The inquiry into how to raise the popularity of maths, lift students' skills and end the dearth of teachers is not a theoretical exercise. Its chair tells Martin Ince that he expects to see his recommendations acted on, no matter the cost

Adrian Smith, rector of Queen Mary, one of the University of London's biggest colleges, does not come across as a traditionalist. But he is now involved in one of the most time-honoured activities of British public life - chairing an inquiry, this one into mathematics.

Unlike similar inquiries over the decades, this inquiry is quick and focused. The emphasis is on mathematics in schools, but Smith's terms of reference make it clear that university maths - particularly the falling attractiveness of maths-intensive university courses and the dearth of maths teachers - is also part of the equation. "We know that mathematics is required across great swathes of engineering and the sciences," Smith says. "But it has an impact in other subjects, too. And there are several points at which people are lost to mathematics on the way to A level."

One focus of Smith's inquiry, established by the Department for Education and Skills and administered by the Qualifications and Curriculum Authority, is the unpopularity of A-level mathematics and the effect this has on the number of applicants for university courses in maths and maths-intensive subjects, such as engineering and physics, compared with subjects such as biology and computer science.

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He suggests that the subject may suffer from the lack of a TV champion, a Simon Schama or a Lord Winston, to convey its excitement to a general audience. "Mobile phones or space missions would never work without maths," he says, "but there is nobody who talks about the subject in those terms."

Smith is emphatic that he has drawn no conclusions yet, but it is very likely that his final report will say that the school maths curriculum lacks excitement and needs an update. He also fears that the path from GCSE to A level and university maths may be too difficult - hence the high dropout and failure rates - and could be smoothed.

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And he is certain to conclude that a massive ingredient of the problem is the shortage of good maths teachers. Many children are taught maths by graduates in other subjects. There are moves to bring in more specialist maths teachers and to keep more of those already in post. Numbers could also be increased by using postgraduates in the classroom. In the longer term, there need to be more of what Smith terms "maths or near-maths" teachers, and the dearth of these desirable people poses a paradox.

As Smith sees it, there has been a huge increase in job opportunities and financial rewards for mathematicians, especially in finance and computing.

But the number of maths graduates available has not grown at the same pace.

"How can we induce people to become mathematics teachers with this sort of competition?" he asks rhetorically. "We will need to look at the issue sensitively, and it is very difficult." Teaching is unlikely to rival the money on offer in the private sector. But Smith also cites "anecdotal evidence" that "the general life of a teacher is very hemmed in by assessment and the curriculum". This is true throughout teaching, but maths is one of the biggest problem subjects.

Smith also wants to know more about the success of "golden hellos" designed to tempt people into maths teaching. They may work in the short term, but long-term career development might be needed to make a real difference.

Tempting mid-career professionals into maths teaching is another promising route if sensitivities among teachers and their unions can be overcome.

One way or another, Smith says, "nobody seems to be happy" with school maths. Employers and universities note that young people have poor mathematical skills. But Smith agrees that maths is not education's only problem area. Similar issues arise, for example, in modern languages, which politicians also enthuse about but which increasingly fail to excite students. Languages and maths have suffered a similar decline, he says, but in maths it is potentially more damaging.

One difference between maths and other subjects, Smith thinks, is that its structure is progressive and vital. "In history, you can probably learn something about the 15th century without knowing about the 14th," he says.

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"In maths, you learn brick by brick and you have to start with the foundations, not in mid-air. You cannot opt in and out of parts of the curriculum. Instead, you need to get under the skin of the subject."

Modularisation might be a particular enemy of good maths teaching because it involves examining small parts of the subject in a way that is inimical to broader understanding.

There is also the issue of what ought to be in the school maths curriculum.

Smith says there is no unanimity about what should be covered. "We need some proper professional insight into what the key ideas are and how they fit together. And we will want to look at whether the existing curriculum strays too far from that path."

He thinks it is possible that material with a tangential relationship to maths is chewing up too much class time. "Twenty years ago, there was plenty of time for subjects such as differential calculus. Now school students meet the subject but do not have enough time to get the skill of using it in detail. The same applies to other key areas."

Such views form part of a wider debate on the amount of material being inserted into the school day. For example, Smith says, computing and data analysis are often taught in time taken out of maths. These are useful skills, he says, but they should not be acquired at the expense of mainstream maths.

Smith is happy to see variety and diversity in maths teaching, but he insists that there should be a core of agreed content that everyone must acquire.

His inquiry is now gathering evidence from a formidable range of organisations - the list of bodies that the DFES recommends he consult is as fat as the telephone directory of a modest city. The key questions being investigated - on teaching, assessment and curriculum - will also be examined by a team of researchers. And the plan is to have a full report in July.

As a theoretical statistician of renown, Smith is doubtful about some of the received wisdom about crises in mathematics and sceptical about international league tables of mathematical achievement. He wants to find out in more detail which countries have problems comparable to the UK's and which think there is nothing to worry about.

But his investigation is not a theoretical exercise. He does not want ministers to "note my findings with interest". Instead, he expects that his "strong recommendations will be acted on", even if it costs money to do so.

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