Down By The Riverside – Long Division and Mr Gibb’s Laundry (part i)

I’ve heard it said that Nick Gibb does some long division practice every day before breakfast.   That may or may not be true, but it may be more relevant than you think, because Mr Gibb is Minister of State at the Department for Education and it’s certainly in keeping with many of his views. Politicians do seem to attach almost mystical importance to long division, though perhaps it’s rather like doing the laundry. Everyone knows the traditional way is to go down to the riverbank and bash your washing with a rock, but I bet it’s a long time since Mr Gibb attacked his shirts with a large stone.

It might be rather nice if Mr Gibb and those in his circle – and the Education Secretary Ms Nicky Morgan certainly seems to be one of them – could be persuaded that there might be other ways of tackling mathematics in the 21st century than automatically applying a mechanical procedure.  After all, I’m at the end of a very long line of people who’ve pointed out that if you want a mechanical procedure it makes a lot more sense to get a machine to do it.

I’d guess one reason Mr Gibb enjoys long division is because division feels different from the other operations. In addition, subtraction, and multiplication you have your two numbers, you do things with them (conventionally beginning with the digits of least value) and out pops the answer.

With all but the simplest divisions it works differently. You do something (starting this time with the digits of greatest value rather than the least) to find part of the answer; then you do another something and find the next part of the answer, and so on. And since finding each of these numbers may involve trying one value, and then another and perhaps another, it’s all akin to a trial and improvement process and yes, it does feel a different kettle of fish entirely.

There’s a parallel to another process. In the sixth form I learned an algorithm that was reminiscent of a long division algorithm on steroids. You thought of a number, did several things with it, did it all several times more, and eventually you found the square root (or more likely, an approximation of the square root) of the number you started with. This process was even more arcane than long division – I recall very little apart from the fact that at one point you needed to double the number you first thought of. In fact, and I may be unique here, I actually used the even more complicated procedure to find cube roots (though I’d certainly appreciate it if you didn’t ask me for any details).

Even in 1958 this was the most pointless activity you can imagine. At no time in my life did I ever need to employ these algorithms and they’ve long since passed into history. Fortunately politicians have never heard of them, so I’ve never heard even the most diehard traditionalist demand that extracting square roots ought to be a fundamental part of the mathematics curriculum.  Otherwise they might still be asking students to find square roots by hand, and indeed do so in the examination room.

Don’t get me wrong; I do actually have some sneaking regard for Mr Gibb, Ms Morgan, and others in their profession. They have qualities which I totally lack, they’ve got to the top of a hugely competitive profession, they’re prepared to tackle big problems, and I don’t doubt they’re motivated by a desire to make things better. But I do wonder how Mr Gibb’s advisers (or indeed the audience) could allow him to speak dismissively of “… inefficient methods such as the grid method for multiplication and chunking for long division …” (London Thames Maths Hub Primary Conference, 27th March).

Now I’m prepared to assume we’re going to devote some curriculum time to the processes of long multiplication and long division and I want to write about these “inefficient methods” in part (ii).

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