Andrew Adonis, the Schools Minister, did not even try to hide his irritation. Writing in The Times on August 21, the day the GCSE results were released, he lashed out at those who would claim that the exams were being dumbed down instead of celebrating the increasing numbers of students getting A and A* grades.

"It is the class-based elitism that instinctively wants to ration success and cap the aspirations of the less advantaged," he wrote. "The underlying premise is that there is a fixed pool of talent in society." And then came this breathtaking assertion: "There is no genetic or moral reason why the whole of society should not succeed to the degree that the children of the professional classes do today, virtually all getting five or more good GCSEs and staying on in education beyond 16."

Why breathtaking? Isn't that pretty much what both Labour and Tory politicians say? It is part of the received wisdom among politicians whenever they talk about education: except for a few children with severe handicaps, they assert, all children can succeed on the academic track if the schools do their job. Politicians argue only about which policies will achieve this obviously attainable result.

Adonis's statement was breathtaking nonetheless because, scientifically, it is not true. His belief that nearly all children can be proficient at academic skills is educational romanticism. Many children are just not gifted enough to learn to read and write at more than a rudimentary level, far short of the level required by a GCSE, and the schools can only tweak their performance at the margins. An educational system that serves all the children must begin by recognising that truth.

The phrase "many children are just not gifted enough?.?.?." would be completely uncontroversial if it described any ability but intellectual. A quarter of a century ago, Howard Gardner, the American educational scholar, famously sought to topple the word intelligence from its pedestal by arguing that there are seven different intelligences: kinesthetic (roughly, athletic), musical, visual-spatial, interpersonal, intra-personal, linguistic and logical-mathematical. Let's accept his classification and apply the concept of "just not gifted enough" to the first five of them. Imagine that each sentence begins with "No matter how much training I get?.?.?."

"I am just not gifted enough to do a somersault with a half twist off the pommel horse" (kinesthetic).

"I am just not gifted enough to understand why someone would choose to compose a piece in B major rather than C major" (musical).

"I am just not gifted enough to see a chessboard in my mind and move pieces on it" (visual-spatial).

"I am just not gifted enough to be a first-rate teacher" (inter-personal).

"I am just not gifted enough to stick with a no-sweets diet" (intra-personal).

None of these tasks is especially difficult for someone who is well above average in the ability in question. All of them are extremely difficult for people who are around the average. All of them are impossible for people who are well below average - not just difficult, but impossible. To be below average in any ability is to be quite limited in the things one can do. And when children show up at the school room door, 50 per cent of them are below average in every single one of those abilities.

Now apply the same test to the last two of Gardner's seven intelligences:

"I am just not gifted enough to understand text with big words and complicated syntax" (linguistic).

"I am just not gifted enough to factor an equation" (logical-mathematical).

Fifty per cent of children are below average in linguistic and logical-mathematical ability. Being below average means that they are limited in the things they can do in reading and maths. It is no more remarkable than being limited in the things one can do in sport or music.

And yet to say such things in public is to invite shock and ridicule. The educational romantics will pummel you with four objections: 1) When children are below average, we can raise their ability; 2) the schools are so bad that children at all levels of ability can learn much more than they are learning now; 3) the rising test scores of the past decade prove that major improvements are possible; and 4) there's no reason why the high educational achievement of children of the professional classes of ability cannot be achieved by all classes.

First, a bit of housekeeping. When talking about ability to succeed in the academic track, two of Gardner's abilities, linguistic and logical-mathematical - the two abilities that dominate IQ scores - are crucial. Rather than referring to them separately, from now on I will refer to the combination of the two as academic ability. This is not to say that those two are the only abilities relevant to success in school. Intra-personal ability in the form of self-discipline and perseverance is also important. But all the self-discipline and perseverance in the world won't help if enough underlying academic ability isn't there.

Think of the relationship of academic ability to academic success as you think of the relationship of height to success as a centre in a professional basketball team. Height isn't the most important factor - for people who are at least 6ft 10in (just over 2 metres) to begin with.

Now to the first issue: do we know how to raise academic ability through interventions? Since the most intensive experimental efforts to raise academic ability have been undertaken in the United States, and by now we have accumulated 40 years of evaluations of their success, I will use American data for the answer: the best we can do is nudge academic ability by a small increment, and even that much is difficult and uncertain.

