The two Harvard professors are convinced the reason so many children are turned off maths is simply that they’ve been taught the wrong way. Maths should be fun, they believe, and to prove it, they’re spending the day at Tynecastle getting four classes of 13-year-olds to work out that some decimals don’t have corresponding fractions, that a graph of x2 is a symmetrical curve and that Pythagoras was right about triangles. “If you want to make order of your lives, math is the way to do it,” says Robert Kaplan, an avuncular 72-year-old. “We’re here to take the fear out of it.”
Whether through fear or plain ignorance, Scotland’s record on numeracy is poor. In the most recent Trends in International Maths and Science Study (TIMSS) report, Scotland languishes below the middle of the table, consistently below England and bunched with nations such as Russia and Slovakia. Taking 10-year-olds as a benchmark, most countries have improved their maths performance since records were first compiled in 1995, but Scotland has fallen back. This is compounded in the classroom by a shortage of maths teachers that has led some schools to cancel lessons.
The Kaplans spend every summer at South Queensferry, a connection which stems from a year-long secondment Robert enjoyed at Edinburgh University in 1991. Should a convenient opportunity arise, they are only too pleased to introduce their deceptively simple approach to classroom mathematics.
To start with, they pose a problem and try to work it out with the class. The students set the pace and do the thinking. There is no right way, merely conjectures they test, frequently making discoveries en route, until eventually they reach their destination.
“If it is boring, it is not mathematics,” Ellen Kaplan, 69, tells the class. “The best thing you can possibly do is to use your brain to avoid boring work. That’s what the human brain is for.”
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The Tynecastle pupils prove to be putty in the Kaplans’ hands. Effortlessly, the couple have got the class to add up every fourth number between 20 and 180. The students get it right — 8,000 — by a technique of their own devising. “When we go back to the States we’re going to say this is the Tynecastle method,” jokes Robert.
It is pupils’ early self-perception of failure in maths that set the Kaplans on their proselytising journey. Ellen came home from her first day teaching at a high school, Robert from his first day working at a university, and both agreed their students had one thing in common. “We said to each other, ‘The only thing our kids know about maths is they don’t like it’,” says Ellen. “That’s when we decided to do something about it.”
The Kaplans, who have published books on the mysteries of infinity and zero, are convinced that anyone could respond to their approach given the encouragement and the feeling that they’re inventing the maths themselves. “You don’t want to be told things, you want to do it your own way,” says Robert.
As evidence, he points to his experience in America of running “math circles”, informal clubs for people of any age to explore the beauty of pure mathematics. “We’ve had 11 years of the math circle, so our earliest students are now going to university. We have a huge number going to Harvard, Massachusetts Institute of Technology and so on, majoring in maths and doing very well. The group is always self-selecting: we take anyone who comes.”
Working together, it is easier to see the husband and wife team a double act, tossing in anecdotes like the one about the Japanese man who memorised pi to several thousand places and recited it in what was surely the world’s most tedious radio broadcast.
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But though they work in tandem, their approach could equally be employed by an enthusiastic teacher working alone. Zack Sweeney, Tynecastle’s principal teacher of maths is plainly impressed. “There were some brilliant ideas about using the maths the pupils can do to help them with the maths they can’t. That’s one thing that I’d like to take on in my own lessons.”
Success is not guaranteed, however. Last year, they attempted a similar session at one of Edinburgh’s most select private schools, St George’s, and got nowhere.
“Part of the problem was it was a circle of about 30 girls and then lots of grown-ups — their math teachers — behind them,” says Ellen.
“I think they felt observed. It takes a willingness to go in, get messy and try things out. I really think we could have done it eventually — we normally have 10 classes and it takes a good bit of time to establish trust.”
Robert says that the difference between a group that works and one that doesn’t is something they take for granted in America: a certain feistiness in the students. “At St George’s the students seemed paralytically polite,” he says.
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“It has so much to do with adolescent shyness and cliquishness.
The well-behaved young ladies at St George’s weren’t going to risk making fools of themselves. Doing math is like swimming: if you throw yourself in, you learn how to do it.”
In the morning’s second session at Tynecastle, 13-year-old Rachel Davidson shows exactly what a difference having a bright spark in the class can make. She is forward, forthright and funny, but never less than engaged in the Kaplans’ number puzzles. “You’re a born mathematician,” Robert tells her. “You’ve got the sense of humour and the stubbornness.”
Despite her contribution, Davidson is convinced maths is not her subject. “I’m not very good at maths and it’s hard to be engaged in something you’re not great at,” she says at the end. “But it was much more fun than a normal maths lesson. There was a lot more logic rather than just maths and it makes a bit more sense than the way the other teachers approach it.”
Lack of confidence in the subject is something with which Sweeney is familiar. “We find it from the very start,” says the teacher. “They come to us in the first year having had seven years of primary school and already they’ve decided they don’t like the subject. Any positive experience that we can give children mathematically has got to be a great thing.”
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Robert explains what impressed him about Tynecastle’s students. “We were struck by the realisation that, in a kid culture with neither the experience of, nor interest in, talking with adults, there were some who had the self-confidence to start a conversation, toss conjectures around like cabers and risk laughing away any supposed solemnity to the event. A group needs to be seeded with sparks such as Rachel or Aaron to catch fire. And what fun it is when that happens.”
Taking careful note of the day’s proceedings, Sweeney is impressed. “The pupils found it very refreshing to work in that investigative way,” he says. “The thought process was very much put on them, and their responses often affected the way the lesson went. I would love to see more of this happening in schools. It’s been a success and we’d like to learn from it.”
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Find more information at www.themathcircle.org