Category Archives: mathematical understanding

Go forth & multiply…

Let’s get one thing straight before we start. Notwithstanding the education secretary’s push for a knowledge based curriculum, I’m taking it as a given that children are being taught their multiplication tables in all schools. I say this, because I’ve not yet encountered any schools who don’t already do this. My own love of the multiplication tables is simply a recognition of what a brilliant tool they are for allowing the human mind to make some very complex calculations.

multi

Multiplication is one of the four basic arithmetic functions; we sometimes liken it to ‘repeated addition’, and it is a skill which learners need to master quite early on, in order to become competent at mathematics. The comparison to addition is revealing, because if children do not learn the basic multiplication facts from 0 x 0 to 9 x 9, then repeated addition (or counting on in increments of n) becomes, for most children, the default strategy for resolving a multiplication problem.

In a nutshell, here’s the rationale for learning the multiplication tables. It doesn’t require any particular skill; it gives the learner the ‘knowledge store’ to multiply together any pair of single-digit integers; it provides a secure foundation for all subsequent work on multiplication and division problems. My own approach to teaching these has always been a case of little and often, alongside the occasional dedicated lesson. I suspect that this kind of rote-learning is best approached using simple, well-practised reading, writing and chanting drills that don’t require many resources. It doesn’t necessarily make for a massively exciting lesson to observe, but it’s time well-spent, easily differentiated and easily assessed. Bat off any criticisms that this approach is “drill & kill” – the evidence says it works, and its critics have yet to propose a better method: (http://www.tandfonline.com/doi/abs/10.1080/135467999387289#preview)

Clearly, secure knowledge of multiplication tables is far from the whole story – this knowledge is not in itself a cure all, but what I’d like to see is very simple. A much earlier and more rigorous approach to learners securing these facts early on, rather than it being a long, drawn out process which, leaves some pupils entering secondary education yet to gain mastery.

The follow-up to this post will examine the introduction of formal methods of performing/recording calculations and (hopefully) a case for the earlier introduction of algebra. I’m excited, even if you’re not!

Post script:
I’m generally cautious of anecdotes and the extension of personal experience to reach broad, general conclusions, but, frankly, this made me smile when I remembered it. At my primary school in the late 70’s, the writing out of multiplication tables was the standard punishment. Our class tables league was dominated by girls & boys, myself included, of a ‘naughtier’ persuasion! It may all just have been a coincidence…

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