The attempts to raise academic ability have focused on the pre-school years, on the plausible assumption that this is the period when the brain and personality are most malleable. During the height of the optimism about the potential effects of social programmes during the second half of the 1960s and throughout the 1970s, many intensive experimental pre-school programmes were mounted. Most of the programmes were haphazardly or tendentiously evaluated, but enough good studies came out of this period to enable an academic group called the Consortium for Longitudinal Studies to conduct a comparative analysis of 11 of the best pre-school interventions.

The consortium found that they produced an average short-term gain of about 17 percentile points relative to a control group (for example, an increase from the 20^th percentile of all students to the 37^th percentile of all students). However, this gain fell off to about 7 percentile points after three years, leaving a trivial net change. The consortium's bottom line was that "the effect of early education on intelligence test scores was not permanent".

Since then there have been other attempts using intensive pre-school enrichment, notably the Abecedarian Project and the Infant Health & Development Programme. They shared a common fate - large gains in the first follow-up, leading to widespread publicity and claims of success, then fadeout to insignificance as the children reached adolescence. The bottom line: at best, we can move children from far below average intellectually to somewhat less below average. No one claims that any project anywhere has proved anything more than that.

Never mind, say the educational romantics. The schools are so bad that even low-ability students can learn a lot more than they do now. Judging from newspaper accounts, there is some truth to that position.

British stories about political correctness gone mad, classrooms where the teachers have given up trying to keep the children under control and schools where nothing is taught and nothing is learned resemble the stories about the worst-of-the-worst inner-city schools of the United States.

Insofar as such schools exist in England, of course the schools can do much better. But in the United States those schools enrol a few per cent of all students. Ordinary government schools in the US have decent facilities, orderly and nurturing classrooms and teachers who range from bad to excellent, with most clustered in the category of competent. Reading and maths are taught energetically and with substance. The main problem with ordinary schools in the US is that history, science and the arts have been stripped of their content in much the same way that reports say they have been stripped in England.

I will assume that most English schools outside the worst neighbourhoods are roughly comparable to my description of an ordinary American school. How much can an ordinary English school do to raise the academic performance of its students? If the question is framed in terms of teaching them bodies of factual material about history, politics and citizenship, science and the arts, the increases in learning across the board could be dramatic. But if the question is reading and maths, the answer is that the quality of the school makes surprisingly little difference.

This counterintuitive result was first exposed in the United States in 1966 with the publication of the Coleman Report. Named after the sociologist who led it, the magnitude of its effort remains unmatched by anything done since. The sample for the study included 645,000 students nationwide. Before Coleman's team began its work, everyone (including Coleman) thought that the study would document a relationship between the quality of schools and the academic achievement of the students in those schools. Any other result seemed impossible.

To everyone's shock, the Coleman Report instead found that the quality of schools explained almost nothing about differences in academic achievement. Measures such as the credentials of the teachers, the extensiveness and newness of physical facilities, money spent per student - none of the things that people assumed to be important in explaining educational achievement were important in fact. Family background was far and away the most important factor in determining student achievement.

The Coleman Report came under intense fire, but reanalyses of the Coleman data and the collection of new data over many years continue to support the core finding that the quality of schools just doesn't make much difference in mean student test scores. Move away from the awful inner-city schools to the schools that are ordinary or better, and much of the slack has been taken out of the room for improvement in academic achievement for the average student.

The educational romantics have an answer for that one too: such results merely show how terrible all the schools are by comparison with what they could be. To fix the problem, the Left advocates innovative teaching techniques and curricula. The Right (in America at any rate) advocates greater use of vouchers and other methods of privatising the schools. Once again, the United States has the most voluminous data for assessing the success of both strategies.

For decades, the US government has given grants for what are now called Comprehensive School Reform (CSR) demonstration programmes. Using the grant, the recipient school implements one of a wide range of teaching and curriculum models. In 2003, a comprehensive meta-analysis of the 29 most widely implemented models was published. The average effect size - the difference between performance of students in the experimental group and students in the control group, weighted by the standard deviation - was +0.15. It is an effect even smaller than the one observed in the studies of pre-school interventions cited earlier. An effect size of +0.15 means, for example, that a child at the 25^th percentile goes to the 30^th percentile.

