Long division and long multiplication have been replaced in schools by chunking and gridding. While the new methods are meant to make maths easier, parents have been left scratching their heads, writes Rob Eastaway.

I used to think I had a good understanding of maths – until my daughter started going to primary school. That’s when I discovered a revolution had taken place in the way arithmetic is taught, and there were techniques and terminology that meant nothing to me.

Let me give you a flavour. In most primary schools, maths lessons are called numeracy. Children work using number lines and learn their number bonds, they fill in Carroll Diagrams, and they calculate using the grid method and something that carries the peculiar name of “chunking”.

Like most parents – numerate or otherwise – my first reaction to this was annoyance. Why have they changed it? Now my child gets cross when I try to explain using my methods. Is this why some people reckon the country’s maths is going to the dogs?

I decided to find out more, and ended up writing a book aimed at parents, like me, who wanted to have a better understanding of how young children learn maths these days.

Victorian schoolchildren in a classroom Until recently, maths was taught using Victorian-era methods

Researching the book was a revelation.

What became clear is that at school I was one of the lucky ones. Being strong with numbers, I had no problem learning the black-box techniques of long multiplication and long division, and usually got the right answer.

But for a huge proportion of children, these techniques were a meaningless chore. Ask most adults today to carry out a long multiplication or division sum and they will look blankly at you.

They may have, sort of, got it once, but they can’t remember how to do it. And anyway, we have calculators now, don’t we?

The point about calculators is important. Many of the techniques we were taught at school date back to Victorian times, when the country needed vast numbers of clerks to perform calculations every day. Today, calculators and spreadsheets can do these tasks far quicker, so the need for everybody to be able to do big calculations by hand has largely disappeared.

The emphasis has moved away from blindly following rules to techniques a child can understand”

That’s not to say we don’t need strong number skills.

We are inundated by numbers all the time, whether it’s somebody flogging us a mobile phone package or a politician trying to convince us about a particular policy. As a society we have to make sense of these numbers if we are to successfully manage our lives.

Do we all need to be able to work out 27 x 43 precisely with a pen and paper? Probably not. But we do need to know that 27 x 43 is roughly 30 x 40, and that this is roughly 1,200. It’s partly the need to have a good feel for numbers that is behind the modern methods.

The revolution in the teaching of maths at primary school kicked in with the National Numeracy Strategy in 1999. The emphasis moved away from blindly following rules (remember borrowing one from the next column and paying back?) towards techniques a child understood.

One of the methods that has been adopted widely is the “grid method” for multiplication, which links to a visual method that many children find easier to understand.

Use the step-by-step guide below for a quick refresher on long multiplication, then an introduction to the grid method.

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Another important method, used for division, is “chunking”. To understand chunking, you need to think about what division actually means. Division is usually introduced through the idea of sharing. You want to divide 18 sweets fairly between six children. How many sweets do they each get? 18 / 6 = 3.

But what if the problem is this: you need to put 18 sweets into bags of six. How many bags do you need?

This isn’t about sharing, it’s taking away sweets in chunks of six until there are none left, and then counting the bags. Here, “division” is really repeated subtraction, but calculated in the same way, 18 / 6 = 3.

Chunking is a method based around repeated subtraction and many people find it an easier way to tackle division problems. Ever wondered why six divided by ½ is 12? Think of it as “how many times can I take ½ a pizza away from six pizzas?” and it becomes clear that the answer is indeed 12.

See the grid method and chunking in action

So is the nation’s maths better thanks to these new methods? Certainly the horror stories of children being punished or humiliated for getting things wrong have all but disappeared, as have the tedious lessons of endless sums. There is also some evidence that children do have a better understanding of the methods they’re using, and make fewer mistakes when they use them.

But that isn’t the full story. To become fully numerate you need to know when to use these methods, you need to practise, and you also need to be able to estimate, which means knowing your times tables off by heart.

My own experience, and the feedback I get from others, is that many children are missing out on these basics. Is too much energy being diverted into taking Sats tests? Does the problem lie with teachers who don’t have enough maths knowledge? Or is too much emphasis being placed on enjoyment at the expense of rigour?

Perhaps it’s all of these things. But we shouldn’t be relying just on schools to impart all this knowledge in any case. Children learn maths at home too, whether it’s helping with cooking, playing board games or helping mum and dad to measure wallpaper.

Forcing a child to learn the methods we were taught can result in frustration and tantrums. For the sake of harmony at home if nothing else, it’s not a bad idea to get familiar with chunking, number lines and the rest.

Maths for Mums and Dads by Rob Eastaway & Mike Askew is published by Square Peg.

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