Hopeless with numbers
By William Leith
Published: May 8 2010 01:46 | Last updated: May 8 2010 01:46
|From calories to currency exchange, more than 6m adults in England struggle to make sense of numbers|
To start with, I was good at maths. At primary school I could add and subtract, I was quick to grasp the concepts of multiplication and division. When it came to the concept of infinity, I was an early adopter. At five, my dad told me that infinity was the largest number. “Well then,” I said, “What’s infinity plus one?”
After that, things started to go downhill. When I tried to multiply large numbers, I began to hate the concept of “carrying”. When teachers said, “Carry one”, or “carry two”, I felt an urge to hit them. In the end, I performed these tasks by rote. I got by.
But maths was slipping away from me. I could feel it. When I looked at numbers, I felt a vague sense of panic. I disliked triangles and graphs. Over time, my brain began to shut down. The less I understood maths, the less I liked it. And the less I liked it, the less I thought about it. The part of my brain that should have been used for doing maths was pressed into service for other tasks. Avoiding maths, for instance. Feeling defeated by maths. Hating maths. And, eventually, wearing my innumeracy as a badge of pride.
Maths should have been the king of subjects: the search for patterns in the world around us. In the entire universe, no less. To think about maths is to think of the very interface between the world and the human mind, and to begin to ask the biggest questions of all. Namely, are we really looking deep into the fabric of the world, and seeing it as it is? Are these patterns real – or do they come from within our imaginations? Maths, at its best, is philosophy with substance – pure ideas that are, rather superbly, demonstrable. I was supposed to be learning about equations in order to have access to tools I could use to organise the world around me. So when I was told that, say, the combined ages of John and Jack were 18, and that John was twice Jack’s age, I should have relished the task of using an elegant equation to calculate the ages of both boys.
Let’s see. John is twice as old as Jack. So if Jack is X, John must be 2X. And we already know that 2X plus X, the combined ages of the boys, equals 18. Which means that 3X equals 18 – which means, in turn, that X is 18 divided by three. What’s a third of 18? Six. So Jack is six! And John, being twice as old, must be 12! Child’s play. But not for me. I slogged through equations such as this. Out of touch with the mathematical parts of my brain, I came to believe that these simple procedures were, in fact, incredibly difficult. I failed my maths O level. Then I failed it again. I went through tutor after tutor.
What happened to me is not unusual. Lots of people give up on numbers. Belinda Vernon is head of research at New Philanthropy Capital (NPC), a think-tank that advises donors and charities about how to make the best use of their resources. Vernon, who has just co-written a report called Count Me In about numeracy problems in England, spends a lot of time thinking about why people are bad at maths and how charities can help them. “One in five adults is effectively innumerate,” she tells me. “They can’t work out the change from their shopping.”
According to Vernon’s report, basic numeracy means being able to manage “the skills you need to do a job (for example using spreadsheets, calculating invoices) and to be an engaged citizen in the modern world (for example, making sense of statistics reported in the media).” So more than 6m grown-ups (these figures are just for England) don’t really understand numbers, or how those numbers are having an impact on their lives. They are confused by supermarket offers and bamboozled by tracker mortgages, calorie labels, and petrol prices. They are bad at maths and it’s hurting them. Vernon thinks these people can be helped. At school, teachers can stop them falling through the cracks. As adults they can be shown that, even if they have lost any connection with numbers, they may not have lost it for good.
In Britain, most of us just give up maths aged 16 and never really think about it again. Dr Graham Sigley is deputy director of Catch Up, a charity that trains teaching assistants to give extra maths help in schools. The former head of a primary school in Greater Manchester, he says we have a collective attitude problem. “We live in a culture where it’s OK to be bad at maths.
“I remember, as a head, talking to parents about their children’s problems with maths. One dad sticks in my mind. He said, ‘I wouldn’t worry, nobody in our family can do maths.’ And I was listening to the radio the other day. It was a pop quiz. Zoë Ball was presenting. She got the score wrong. She said, ‘I’ve never been good at maths.’” (Ball’s father, Johnny, presented many children’s television programmes – about maths).
So, lots of people are bad at maths, and nobody seems to care. As Vernon says: “It’s OK to say you’re bad at maths. It’s even rather fashionable to be bad at maths. It’s OK, because you might be creative.” Somehow, we have come to see maths as one side of a coin, and creativity as the other. Another thing, says Vernon, is that children often lose their connection with maths at age 11 or 12, when they move from primary to secondary school. “That’s when maths moves from practical to abstract,” says Vernon. In other words, when they stop thinking about how many apples Jack has, if he starts out with four, and gives one to John, and when they start thinking about this differential expressed as a percentage. Jack had all four apples. Now he has 75 per cent of the apples he had before. And if he gave John another apple, he’d be giving him 33.3 per cent of the apples he had left. And if he gave him a third apple, he’d be giving him 50 per cent of his remaining apples. It’s at around this point that thousands of children begin to give up on maths, and enter the long slog of life as a virtual innumerate.
This is what happened to me. But why? People don’t lose other skills in the same way. Take reading. Why don’t people lose their ability to read in such a dramatic fashion? The consensus seems to be that, in some way, numbers are harder to grasp than words. Understanding numbers demands rigour. When you do maths, you learn lots of little steps; if you miss one step, you can’t progress.
