The burden of proof
Underqualified primary school teachers leaving children ignorant of basic concepts, the loss of potential mathematicians to other more "glamo rous" subjects, and even the introduction of calculators and computers are some of the reasons given for the perceived decline in standards.
The general feeling that school leavers are poorly prepared for mathematics-based degrees was confirmed by an Engineering Council survey* this month which reported that the mathematical knowledge of first-year undergraduate engineering students had declined compared to 10 years ago. The Council blamed lower entrance requirements and an increase in the number of undergraduates from vocational backgrounds.
Meanwhile, dozens of universities are introducing four-year degree courses because students are arriving with gaps in their mathematical knowledge and need time to catch up. Faced with such evidence, the School Curriculum Assessment Authority has called for a "back to basics" approach while maintaining that the content of the curriculum is basically sound. But it has been singled out for criticism by a group of academics for having no mathematicians among its members.
One of them is Sir Wilfred Cockcroft, whose 1982 report laid the ground for the introduction of GCSE maths and recommended improvements to teaching, training and examinations. Thirteen years later the same areas are under scrutiny. "It's the attitude towards the students that worries me," he says. "In the present debate those who are receiving students from school seem to be more vociferous and we must take their criticism seriously because they dictate what goes on in schools. It is the attitude towards the students that worries me because they are the losers at the end of the day and they only get one chance."
Despite pressure from the academic establishment, the national curriculum is to remain unchanged for the next five years, and the one thing that most people are agreed on is the need for a full discussion of the issues so that perceived problems within the system can be rectified for the next millenium.
Professor Geoffrey Howson, of Southampton University, says that A-level results have improved from a position 10 years ago when 30 per cent of candidates were routinely failed under norm referencing. "The whole thing about standards at A-level is that they have fallen and they needed to. What we have to ask now is whether those standards, aims and contents are appropriate. "
Professor Howson, committee chair of the London Mathematical Society, the subject's national body, believes that we should be testing new materials in the classroom. "What we need is curriculum development and not curriculum change."
David Burghes, of Exeter University's Centre for Innovation in Mathematics Teaching, challenged the notion that standards are falling by comparing past and present exam questions. His research found that A-level maths is harder now than it was 40 years ago.
"The debate has got too extreme," he says. "My biggest worry is that fewer people are doing A-level - they are doing business studies or physics instead. Maths A-level is regarded as being too difficult. Over the past five years the number of A-level maths candidates has dropped by more than a third. This, rather than the question of standards, is the real worry. Maths teachers are demoralised by what is going on. We have become good at preparing kids for examinations but that doesn't help kids educationally. Exam success is not the same thing as knowing what it is about."
Professor Margaret Brown, chair of the Joint Mathematical Council, believes that mathematics is not attracting the calibre or number of students that it used to and is suffering from something of an image problem: "A-level maths used to be a much clearer group of students -they would do double maths and physics or maths, physics and chemistry. But the world has changed and far fewer people do double maths because many schools are not able to offer it and because people found it too difficult. One thing that everybody could agree about is that we have to make maths more attractive. Universities are beginning to realise that there is not a constant source of mathematicians. There will always be a group of students who love maths but they also have to sell the subject."
Selective reporting in the media has given an erroneous impression of falling standards, she says. "There is not a lot of evidence that standards have fallen. There was a big gulf between O-level and A-level and there is now an even bigger gulf between GCSE and A- level. The move towards mixed ability has held back some of the bright children. The national curriculum was intended to move us forward but it is only this year that children will leave primary school with a level in maths."
Peter Saunders, professor of mathematics at King's College, London, is widely credited with having started the row, but he says it has been going on in academic circles for years. He criticises David Burghes's research, ("it's not statistically sound") and says we only have to look at the extension of university degree courses for evidence of decline.
"Students that are coming up to university to read maths or anything that involves maths like engineering, are weaker and weaker. Leaving A-levels the way they were has made it unnecessarily difficult for the kids. They have not been sufficiently well prepared but it's not their fault.
"University departments all over the country are redesigning their first year courses to make them easier - that is a sign of the falling off of standards in schools but the people in charge seem totally unwilling to accept that anything has slipped at all.
"Until we can agree that there is a problem and what the nature of the situation is then we can't do anything. If kids can't manipulate simple formula easily then they have got a problem and the problem starts in primary school. Too many primary school teachers are uncomfortable with maths which, at that stage, means fractions."
He suggests one solution to this might be to introduce specialist maths teachers at primary level to instil basic mathematical know-ledge: "If you fail to pick up certain things early on then it makes everything you do later on more difficult." Failure to understand fractions can lead to problems with algebra which in turn makes students ill-prepared for more advanced calculus.
As evidence, he cites the notion of proof, which he says was more widely taught in the past and under the national curriculum is not studied until level 10: "People nowadays think to refute means to deny in a very loud voice - you hear them say it all the time in Parliament. But it really means to prove that something is wrong."
The five-year moratorium on change could be a good thing because it will give teachers a chance to catch their breath. To do a reasonable job of revision would, he says, take five years at least.
"In the next couple of years we must have a serious look at the whole situation so that if it turns out that something needs to be changed it can be," he says.
* The Changing Mathematical Background of Undergraduate Engineers is available free from The Engineering Council, 10 Maltravers Street, London WC2R 3ER. Send SAE with 45p stamp.