My Column – Right for All the Wrong Reasons: Times Tables by Age 11

We’re living in a technology-driven world. Calculations can be done in an instant; you no longer even need to reach for your calculator. A tablet, ipad, laptop or mobile telephone will almost certainly have a calculator function – you’re never far away from something that will help you to deal with basic arithmetic if you can’t do it for yourself.

Why, then, is learning times tables in any way relevant in a modern classroom? You’d be forgiven for thinking that Education Secretary Nicky Morgan has got it wrong, yet again, when she suggests that all children should know their times tables up to 12 x 12 by the age of 11. Yet as a former Maths teacher I’m convinced that knowledge of such essential arithmetic by the end of primary school is vital. I have a sneaky suspicion though that she may be correct by accident; right for completely wrong reasons. The unions have now come out and opposed Morgan, for the puerile and overly-simplistic reason that ‘everyone has a calculator now’. I speak from personal experience when I say that this spectacularly misses the point. Shouldn’t the teaching unions be talking to the maths teachers they represent?

There’s a tendency in the Conservative Party to hark back to the ‘good old days’, to suggest that education has lost something in recent decades as trendy teaching methods have replaced the traditional, that a certain amount of learning by rote can be a useful academic exercise and develop concentration. As a former teacher, I think that’s an over-simplistic approach which has the occasional grain of truth. Different children learn in different ways. The modern approach encourages children to develop skills of problem-solving, which in some ways offers a significant advantage. But it also risks leaving other children behind. Depending on the subject, or even the topic, factual learning is vital.

When I learned Spanish at school, there was an emphasis on vocabulary and verbs. If you don’t learn the words you need to know, or learn patterns of regular and irregular verbs, you won’t be able to speak the language. As teaching of modern foreign languages has lessened its emphasis on such learning, I’ve noticed a decline in the ability of students to speak correctly in the target language. Recently, on one of the Spanish islands, I was discussing an image with a graphic designer. He made a change which I hadn’t requested, and it didn’t look right. “No, the one you had before”, I said. He undid the change, then said “When English people speak Spanish they always get the verbs mixed up. But you use them perfectly”. In Spanish (as in English) there are many past tenses. All I’d done was choose the correct one. Learn a couple of phrases which use the tenses correctly, drop them into an exam – and hey presto, you’ve fooled an examiner into believing that you know the tense. Great for picking up a decent exam grade, but unhelpful for actually using the language.

Here’s the point: factual learning should never be done for the sake of it, harking back to some halcyon days that probably never even existed in the first place. When there’s a genuine educational need, that’s a different matter altogether. There is such a need for learning times tables, but I haven’t heard it come from Nicky Morgan’s mouth.

When I was teaching Mathematics, I always found it far easier to teach a range of topics, from algebra to geometry, from trigonometry to Pythagoras, to those who already had a basic arithmetic knowledge. The difference became more striking to me when teaching older children; at age 15 or 16 it became more important than at age 11. Questions might require, say, five steps of working out. At different stages, there will be a need to perform a simple arithmetic calculation. Those who did not know the answer would either have to work it out, or (if a calculator was allowed on that examination paper) input the numbers into a calculator. The thought process was broken; in having to take time to deal with basic arithmetic they would forget some of the detail of the question. From there, mistakes would creep in. The student who knew their times tables (and was proficient in adding and subtracting quickly) was in a position to continue and solve the problem uninterrupted. Those who possessed basic arithmetic proficiency would consistently outperform those who did not. If we want to improve mathematical standards in our secondary schools, then it is important to make sure that we first improve standards of numeracy in our primary schools.

To take a more advanced example, as a personal point of professional awareness whilst teaching I made sure that I knew all of my square numbers up to 50 x 50. If you know that 10 x 10 = 100, then 11 x 9 is one less than 100, which is 99. Know that 12 x 12 = 144? Then it follows that 13 x 11 = 143. Using that simple trick, and because I knew 23 x 23, I could work out instantly that 24 x 22 = 528. After learning a few more similar tricks, two-digit multiplications became very easy for me – though no doubt politics has dulled some of my sharpness by now.

At age 11, knowing your times tables up to 12 x 12 is hugely beneficial. It doesn’t need to be done by government diktat with league tables created to show how well one school is performing against another. It doesn’t need to be a cause of stress for teachers worried about how a poor performance from their class will reflect upon them. All that is needed is for a renewed focus and emphasis on times tables in primary education. This is the point that the unions should have focused on: introducing a battery of new tests ready to be rolled out across the country is a bureaucratic waste of time and money. Morgan misses the point here once again, but at least she was correct – albeit for the wrong reasons – on the issue of times tables.

This article was originally published on the Huffington Post website. You can view it here.

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