It really shouldn't happen to a maths teacher. In a quiz on the basics of numerical and geometrical concepts, classroom trainees from across the world were asked to submit their answers to an array of straightforward questions. Is a square ever a rectangle? What is the square root of 49? How many days are there in ten weeks and two days?
The results were fascinating – a sample of the varying standards and diverse teaching practices from Beijing to Budapest. But one thing was clear: if this had been an A-level, a GCSE or even a school Standard Assessment Test, Britain's maths teachers would have conclusively failed.
For instance, asked how many sweets you had to take from a bag stuffed full with five different varieties to make sure you had three of one type, only 21 per cent of participants from the UK gave the right answer – compared with 97 per cent of Russian teachers. The answer is 11.
And, when it came to the question, "If the result of squaring a number is 49, the original number must be 7 – true or false", only 53 per cent from the UK got it right compared with 100 per cent from China. The answer is false – it should be minus 7. (For those of you still unsure, a square is always a rectangle. But a rectangle is not always a square.)
The findings came at the end of a week in which a worrying drop in the standards of maths in the UK was exposed by a series of reports that highlighted not only the lack of pupils pursuing the subject to A-level but also a shortfall in qualified teachers.
The right-of-centre think-tank Reform said that Britain was suffering from a "lost generation" of mathematicians with 440,000 fewer young people were studying the subject at A-level than would have been the case if numbers had held firm since the 1970s. This, it was claimed, had cost the economy £9bn as a maths graduate, on average over their lifetime, earned £136,000 more than a non-maths graduate.
The Government's own curriculum staffing survey then gave a clue as to why so many students have ditched maths. One in four teachers taking lessons in state secondary schools, it reported, had not been trained in the subject – leaving academics to claim that it was therefore hardly surprising that pupils could not be inspired.
The researchers at Reform were arguing that pupils were being put off pursuing maths because it had become "dumbed down" at GCSE (questions no longer probed the theory of algebra and geometry, concentrating rather on making the subject more "relevant", ie about shopping trips and travel bills). Students, they said, no longer had the basic knowledge to progress to an A-level course.
This view was echoed by the Oxford maths professor Marcus du Sautoy, who criticised examiners and claimed they were "too frantic" to make maths seem relevant to young people's lives. The subject had been "emasculated by a move away from rigour and logic" in pursuit of relevance, he said, and this had "ended up making the subject boring".
Ministers and teachers' leaders had for years grappled with the problem of trying to create interest where there is none. If they were not allowed to make it "relevant" – and therefore capture pupils' imagination – how on earth could they generate interest in the subject?
Professor Alan Smithers, director of the Centre for Education and Employment at the University of Buckingham, said: "I think we've made a big mistake about the way we've gone about teaching maths in England.
"Experts in maths have been interested in it at a deep level and have wanted to teach about it at a deep level. "You need to build up to that from a functional level – give kids a good platform at kindergarten. You can learn to add, subtract and multiply at primary level and do a lot of mental arithmetic and then build on that in secondary school."
At the moment, according to the Confederation of British Industry, maths teaching in UK state schools is failing – and billions of pounds of export orders are being lost as a result. A survey of employers revealed 50 per cent were dissatisfied with basic numeracy standards.
It also revealed stories of Polish workers outclassing their British counterparts. "If businesses can't find the skills or work attitudes that they need in the national workplace, they can perfectly well recruit them elsewhere," said the CBI's director general, Richard Lambert.
Attempts by the Government to tackle the lack of numeracy skills among adults in the workplace appear to be floundering.
A report by the National Audit Office revealed that only 2 per cent of workers who lacked basic numeracy skills had responded to a government drive to persuade them to study for a qualification – leaving an estimated 24 million adults struggling with numeracy problems.
How can we ensure the next generation do not leave school with the same problem? The international survey of trainee maths teachers, conducted by the University of Plymouth and published in the Times Educational Supplement, would seem to suggest that we have our work cut out.
David Burghes, the director of the Centre for Innovation in Mathematics Teaching at Plymouth, said he was alarmed that so many had got "very basic questions" wrong. "We are so far behind other countries and the international average in terms of logic and rigour," he said.
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