abilities often remain undeveloped.
I shall focus on maths, but my analysis may apply to other "hard" subjects.
In maths, the numbers taking A-level have slumped, despite attempts to make the subject more accessible. Universities find it increasingly hard to find home-grown applicants, and international comparisons show that few Year 9 pupils can solve simple two-step problems. What has gone wrong? And what needs to be done?
First, we have embraced a false view of education as a single ladder, up which all pupils scramble at different speeds. To make the ladder accessible to the majority, its steepness has been reduced. The only challenge for able pupils is to proceed more quickly. There is a national curriculum but no uniform mathematical "ladder". A taller building demands stronger foundations. Those who wish to climb higher must first "dig deeper". The national curriculum provides a common framework, but that framework has to be interpreted for different groups - without blocking future pathways unnecessarily. The idea is implicit in specialised diplomas. But we have failed to apply the lesson to improve school maths for able pupils.
The second error is in the choice of target group. No policy can be based on targeting 5-10 per cent of each cohort. To focus on such a small group draws attention away from ordinary classroom teaching - as if out-of-school activities suffice to nurture ability. Extra-curricular activities are fine, but daily classroom maths is where those experiences take root. The point was central to the original Ofsted review of the gifted and talented strategy but has never been taken seriously.
We need a realistic target group (around 25 per cent) and a curriculum and assessment framework to support schools in improving daily provision for them. This would give every school appropriate objectives for at least one top set. A second maths GCSE from 2010 offers an ideal opportunity to incorporate such provision, so that 50-plus per cent of 16-year-olds emerge with a better grasp of elementary maths, and those among them with real ability can mature slowly and effectively.
The author's new series, Extension mathematics, will be published by Oxford University Press later this year
Dr Tony Gardiner is Reader in Maths and Maths Education at Birmingham University