly, Lament needs savouring. And it’s an easy read, which helps.?

If you partake, there are two critical questions you will ponder:

1. What the heck is mathematics??
2. What is it that mathematicians do?

Below are a few paragraphs to whet your appetite:?

The first thing to understand is that mathematics is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognize math as such. Everyone understands that poets, painters, and musicians create works of art, and are expressing themselves in word, image, and sound. In fact, our society is rather generous when it comes to creative expression ... So why not mathematicians??

Part of the problem is that nobody has the faintest idea what it is that mathematicians do. The common perception seems to be that mathematicians are somehow connected with science - perhaps they help the scientists with their formulas, or feed big numbers into computers for some reason or other.”

… Mathematics is the purest of the arts, as well as the most misunderstood. So let me try to explain what mathematics is, and what mathematicians do.”

… Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary. For example, if I’m in the mood to think about shapes - and I often am - I might imagine a triangle inside a rectangular box:?

I wonder how much of the box the triangle takes up? Two-thirds maybe??

The important thing to understand is that I’m not talking about this drawing of a triangle in a box. Nor am I talking about some metal triangle forming part of a girder system for a bridge. There’s no ulterior practical purpose here. I’m just playing. That’s what math is - wondering, playing, amusing yourself with your imagination.?

... The triangle takes up a certain amount of its box, and I don’t have any control over what that amount is. There is a number out there, maybe it’s two-thirds, maybe it isn’t, but I don’t get to say what it is. I have to find out what it is. So we get to play and imagine whatever we want and make patterns and ask questions about them.?

But how do we answer these questions? It’s not at all like science. There’s no experiment I can do with test tubes and equipment and whatnot that will tell me the truth about a figment of my imagination.?

The only way to get at the truth about our imaginations is to use our imaginations, and that is hard work. In the case of the triangle in its box, I do see something simple and pretty:?

I’ll leave it there for the quotes for now. What Lockhart does next with his shape, is in my view, genius.

But even more powerfully, Lockhart uses these examples to explain what maths ISN’T. And spoiler alert, it turns out that what maths ISN’T is a close cousin to what’s been happening in mathematics classrooms for the last century or two.?

And, so it turns out, especially in my classrooms all those years ago as an early teacher!

This is a beautiful piece of writing, a cry for change, a call for sanity in these crazy times of education reform, standardized testing and ridiculously overcrowded syllabi.??

And delightfully utopian.

Fortunately, Lament is now accessible as a PDF, given that Keith Devlin 2009 convinced Lockhart to publish it as a web-based article.?

So do yourself a favour, schedule thirty minutes, and savour A Mathematician’s Lament.

You can?access it here.

Oh, and hang onto your hat!?