Monday, 22 August 2011

Pointless algorithms

When I was studying O-level maths many decades ago, I was taught how to find the square root of a number. This was a complicated algorithm which I never understood at the time, and, frankly, I don't really understand now. But I was a willing student with a good memory and I learnt the process and even got a certain amount of satisfaction from practising it until I had mastered it. I was the exception: most of my schoolmates never got the hang of it. Many didn't even bother to try and the experience just added to their perception of maths as a subject that doesn't make much sense.

To my surprise, I find that I can still remember how to do it. You give me any number you like and I can work out its square root to any number of decimal places. I won't demonstrate this skill here – I never like to teach any mathematics without understanding. So, you'll just have to believe me.

When I left school I read mathematics at university and went on to have a career in mathematics education. But not once in all those years have I ever used this skill that I spent so many hours at school mastering. If ever I needed a square root, I used a set of square root tables, a slide rule or, mostly, a calculator. What a pointless waste of time it was learning that meaningless process. How insightful of my friends at school who decided not to bother to learn this mysterious routine!

Now, here's the point of mentioning this.

Is anyone able to convince me that the long division algorithm – which some prominent people (eg Carol and Michael) want to see back in the primary school maths curriculum – does not have exactly the same status today as the algorithm for 'extracting the square root' had when I was a lad? Do we really want to go back to making children spend hours at school trying to learn a procedure they won't understand and – in an age when a calculator is cheaper than a cup of coffee – will probably never need to use?

1 comment:

  1. Is there an email adress where i can contact you? I had some questions regarding the tasks in your article "recognizing mathematical creativity" from 1997 (zdm).