Yet reading is just as difficult as maths. In fact, lots of scientists say it’s even more difficult. In her 2008 book, Proust and the Squid, Dr Maryanne Wolf, director of the Center for Reading and Language Research at Tufts University in the US, makes a striking point: we were not born to read. Our brains are hard-wired to speak, and to understand mathematical concepts such as the ratio between things. But everybody must learn to read from scratch.
To read, we must recognise symbols, construct these symbols into words, and form the words into sentences. And as you’re doing all this, you must scan ahead constantly, simultaneously processing many bits of information in a fraction of a second. But almost all of us can do this. Which is harder – reading a page of text in two minutes, or calculating the ages of John and Jack when their combined age is 18, and John is twice Jack’s age? The reading is harder, of course. But almost everybody can do the reading without thinking, whereas one in five of us, when asked to do the equation, loses the will to live.
The difference between numbers and letters is that we have to decode letters to survive and thrive. If 20 per cent of us were illiterate, the world would grind to a halt. People wouldn’t be able to read warning signs or instructions. The world really, really wants us to read.
But the world is not so bothered when we can’t do maths. Politicians don’t mind when we buy their phoney statistics; banks don’t mind if we fail to understand variable interest rates when we sign our mortgage. Credit card companies rather like us to be unable to calculate compound interest in our heads. Being illiterate makes people into a liability. Being innumerate might even make you into a better consumer, from a salesperson’s point of view.
The problem with maths is not that it’s hard. It’s that we don’t do it very much. If you use the maths part of your brain, it comes alive. The difference between hating maths and loving maths can just be a matter of practice. I know this. I was bad at maths. Then I walked up Mrs Peeling’s garden path. She was brilliant. I got matrices, equations, geometry, and algebra – all in seven furious weeks. She explained it, I got it. I passed my maths O level at the third attempt.
Can we improve our attitude to numbers? The NPC report mentions several charities working to improve numeracy. But what it really wants is a bigger solution – a National Numeracy Trust. This would be similar to the National Literacy Trust (founded in 1993 as a focus for efforts to improve the nation’s reading habits). But what would a National Numeracy Trust have to do to make sure that we are well taught and that our numeracy skills don’t slip away?
Make maths exciting. Make it compelling. That’s the verdict of Marcus du Sautoy, professor of Mathematics at Oxford University. “The problem is that we’re not pushing people beyond numeracy to the really exciting bits,” he says. “In English literature kids get motivated by being exposed to great literature. That’s key.” In other words, we should be engaging with Euclid, Pythagoras, Fermat and Fibonacci. “With maths you should play around. See patterns. It can lead to really exciting ideas,” du Sautoy says.
The first job of a National Numeracy Trust, then, should be to get people to practise maths all the time, in the same way that they read all the time. Then it would become second nature. And we all have to grasp a single key concept: numbers are important. Perhaps this era of large debts and austerity cuts will finally give us a reason to think twice about all those noughts on the end of impossibly large figures. Once we understand the importance of numbers, we will start to think about them. And maybe, just maybe, we won’t stop.
The other day, I told my son, who is five, that infinity is the largest number. He thought about this, and said, “What’s infinity plus one?” I hope numbers are different for him.
You can download the NPC’s Count Me In report at www.philanthropycapital.org
Back to basics: the joy of numbers in Japan
In his new book, Alex’s Adventures in Numberland, the journalist Alex Bellos offers compelling reasons for all of us to love maths. One of my favourite bits is his explanation of why Japanese children are adept at doing mathematical calculations in super-quick time.
These schoolchildren practise with an abacus, an instrument that has been around for hundreds of years. About a million Japanese children use the abacus. In fact, the Japanese version of the “Three Rs” – reading, writing, and ’rithmetic – is known as yomi, koki, soroban – reading, writing, abacus.
Bellos goes to an abacus club, where a teacher, Miyamoto, stands in front of a group of children. Each child has an abacus. Miyamoto calls out the numbers with frantic speed, and the kids rattle the beads to make the calculations. Abacus training, Bellos says, is organised along the lines of a martial art, where the levels of the kids’ ability is measured in dans. There are competitions all over the country to see who is the quickest.
Bellos writes: “Abacus club is fun. I saw that in the faces of the pupils at Miyamoto’s school. They clearly enjoyed their dexterity at flicking the beads with speed and precision. The Japanese heritage of the soroban generates national pride. Yet the real joy of the abacus, I thought, is more primal: it has been used for thousands of years, and, in some cases, is still the fastest way to do sums.”
Some Japanese children become so skilled that they no longer need a physical abacus to perform calculations. They learn to do it in their heads, by imagining a virtual abacus.
This skill is known as anzan, and now anzan competitions are all the rage. In a game called “flash anzan” numbers are flashed on a screen, and competitors add the numbers in their heads as they appear. Each number appears for 0.2 seconds. Bellos watches a Japanese flash anzan champion called Naoki Furuyama calculate the sum of 15 three-figure numbers as they flash on the screen. By the time the last number has appeared, after only three seconds, Furuyama has the answer: 7,907. And why does Furuyama do this? It helps him with his concentration and self-discipline, he says.
‘Alex’s Adventures in Numberland’ (Bloomsbury) by Alex Bellos, £18.99