In its preoccupation with basic numeracy and mental arithmetic, this government is ignoring our continuing mathematics crisis. Ministers (and journalists) appear convinced that no child in the United Kingdom can add up - which is simply not true. Their policies also imply that constant arithmetic drill - in primary school, secondary school and teacher training - is the economic priority. That isn't true either - worse, it is distracting us from reforms that matter as much, and probably much more, to the UK's future.
The numeracy panic is ironic given the three decades of emphasising lower achievers and the common core. That policy had its triumphs, notably through GCSE, where all but 9 per cent of our 16-year olds now complete a full mathematics course. Meanwhile, we have ignored the effects on mathematics for our higher-achieving students, and have failed to reform our sixth-form studies. The result is a widening gulf between the UK and the rest of the industrialised world in the adequacy of our education for an economy built around symbolic and mathematicised systems.
Whatever their relative "difficulty", a 1998 higher-tier mathematics GCSE and an O-level from the late Sixties or early Seventies are very different creatures. As a cursory comparison shows, O-level demanded far more practice in algebraic formulation and manipulation, in series, in geometry, in proof. The contrast between O-level and the intermediate tier is more stark yet - a candidate with a B grade obtained on the latter may have done virtually no algebra, and is encouraged to use "trial and improvement" (trial and error) methods to solve problems - "what is not algebra is called algebra" as the Royal Society has complained. Yet these are some of our highest-achieving students, and this is the last formal mathematics many of them will ever study.
Does it matter? A report last month from the London School of Economics quoting 10 per cent pay differentials for those with maths A-level suggests it does. Western graduates from elite universities nominate the big management consultancies - McKinsey, BCG, Bain - as top "first destination". Of last year's London intake at one of these, the degrees of 80 per cent were highly quantitative (maths-oriented), of another 10 per cent slightly less so. The City and the computing industry soak up good maths and physics graduates. Older, often foreign-born, applicants are what keep my own institution's PGCE mathematics afloat.
Or consider Roger - safe "B" at GCSE on the intermediate tier. His school's advice? Better not risk a C on the higher tier. Hard-working; good grades in A-level geography, economics and history; reading economics at university. Or rather, attempting to. Because his university can specify only GCSE, and not A-level maths if it is to fill its places; and with GCSE maths at intermediate tier, Roger simply cannot read the literature of economics.
Similarly, in a highly-rated biology department, Lindsay despairs - the evolutionary theories that have transformed her subject are mathematical and so inaccessible to many students.
Pharmaceuticals is one of the few areas in which we possess truly world-class companies. Our best universities are struggling as many of their bright chemistry students now enter with a two or three-year gap since their last (GCSE) maths lesson. How long, in this situation, can British pharmaceutical companies and universities maintain a world-class ranking?
It was always crazy to stop teaching mathematics to our future managers, professionals and academics at the age of 16. To create the modern GCSE and make that the end-point was crazier still. Worst of all was the decision to make a B grade available on the intermediate tier in the context of points-based league tables. Overnight, the percentage of upper-tier entries plunged from 29 per cent to 17 per cent of the cohort.
The UK is unique in effectively forcing large numbers of its children to abandon mathematics at age 16. Among all our European neighbours, mathematics is a core part of every student's timetable through to the end of upper secondary schooling, and a formal requirement in vocational and apprenticeship programmes. In the United States, a concerted effort to upgrade mathematics teaching in high school has raised the proportion of graduates completing the demanding pre-college programme tenfold in little over a decade.
Many readers will have heard of Sarah Flannery, the Irish schoolgirl who has developed a new way of encoding electronic communications (The TES, February 5). Not an ordinary child, not an ordinary maths teacher - but a completely ordinary Irish school, in a country where a large part of the cohort will quite naturally take mathematics through to Leaving Cert, not abandon it at Junior Cert at 15.
Our system implies that only a tiny elite needs any serious mathematics. Untrue - and even on its own terms, that system is failing. Sixth-formers, with a realistic grasp of life in a rapidly changing economy, are increasingly unwilling to specialise. More and more opt for mixed A-levels. The popular choice is now a single maths A-level, not the "pure" or "applied" of mid-century. The result may be more balanced, but it cannot provide the preparatory in-depth specialisation our three-year maths-related degrees assume. Fewer than one in 10 maths A-level entrants now takes further maths: in the past five years, entries have continued to fall in percentage terms, from 8.4 per cent to 7.9 per cent. Our universities cannot now demand more than one maths A-level, even for maths and physics degrees.
How did we get here? Our sixth-formers are not suffering from cumulative maths terror - in relation to cohort size, maths entries have actually risen slightly in the Nineties, and encompass a large proportion of higher-tier as well as some brave intermediate-tier graduates. Further mathematics, by contrast, is threatened by low demand, teacher shortages and restrictive funding regimes.
The pattern of entries for further maths is hugely unbalanced. For the past five years, on average, the independent schools have provided a fifth of the maths A-level entries, but a third of those in further maths. The further education colleges enter a steadily decreasing percentage of maths A-levels entries - now down to 6 per cent - and only 2 per cent of further maths: this from the UK's main providers of second chance and adult education. There was justifiable delight that two of last year's Fields medals (mathematics' own "Nobel prizes") went to English mathematicians: but was it chance that both were educated in the highly selective fee-paying sector?
The Qualifications and Curriculum Authority, to its credit, is concerned at the low level of upper secondary mathematics and is promoting new qualifications (see page 24). But politicially, numeracy reigns.
Are ministers aware that their policies encourage schools to make A-level mathematics inaccessible to the bulk of GCSE candidates, threaten the survival of high-level school mathematics outside the independent sector, and are creating a workforce whose education is increasingly out of kilter with the growth sectors of the 21st century?
Alison Wolf is professor of education and head of the mathematical sciences group at the Institute of Education, University of London