Divisible By Pi

A while ago, I was browsing through a long list of unwatched TED talks (I subscribe on iTunes) and I came across a talk titled Arthur Benjamin’s formula for changing math education. This got me pretty excited — one of my pet peeves (as anyone who has spent longer than five minutes talking to me will know) is the horrendous state of secondary maths education, so anybody who has an idea on how to change it is certain to get my ear. So then, what did he have to say? Best if I let him explain…

Okay, so overall I was pretty unimpressed with his suggestion — while his enthusiasm is laudable and he’s crazily smart (fun fact — his page on Wikipedia links to the page on child prodigies) I don’t think that his idea actually tackles the problems in maths education at all.

For those of you who didn’t watch the video — FOR SHAME! — his primary idea is to change the structure of secondary school maths so that rather than building up to learning calculus as the apex of the ‘learning pyramid’, the climax of secondary school maths is probability and statistics.

Now, I don’t disagree that probability and statistics are important things to learn; in fact I agree that they should be taught at the highest levels of secondary school maths. However the implication that there is a dichotomy, that we can only teach either calculus or statistics, is entirely incorrect in my opinion (an opinion that can be at least partly backed up by the fact that in Victoria both are already taught).

Arthur Benjamin also suggests that teaching probability and statistics is important because it has or should have relevance to real life, as opposed to calculus which is rarely used in the average person’s workday. This is stretching things a bit, really — the level of statistics which can be taught at high school level may be somewhat useful, it’s not really something which is going to be used everyday or even necessarily more often than calculus. Knowing what two standard deviations from the mean means is certainly a good idea, but it’s the basic principles of reasoning with uncertainty that are going to crop up on a day to day basis, not the specific techniques used to perform statistical analysis.

There’s another layer to this that I disagree with, however, and that is that the maths skills one should develop during high school should be ones relating to critical thinking, creativity and problem solving. The level at which probability and statistics can be taught at high school is not one that lends itself to deep understanding of concepts or an understanding of where theorems and techniques actually come from — ironically, there are plenty of aspects of statistics that require grounding in calculus to derive and understand.

Ultimately, I think the end result (unintentional as it no doubt is) of Arthur Benjamin’s plan is a drive towards an even more plug-and-play formula based maths education than already exists. What maths education really needs is a drive towards more open ended, concept and reasoning based problems. As an example of something I think is going in the correct direction, take a look at this video of Dan Meyer (funnily enough, also a TED talk), where he talks about his approach to teaching maths and his issues with current maths textbooks:

Problems that are easy to state, but that require creativity and critical thought to solve — that’s the sort of thing we need more of in maths education; I’m betting that with more engaging and challenging problems, maths will seem more interesting as well. After all, where’s the fun or challenge in finding a formula and plugging values into it? Young people are (for the most part) inherently creative, and we should be engaging that in maths as much as in any other subject.

Besides, we already have a name for things that can uncreatively evaluate formulas. We call them ‘computers’.

Filed under: Maths