Can we solve the maths crisis?

Maths, it seems, has officially been designated as "in crisis". A year or more of gloomy headlines about falling standards and teacher shortages has been followed by a tacit admission that something is seriously awry with the appointment of a government inquiry.

No one seriously disagrees that the inquiry is needed. Unease about what was happening in the profession rocketed after embarrassing results in the first year of the new maths AS-level, 2001. Almost one-third of candidates failed; an unacceptably high rate, which has had a knock-on effect because students have been deterred from attempting A2-level.

That, in turn, has affected university applications, where the numbers declined again this year – by 4 per cent. That's on top of last year's 12 per cent drop.

"Spiral of decline" has become the most-used phrase to describe the resulting non-virtuous circle. Fewer graduate, fewer go on to teach maths, and fewer well motivated, qualified teachers make it back to the classroom, leaving pupils with less than satisfactory teaching which, in turn, makes it less likely that they will opt for maths themselves.

In the circumstances, the higher education minister, Margaret Hodge, might have been accused of understating the case when she said late last year that there had been "unease" about the current curriculum framework and about standards in areas relying on good mathematical skills. Her solution – the appointment of an inquiry into the entire state of post-14 maths, headed by the Principal of Queen Mary, University of London, Professor Adrian Smith – is welcomed as a sign that the Government recognises that the situation requires attention, despite concerns about the timetable. Professor Smith was due to appoint his steering group at the time we went to press. He is expected to report by June; a tight six-month turnaround, which some in the profession contrast unfavourably with the three years devoted to the last major maths inquiry by Lord Cockroft.

If Professor Smith is resigned about the timetable, however, he is determined to seize the moment and to try, as he puts it, to "bottom out the myths" that have grown up around the subject. "There is a lot of work to do in assembling an evidence base. There is a lot of anecdote around, and possible prejudice," he says.

This might be because there still seems to be real disagreement in this country about what maths is for. According to Crawford Craig, the head of maths at a Leicestershire upper school for 14- to 18-year-olds, Bosworth College, maths is subject to the push and pull of two opposing forces. There are some university-based specialists who want maths to be as difficult as possible, and who have an interest in the elite among maths achievers. And there are those who want it to be easier and more accessible.

Since the early Nineties these forces have slugged it out, it seems, with maths syllabuses vulnerable to criticism for dumbing down. Mr Craig's experience – he is a former council member for the Association of Teachers of Maths – has led him to plump unashamedly for easier access. He recognises that this is a controversial view, although it is shared by many members of the association.

"If we want a society in which a lot of people feel good about maths, and can look back on their classroom experience with fondness, and a feeling they've succeeded, we are going to have to let them pass exams," he says. He realises that this comes at a price, in the levels of attainment of those reaching university, but believes that the top 3 per cent of attainers who can tackle upper-end maths will always do well – they have the ability to build on what they are taught.

Acting as referee in this academic joust, with feelings often running high, will prove difficult. The inquiry will have to take a view on some central points. Its terms of reference include making recommendations on changes to the curriculum, a prospect not terribly inviting for those at the chalk face who feel they need a break from constant innovation. But current GCSE and AS-levels in particular are not satisfactory; a fact recognised by the Qualifications and Curriculum Authority (QCA), which has just published revised criteria for AS- and A-level maths.

Chris Belsom, a member of the Advisory Committee on Maths Education (Acme) and the head of maths at Ampleforth College, points to the need for a modified GCSE, ensuring better-prepared candidates at AS-level, and AS- and A-levels that are broadly comparable to other subjects in difficulty. These, he says, have to be set within more varied provisions for post-16 to encourage people to take the subject up.

"We don't want a quantum change, but a carefully planned transition," he says. "Schools have been subject to a lot of change. If there are to be more changes, we need a short transition from where we are now to where we agree we need to be."

AS-levels, he says, have been stretched to breaking point to accommodate a wide range of ability and interest, so wider provision is needed. Free-standing maths qualifications already exist and are well regarded. They need to be brought into a more coherent package and widely recognised by universities so that students are happy to take them.

For the most able, he would prefer "enrichment rather than acceleration" – for example, giving them proper challenges such as good use of information technology. That, he says, requires good teaching.

His colleague at Acme, Annie Gammon, who is the head of a 1,000-strong comprehensive in Tower Hamlets, east London, agrees that the situation at GCSE is part of the problem. Maths is the only subject to have three tiers – higher, intermediate and foundation.

This was a deliberate strategy to cover the wide spread of attainment in the subject. But it has had some unfortunate consequences, because schools wishing to play safe enter even bright students for the intermediate rather than the higher level, which would be a better preparation for A-level. And lower down the scale there are frustrations. A pass at foundation level, where the highest grade is a D, doesn't cut much ice with universities or employers looking, usually, for a C grade. The QCA is currently piloting a two-tier exam.

Exam reforms aside, the aim, Ms Gammon says, should be for everyone to carry on doing maths in some form, if necessary with strong IT or vocational elements.

That would need more teachers. And there is perhaps a ray of hope – she is cautiously optimistic that the Government's "golden handshake" policy of encouraging more mature teachers back into the classroom is making inroads. A recent tour she did of 15 different schools in Tower Hamlets, as maths consultant for the borough, did show that they were beginning to turn up, she says.

Maths is still one of the top subjects for teacher shortages, however – 17 per cent of all teacher vacancies in secondary schools are for maths teachers. Acme has proposed a new national academy to co-ordinate local maths centres, which would see those from universities and schools working together to plot a way forward. Similar centres operate in France, which now has a surplus of maths teachers to contrast with our acute shortage.

The demand for maths is increasing in many subjects, says another Acme member, Celia Hoyles – not just in science and physics, but in economics, social sciences, geography and business studies. And although you don't need maths for a general degree, it does help to be numerate.

And in the end it is perhaps the failure to prove the subject's worth to the merely competent or the less able that is the most disappointing, and most harmful to a country where it is still, shamefully, fine to admit that you can't add up.

What is certain is that more negative headlines of the sort we have been seeing will only contribute to the decline of maths, with serious implications for the knowledge-based economy the Government is so keen on developing, let alone for our individual mathematical health. Professor Smith says that his inquiry, provided it is creative enough in its recommendations, and that there is the political will to follow them up, could provide a "one-off opportunity" to stem the tide.

He also says that "the challenge begins in schools". There is no quick fix – the changes mooted for AS- and A-level won't even get into the classroom for another year, and maybe the sort of changes needed to turn things round will take a generation or two. But his inquiry needs to at least start to address the complex issue of what sort of maths we want in our schools, and who it is aimed at. Perhaps one day we could even become a nation of maths lovers, able to spot a piece of statistical trickery when we have to. It is much needed.

education@independent.co.uk