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Make maths count

Why do our pupils struggle to solve simple equations once outside the exam hall? Tony Gardiner searches for the root of the problem

Tutors in despair at illiterate freshers" ran the headline in The Times Higher Education Supplement (February 10). "Undergraduates are entering university less numerate than ever before," it said. Should we be worried? Or is this another case of academics failing to adjust? The reality is more complex, but in mathematics it is no less depressing. The "tutors" were from the Russell group of universities, those "just below Oxbridge" in the pecking order. Having suffered separately in silence for five years, they have spoken out together.

The problem is especially acute in maths and related disciplines. Why have Oxbridge colleges not joined the complaints? They are struggling to reach more "ordinary" schools; perhaps joining a chorus of complaints about "standards" could compromise these efforts. But they are also international universities: if the supply of good home-grown applicants dwindles, they turn to applicants from elsewhere. Recent years have shown a steady decline in the number of UK-plus-EU maths undergraduates they have accepted of between 5 and 7 per cent a year. UK numbers alone may have declined even more sharply.

School maths matters. Modern society cannot function without serious maths - it is at the heart of everything from machine tools to product design, from the stock market to the distribution of goods, from the internet to mobile phones. If the number of competent home-grown school-leavers does not increase, it is not just call-centres that will be outsourced to distant lands: we risk sliding from the G8 into the ranks of the Banana Republics. The number of A-level maths students has slumped from 85,000 in 1989 to 66,000 in 2001, and (thanks to the misconceived Curriculum 2000 reforms) to just 52,000 in 2004.

In his 2004 report on post-14 maths education, Making Mathematics Count, Professor Adrian Smith used undiplomatic language. "If there is no significant restoration of numbers within the next two or three years, the implications are so serious that consideration should be given to offering incentives for students to follow these courses," he wrote. He argued for incentives such as giving A-level maths additional UCAS points.

Two years later, nothing has changed. A recent study by the Qualifications and Curriculum Authority (TES, February 10), struggled to assemble relevant data; but the authors lacked the authority to propose "solutions". They repeatedly glimpse the truth, but close their eyes. They realise that GCSE maths provides an inadequate foundation for subsequent work; but fail to draw the obvious conclusion. Adrian Smith insisted that GCSE be more focused; this report sits on the fence. Professor Smith urged the QCA to develop an "extension curriculum and assessment framework" to allow able 14 to 16-year-olds to experience elementary maths as something worth pursuing; this report remains unaware that the QCA has consistently blocked this.

Since the late 1980s, A-level maths has struggled to serve two groups with quite different needs: a core of basically competent students, and a large rump of reluctant fellow travellers. Yet this report dare not advocate "courses for horses" - which is the only justification for treating 14-19 as a single phase. (The same misplaced egalitarianism affects the QCA's advice on changes at 14-16.) The report estimates neither the relative sizes of these two groups, nor their potential for "growth". Nor does it propose structures that might lead to "significant restoration" in numbers.

Instead, it assumed there is no scope for attracting able students: "It is those who are less strong that must be appealed to if A-level maths is to increase its participation rates significantly". Who cares about "participation rates" if what they participate in is no longer maths? There are 31,500 students achieving A* grades in GCSE maths; yet the authors have no idea how many of these take maths A-level. One might expect between 10,000 and 15,000 to go on to A-level (the current number is probably much lower), and one can imagine incentives that would increase this to 20,000-plus. So there may be considerable scope for attracting more able students to take up A-level. And a carefully conceived "extension curriculum" at key stages 3 and 4 could uncover many more mathematicians manque.

Professor Smith also highlighted the destructive effect of "modularisation"

on A-level maths teaching. Yet the report ignores this. The QCA even seems determined to extend "unitisation" to GCSE - which may appeal to bureaucrats, but it will tear the heart out of elementary maths.

Which leads us back to the national curriculum. International comparisons at Year 9 suggest we do a poor job at this level. Our position is especially weak at the top end. Where comparable countries have 13 per cent or more of Year 9 pupils performing at a "higher level", England has just 5 per cent - worse than several developing countries. The national strategies have spent megabucks "driving up" standards in literacy and numeracy. But one cannot "force" things to improve. The quality of maths education depends on how it is taught over an extended period. Practice is essential; but genuine improvement (as opposed to improved test scores) cannot be achieved by repeating meaningless tasks "because they will appear on the test". In a recent study Year 5 pupils in 29 countries faced "15x9 = ?".

This is exactly what the strategies have focused on; yet English children performed poorly. (The international average success rate was 72 per cent.

The Far East and Russia - where children start school two years later than here - managed more than 90 per cent. England achieved just 59 per cent.) Maths has to be taught as a coherent subject, not a list of separate exam topics. Our test-driven approach has produced a nation of experts in completing predictable "one-piece jigsaws". Those emerging from our schools cannot handle the simplest multi-step problems. No wonder those tutors complain.

Dr Tony Gardiner is reader in mathematics and mathematics education at Birmingham university

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