What is school mathematics for? Is it a) to provide the skills needed by future economists, engineers and scientists; b) to enable people to deal with everyday situations such as understanding bus timetables and tax returns; or c) to train young minds to think logically and analytically and improve their problem-solving skills?
The answer is all of the above. Yet, for more than a decade, government policy has concentrated on numeracy, or basic maths skills, such as addition and multiplication.
The national numeracy strategy is based on the belief that if school leavers could master their multiplication tables, they would be more employable.
Numeracy levels have improved, but the goalposts have shifted. Globalisation and technology mean workers need more complex skills. Technological developments are unpredictable, but some academics suggest that if more weight were given to problem-solving, young people would be better equipped.
"When the numeracy strategy was brought in, it was a downgrading of maths to elements that mathematicians themselves would not regard as important," says Dave Pratt, professor of mathematics education at the Institute of Education in London. As the strategy developed, it did cover a wider range of skills than the traditional syllabus, he said. But students needed to be introduced to higher level ideas, too.
The numeracy strategy has reduced mathematical underachievement. Britain surged from 24th in international comparisons of the maths skills of 14- year-olds in 1999 to 10th by 2003. But at a cost.
"The worst lessons got better, but the numeracy strategy was prescriptive, so it also restricted teachers and we lost some of the best teaching," says Margaret Brown, professor of mathematics education at Kings College, London. "The problem is depth of understanding. The exam system does not equip people to solve difficult problems, it trains them to solve routine ones."
This view is echoed by many others. Paul Andrews, a senior lecturer in education at Cambridge University, has researched maths teaching in Hungary and Finland. Both perform better than England in international comparisons.
"In Hungary, no two problems worked on in class are the same. Here they are all similar. We don't teach maths in this country, we teach routine skills and procedures," Dr Andrews says.
Recent Ofsted subject reports found that too few secondary pupils could transfer what they have learned to different situations and solve problems.
Teachers, particularly in primary schools, admitted it was difficult to find engaging real-life examples that use numeracy.
Exam questions were "embedded in artificial contexts, in a failed attempt to make everyday experiences the basis of the question," said the think tank Reform in its 2008 study "The Value of Mathematics".
Research into how workers use maths shows the difficulties of transferring numeracy to employment. "Very little numeracy is used in the workplace. Even the till at the supermarket calculates the change," says Richard Noss, professor of mathematics education and co-director of the London Knowledge Lab at the Institute of Education.
The Knowledge Lab studied how different non-graduate groups such as nurses and car mechanics use maths and technology at work.
"We call this techno-maths, because it combines maths, ICT and workplace- specific skills," says Professor Noss, "Computers open doors into deep mathematical ideas that would not have been possible before."
While it could be argued that the first wave of computerisation led to deskilling, this has been accompanied by the need to upskill and understand what lies behind the technology. Numeracy does not deal with that. "A mathematical way of thinking should be the single most important outcome of 13 years of maths education," says Professor Noss. "But there is this tension all the time in maths - it is a subject we need, but it must also be useful."
In the latest international comparisons, England is middle-of-the-road in maths skills. The Trends in International Maths and Science Study (TIMSS) released last year, put England's 8 and 14 year olds ahead of countries like Germany, Australia, and the US. But improvements have slowed compared to 1999-2003.
East Asian countries such as Singapore, Japan and South Korea are still way ahead, particularly on higher level mathematical thinking where the average skills are "out of reach" of 90 per cent of British pupils.
Although Asian countries have moved on from traditional maths to problem solving, there it is regarded as mental training.
"Our maths curriculum talks about developing intellectual competency and using maths as a platform for good thinking," says Dr Yeap Ban Har, assistant professor of mathematics education at Singapore's Institute of Education. "Dealing with abstract maths helps develop the mind, which is very useful to a person."
"Maths is crucial for mental development," agrees Celia Hoyles, director of the National Centre for Excellence in the Teaching of Mathematics and a former chief government adviser. "Every child deserves a good maths education for its own sake."
Many secondary pupils in England would find that challenging. Ofsted highlights pupil motivation problems, even though studies show that pupils here enjoy maths more than their East Asian counterparts.
But some argue the government and teachers are making excuses on behalf of children who have an issue with maths teaching, not the subject itself. The latest study showed three out of four 14-year-olds in England valued maths highly - a rise of 10 per cent on 2003.
Political thinking has shifted slightly under Gordon Brown. Maths is important if the country is to remain economically competitive, not just for employment skills.
That was the view when financial services, requiring high level mathematical skills were a major driver of the economy.
It will become more true if science and innovation replace a busted financial services sector in driving economic growth post-recession. Hence the announcement in March to increase the number of A-level maths students from 56,000 in 2009 to 80,000 by 2014. Impressive, except that the number of students doing maths A-level was 86,000 in 1989. Mathematics made up almost 13 per cent of A-level entries that year. By 2007 it was 7.4 per cent. The think tank Reform calculated that if the number of A-level mathematicians had remained constant, there would have been an additional 430,700 since 1989. However, attitudes may be changing. Those doing maths at university rose 8 per cent last year, according to the Higher Education Funding Council for England.
Meanwhile, a new kind of maths has appeared on the government's skills agenda. Functional mathematics will be taught as part of the new twin maths GCSE which the first pupils will sit in 2012.
One GCSE will emphasise application (functional maths) and the other reasoning, or pure mathematics. The two GCSEs will have different but overlapping content, not significantly exceeding what is taught now, according to the Advisory Committee for Mathematics Education (ACME).
But there is widespread scepticism. "If you only do functional maths, you are certainly doing less maths than at GCSE," Professor Hoyles says. "We don't want that to be the limit of aspirations."
"The original intention was that if maths is taught well, learners would tend to pick up functionality anyway," says Jane Imrie, President Designate of the Mathematics Association. "Labelling it separately does not mean it is new."
Dr Edwards is more scathing. "Functional maths is nothing to do with mathematics," he says. "It is social maths and could easily be taught in PSHE lessons."
ACME, under the auspices of the Royal Society, acts as a voice for the maths community. In a recent position paper on functional maths it expressed concerns: "There seems to be no appreciation of the fact that an important aspect of understanding mathematics is the ability to think abstractly.
"This is not easily tested or enhanced by linking mathematics to its applications in everyday life".
Then there is the new modular GCSE. Modular courses are already blamed for a decline in A-level standards, and the exams could scupper hopes of the dual maths GCSE improving the teaching of mathematical concepts.
Whether it is functional maths or numeracy, the problems remain the same. Jane Imrie says: "If the subject isn't a vehicle for wider mathematical skills, then you are not future-proofing the kids."