To put it another way, no model of school reform that has been tried in the United States has demonstrated, with evidence that withstands scientific scrutiny, the kind of dramatic impact on academic performance that the educational romantics say is possible. I have been unable to find rigorous examinations of experimental learning models in England. I hope this article will unearth empirical evidence of dramatic success that I might have missed - which I look forward to examining with a fine?tooth comb.

American advocates of school privatisation (I am one) fare no better than the advocates of government-sponsored reforms. Vouchers and tax credit experiments have been successful in many ways - providing safer and more nurturing school environments, freeing able students from peer pressure not to perform and installing more substantial curricula. But the reading and maths scores of students in these schools compare favourably with students in government schools only when the comparison is with the worst inner-city schools. When the comparison is with ordinary government schools, the differences have been trivial.

Does the English experience of the past decade refute me? When it came to power in 1997, the Labour Government set out to achieve ambitious increases in test scores, and it succeeded. English Key Stage 2, Key Stage 3 and GCSE scores all bear witness to this achievement.

I haven't the space to present the technical evidence that teaching to the test and dumbing down of test content explain these increases. I refer you to the websites of the Curriculum, Evaluation and Management Centre (CEM) at Durham University and the think tank Civitas for an impressive array of such evidence. Put those two issues aside and consider just the results whenever English students have been tested by people who are not connected with the government.

In reading, the CEM has conducted independent studies using its Performance Indicators in Primary Schools (PIPS) examination and found a meaningless one-point increase in reading scores between 1997 and 2002, the same five years when the Government's Key Stage 2 showed a large increase in the percentage of primary school students reaching Level 4 or above. The Progress in International Reading Literacy Study (Pirls), a sophisticated and rigorous testing survey covering large samples from 40 countries, showed a statistically significant decline in reading scores among English nine-year-olds (Year 4) from 2001 to 2006, years when the Key Stage 2 continued to show improvement.

In maths, the Trends in International Mathematics and Science Study (TIMSS), conducted by the same organisation that administers Pirls, tested English 13-year-olds (Year 8) in 1995, 1999 and 2000. During that period the Government's Key Stage 3 test shows the percentage of students scoring at Level 5 or above as rising impressively from 58 to 71 per cent. The TIMSS results? The scores for 1995 and 2003 were identical (498, on a test with a mean of 500). In 1999, the score had dipped trivially to 496.

To sum up, I have been unable to find an independent assessment of the achievement of students leaving secondary school that shows the increases in test scores since 1997 that the government figures show. Once again, I hope this article will unearth evidence to the contrary that we can all examine carefully.

There is some good news in the TIMSS maths scores: English nine-year-olds showed a large and statistically significant increase. And therein lies a story that has also bedevilled attempts to raise maths scores in the United States. Maths in the early years is based on simple concepts (how many sides to a triangle) and on arithmetic - rudimentary skills that almost all children should be able to learn. When the schools begin to put more emphasis on drill in arithmetic, and make sure that the curriculum does indeed teach children about the shape of triangles, test scores can show large improvements. But when mathematics moves beyond the simplest concepts and arithmetic to the abstractions of algebra and the logic of geometry, large numbers of children fall by the wayside - they are just not clever enough in logical-mathematical intelligence to keep up. That's the reason why a test at the age of nine (Year 4) can show improvement while a test at 13 (Year 8) does not.

It is a gradient that, given fine-grained tests, will be found to apply from Year 1 to university. In Year 1, it is indeed true that almost all children can learn everything that Year 1 teaches. Some will learn it faster than others, but almost everyone can learn to read and do maths at Year 1 level. But every year the number who cannot keep up increases. By the time children reach their teens, some large proportion - a third at least, arguably more - should not be on a continuing academic track. By the end of secondary school, that proportion is around 80 per cent or 90 per cent.

The last refuge of the educational romantics is the extremely high proportion of children of the professional classes who do well in school. Surely that must be explained by affluence and access to the best schools. Or as Adonis put it: "There is no genetic or moral reason why the whole of society should not succeed to the degree that the children of the professional classes do today." Actually, there are both genetic and moral reasons, along with environmental ones.

The genetic reason arises from two politically unfashionable but empirically irrefutable truths.

The first is that IQ, which is nearly coincident with academic ability as I defined it, is somewhere around 40 per cent to 60 per cent heritable. The evidence for the substantial heritability of IQ has become so overwhelming that it is no longer a subject of serious debate, except over the exact figure. The second is that people in the professional classes are, on average, far above the rest of the population in IQ.

