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# Why parents can't do maths today

## In today's Magazine

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.

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.

## “Start Quote

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

End Quote Rob Eastaway

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.

BACK {current} of {total} NEXT

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.

## Find out more

• Hear Rob Eastaway on More or Less on BBC Radio 4 at 1330 BST on Friday, 10 September
• He will teach four adults how to get to grips with some of these techniques

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.

I have an 8-year old son at school and I'm so glad I caught this article. I love these methods. I could bash out the sums on paper easily at school, but it was much harder to do entirely in my head because I couldn't keep track of all individual digits in their columns. These methods are much more spatially orientated - visual, if you like - and that's far simpler. I'd more or less dumped the techniques I learned at school and cobbled-together my own methods not too dissimilar to these. Sometimes progress is a good thing.

I could have done with seeing this at the beginning of this week. My son had maths homework and I couldn't for the life of me understand what he was on about and he couldn't understand how I would have done it. In a way the 'chunking' seems to be easier than the way I would have done it, but I don't believe that children are learning the logic behind maths nowadays. I think this will be a problem.

I am a secondary maths teacher and I have a mathematics degree, I know this issue very well from both sides. I was taught the traditional methods, but in training to teach, found the benefits of these alternative methods. Pupils learn in different ways, so having a variety of methods is very useful. Most are very confident with the grid method, but I also teach the traditional as some prefer it. There are many other methods as well, the Chinese method is far stronger still. Though it looks alien at first, this is the most favoured method in my classroom and I teach all pupils this way. New ideas move things forward, but certain things shouldn't change. Too many children do not know their times tables and this should still be drilled in from an early age, which it isn't as much anymore. It is holding so many back.

I was surprised to see that 'chunking' actually isn't new at all. I was taught this method at school some (ahem) 32 years ago - so as a new and older Mum I'm guessing that a lot of parents will already be happy with this method. Phew - I have slightly less to learn again.

What's new with chunking? Isn't it the way the Romans did it with 'roman' numbers? long before all these newfangled 'arabic' numbers became fashionable?

It never ceases to amaze and annoy me that any sort of numerical manipulation is automatically called 'maths' when really it should be called 'arithmetic'. Shame on you that your programme, concerned with numerical accuracy, should make such a mistake. Mathematics includes other disciplines such as algebra, trigonometry, geometry, calculus etc, as well as arithmetic, and if one cannot do arithmetic then one most certainly cannot do maths.

I found these new methods hugely complicated. Overly complicated (especially the long division). To help children learn maths, parents will have to "relearn" maths. How many working parents will have the time or inclination to do this, the result being that parents won't be able to help children with their homework. Own goal.

These new methods mirror the way I do maths in my head. To me these are much more intuitive and also enable quick guesstimates to be made on magnitudes when faced with multiples sums. I think these ways of thinking will better enable kids to do maths in their head and hence to be creative with their maths, which is fun. A good move.

I honestly believe that these new methods will help children understand why they are doing what they are doing instead of simply learning a method. Having said that, I still fall back to using the old methods that are second nature to me now but confuse the hell out of my children.

I'm a quilter and patchworker - people have been working out patchwork designs and cutting out using methods like these for years, just never (as far as I know) giving them a name. It's just logical and the way your brain works. Plus, I'm sure we were taught something like gridding at school anyway, as a kind of shortcut - but it wasn't given that name.

I finished primary school in 2000. Back then we only did long multiplication, however my father who is an accountant taught me the grid system when I was a child. It really is much easier, particularly for mental arithmetic I find. There is no way I could keep track of all the numbers that get carried over in my head with the old way. Don't think that the grid system is dumbing down maths, it isn't. It is making calculations more efficient and much easier to do without paper.

I always thought that maths teaching had gone downhill and was aimed at the lowest common denominator (no pun intended) until I attended a session at my daughter's school aimed at teaching parents the new methods. Not only are these methods much more in keeping with how our brains actually work but in my daughter's schools case they eventually end up using the methods we were taught but because of the foundations they should now understand why they are doing what they are doing. Have to say I was a sceptic but am totally converted.

I was taught the traditional method, but now when working out long multiplication and division in my head I use the grid and chinking methods - not that I realised that's what they were called, I just worked out that was the easiest way to do it as it's easy to visualise. The basic rules and times tables are vital to be able to do this, as Rob says.

I'm a grandfather now, and this is very interesting. Like you (and also good with numbers at school tho' less good at other parts of maths), I was surprised when my eldest, who started school in 1972, started coming home and talking about sets and showing me operators I'd never heard of. I understood that this was in response to mathematicians' saying children weren't actually taught "maths". I found set theory interesting but couldn't really see how it benefited primary pupils, and having mentioned it to young acquaintances and got blank looks, I wonder if it too was superseded, or discarded like ITA, also new when my daughter was at school. I'll be paying attention to how/what my 7-yr old grandson is taught.

That grid method thing is awesome! Well better than the old way; easier, more visual and already I can use it quicker than before. So wish I was taught that at school.

My father was a maths teacher and I am a school governor and we have reservations about the current trends in maths education. Unfortunately whilst "chunking" and the "grid method" can make maths easier at a superficial level these are not universal models. Only holding true for basic arithmetic, anyone wishing to take mathematics to a higher level has to go back and learn the same rules that we did at school. I see this as another example of the dumbing down and "we must include everyone" dogma in British education.

I believe many children fail to understand numeracy is because teachers often fail to explain mathematical methods logically. Instead teachers often expect children to make the same assumptions they do in explaining the technique. For instance, in this video when the man was explaining chunking for division he failed to explain why we can still take away three chunks. He then failed to tell his audience that you are supposed to multiply 14 by 3 to make 42. He also failed to explain why this gave you the answer. Which is because the multiplication of the last chunk gave you the same answer as the multiplication of the second chunk we are no longer able to divide the chunks. Therefore, we have found the answer. So in short, he did not explain all the steps of chunking logically nor explained the methodical goal of chunking, i.e finding that last number which is no longer divisible. So instead he assumed that his audience would follow the leaps in logic.

Working in 6th form education I have noticed a decline in numeracy levels over the years. Most students have a numeracy level 2 or 3 years below their age level. Perhaps this is because they're not taught how to do long division and multiplication? Which isn't a hard process to go learn and use at all.

The grid method is really just long multiplication, but laid out differently on the paper. If you asked a mathematician, they would just tell you they're the same algorithm. Multiplication becomes more interesting when you realise that there are other algorithms too, which become more efficient for very large numbers. These algorithms are also surprisingly new: no earlier than 1952 did the great Soviet mathematician Andrey Kolmogorov conjecture that the classical long multiplication algorithm was asymptotically optimal (meaning that no other algorithm outperforms it as the numbers to be multiplied become very large). He was shown to be incorrect almost immediately. You really need to be worried when your 8-year-old asks you to explain how the convolution in long multiplication can be calculated more efficiently using a Fourier transform.

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