Presenting evidence for the high IQ of professionals is superfluous for successful physicians, engineers, barristers, scientists or university lecturers. Possession of an IQ in at least the top 10 per cent is virtually guaranteed by the nature of the academic filters required to finish the professional training. But such evidence is plentiful even when we move to occupations such as business executive. There are many thick people working in business, but studies of the relationship of tested IQ to career success indicates that the overwhelming majority of successful executives are somewhere in the top 10 per cent of IQ.

And so it comes to pass that when a man and woman in the professional classes set out to have a baby, it is extremely likely that at least one gene contributor has a high IQ. In today's society, it is ever more likely that both contributors will be in that category. Think of all the couples you know who consist of two professionals, or ones in which perhaps only one works outside the home but the other has an advanced academic degree. Given this kind of genetic background and a heritability of 40 to 60 per cent for IQ, the children of the professional classes have a meaningful academic advantage at the moment of birth (as a group - individual exceptions abound).

When we turn to the 40 to 60 per cent of IQ that is environmental, children of the professional classes also have an advantage, but little of it has to do with money. Talking to infants and reading bedtime stories to toddlers every night do not cost money - but such behaviour goes from "almost universal" to "rare" as social class goes from top to bottom. To refrain from smoking, alcohol and drugs during pregnancy costs no money. But such restraint is once again correlated with social class, and children of the professional class are the beneficiaries. How are school reforms to compensate for these environmental advantages of the professional classes?

Another environmental factor brings me to the moral reason that stands in the way of equalising the educational success of those in the professional classes and those towards the bottom - moral, at least, for those of us who think that whether a baby has a father as well as a mother is a moral issue. One more empirical finding that is no longer in dispute in the United States among scholars of child development is that children do best when they are raised by married biological parents.

Children raised by a divorced mother do next best (whether she remarries doesn't make much difference). Children raised by an unmarried mother do worst of all. Let me emphasise that these results are found after controlling for a host of socio-economic background variables. Poor and rich children alike benefit from growing up with both biological parents and suffer from being born to a lone mother. In the United States, even the scholars who used to believe otherwise have changed their minds on this one.

The advantages of growing up with married biological parents do not include higher academic ability. But they do include all sorts of other advantages that affect success in school. Children raised by both biological parents are more likely to grow up psychologically healthy, accustomed to a regular routine and self-disciplined than children who grow up with unmarried mothers (again, even after controlling for socio-economic variables). They are more likely to have someone watching over their homework and noticing if there are problems at school.

If the incidence of marriage and lone parenthood were evenly distributed throughout the social classes, the advantages of marriage would not benefit the children of the professional classes. But lone parenthood is concentrated in the lowest socio-economic levels of English society. Consider the examples of Wokingham and Southwark, local authorities that epitomise the socio-economic top and bottom. As of the 2001 census, 13 per cent of Wokingham households with dependent children had a lone parent. In Southwark that figure was 45 per cent.

The example of Wokingham and Southwark applies generally, and has done for many years. I once used the 1991 census data to compile the percentage of extramarital births from all of England's local authorities. Just knowing the percentage of people in the lowest social class in the local authority area statistically explained about half of all variation in extramarital births. When that kind of disparity exists between marriage in the top and the bottom social classes, all sorts of disparities in outcomes for their children are guaranteed.

No one wants to be the person who says "Bah, humbug" to attempts to improve the education of children who have got the short end of the stick through no fault of their own. The impulse to romanticism is overwhelming. But it has led us to treat children who are not suited for the academic track in ways that are not in their best interests. It is time to recognise that even the best schools under the best conditions cannot overcome the limits on achievement set by limits on academic ability.

This is not a counsel of despair. The implication is not to stop trying to help but to remove the ideological blinkers and stop pretending that all children can or should pursue the academic track. There is a healthier and attainable goal of education: to bring children to adulthood having discovered things they enjoy doing and having learned how to do them well. The goal applies equally to every child, across the entire range of every ability.

The schools can achieve that goal, if they pay more attention to their students' diverse talents and give them diverse opportunities to develop those talents. The way is open for dramatic improvement in education in both our countries - once we get a grip on reality.