Last year, a mother of two in Ohio was jailed after lying about her address to get her daughters into a “better” school.

The severity of the punishment may be extraordinary. But the fact that Kelley Williams-Bolar was willing to risk prison shows just how high the stakes in the battle for school places have become.

Parents in England regularly pay tens of thousands of pounds extra to buy houses in the “right” school catchment areas. Others complete admissions forms fraudulently, while atheists attend church and baptise their children.

Winning a “good” school place has become the be-all and end-all in today’s paranoid, hyper-competitive society. And it is not just the parents. Politicians are also convinced that it is schools that make the difference between success and failure in education.

For education secretary Michael Gove, they should be “engines of social mobility”, while Prime Minister David Cameron says that “there is now irrefutable proof that the right schools . can transform the education of the most deprived children”, whereas “weak schools smother children’s potential”.

Schools have become the currency of educational “standards”. That is why ministers put so much pressure on them to improve. And it is why some heads resort to cheating Ofsted inspections and entering pupils for dubious qualifications that boost their league table scores - to demonstrate, at any cost, that they are improving.

But what if all this was for nothing? The parental nightmares, the sacked heads, the grand ministerial school-improvement plans, the league-table scams, the academy conversions - all completely pointless.

What if it made no difference at all what school you went to? What if your academic success was determined by factors completely outside your school’s control - your parents’ wealth, your ethnicity, your prior attainment?

What if your child’s exam results could pretty much be predicted before you even began the race for a good place?

This is not some dystopian vision of the future. According to two recent analyses from respected sources, this is effectively the reality in England today.

A `horrific gradient’

In February, the Financial Times published a data analysis that explained, with brutal, unsparing clarity, an uncomfortable truth that many educationalists and teachers of disadvantaged pupils have been shouting about, largely ignored, for 20 years.

To do so, it plotted the GCSE results of every state school pupil in England who sat the exams in 2010 on a series of graphs. The vertical y- axis on the charts indicates how far above or below each pupil’s results are from the national average. The horizontal x-axis plots the level of deprivation in each pupil’s home postcode, with the least advantaged on the left and most advantaged on the right.

“If the school system were able to overcome all of a child’s background, the line would be flat,” wrote the article’s author, Chris Cook, a former education policy adviser to the Conservatives. “As you can see, it is not.”

The line (see graph 1, page 24) actually begins in the bottom left-hand corner, showing that pupils living in the most deprived areas got the lowest GCSE results. Only as the prosperity of the postcodes gradually increases do the results improve. The line runs diagonally across the graph in a near-straight trajectory towards the top right-hand corner, showing that the pupils from the richest areas scored the best GCSE results.

Statisticians then progressively stripped out all the pupils from schools with low overall GCSE results to see if these “failing” institutions were the real reason behind this “horrific gradient”.

First, they removed all results from schools that failed to meet the government’s floor target of 35 per cent of pupils gaining five A*-C GCSEs including English and maths. After that, schools where fewer than 40 per cent of pupils met the target were cut, then fewer than 45 per cent and, finally, fewer than 50 per cent. By this time, the “worst sixth of all secondary schools” had been removed.

But every time they made a cut, virtually nothing happened. The graphs showed that the results of the remaining pupils from the poorest areas moved slightly closer to the national average than those of their counterparts in schools with low overall results. But they were still a long way off, and the slope of the graph remained “horrific”, with results continuing to climb in line with the prosperity of pupils’ backgrounds.

As Cook puts it: “The killer problem for social mobility is not that there are a few schools that have all the poor children in them (though that is a factor), it is that poorer children tend to do badly even when they go to good schools.”

He describes this as a “rather startling truth”. But legions of veterans and casualties from the battle for school improvement would protest that it is anything but startling.

The targets trap

Heads in poor areas have been arguing that they do not have the means to compensate for the huge social disadvantage and deprivation of their pupils ever since ministers began to “name and shame” schools with low exam results in the early 1990s.

And their warnings have been largely borne out as a long list of school improvement schemes provided by governments of all political hues have failed to solve the problem.

Academies are only the latest attempt. Those that came before include Fresh Start, Excellence in Cities, church takeovers, Education Action Zones and “superheads”. None provided the silver bullet ministers were searching for.

Ralph Tabberer, then director general of schools at the former Department for Children, Schools and Families, admitted in 2007 that a decade of pushing the weakest schools to improve exam results had done little for the country’s most disadvantaged pupils. Instead, they had been able to meet ministers’ improvement targets by simply concentrating on their “average” pupils.

Today, the same floor target-based drive for school improvement continues - with added, “no excuses” zeal. Ministers from the coalition government have abolished the contextual value-added measure that attempted to take pupil disadvantage into account, dubbing it “morally wrong” for entrenching low aspiration.

“For far too long we have tolerated the moral outrage of an accepted correlation between wealth and achievement at school; the soft bigotry of low expectations,” Cameron and Deputy Prime Minister Nick Clegg wrote in the White Paper that announced the change.

But Cook’s analysis shows that - whether acceptable or not - that correlation does exist. It is not just a fiction created by a minority of weak heads, making excuses for failing schools.

And it exists in what Cook describes as “good” schools as well. His study suggests that these schools might perhaps owe their success to advantaged pupils likely to do well wherever they are educated.

That is not the case at Stockwell Park High School. The South London secondary is better than good - “outstanding”, according to Ofsted - and two-thirds of its pupils who fit the government definition of “disadvantaged” achieve the main GCSE benchmark. So how does a comprehensive where 56 per cent of pupils do not have English as a first language and 58 per cent of pupils are eligible for free school meals achieve this success?

Judette Tapper, the head, says that her staff have an “unshakeable belief in children”. “It might seem simple, but you have to put a virtuous circle around your school,” she says. “You have to say, `On this ground we believe in this and you must abide by the rules.’”

But Stockwell Park is an exception. And for those who believe in the power of the schools to overcome pupil disadvantage, the reality may be even bleaker than Cook’s work suggests, because the analysis takes no account of the “peer effect”. A school that manages to achieve excellent results with a single disadvantaged pupil, surrounded by middle-class peers, may find the same trick harder to pull off with a majority of disadvantaged pupils.

In a Radio 4 Analysis programme in January, journalist Fran Abrams concluded that teachers are “hopeless optimists” who “believe the lie that they can make a difference”. The basis for her depressing prognosis was the work of statisticians using figures from the government’s pupil database, which contains the results and background details of the half a million or so pupils who take GCSEs every year in England.

After stripping out the impact of factors such as gender, ethnicity, deprivation and prior attainment, they can produce a figure used to gauge the average difference going to a particular school can make to pupils’ performance. That is, not the difference that going to school makes but the potential effect of going to a particular school.

“The school effect tends to be rather small,” Harvey Goldstein, professor of social statistics at the University of Bristol, told the BBC. “Maybe it accounts for 10 per cent (of the variation between pupils’ results).” It can actually vary between 2 and 20 per cent, depending on which analysis you look at. But the 10 per cent figure is fairly widely agreed on by academics. And it is, in Goldstein’s words, “not enormous”.

International studies suggest similar situations all over the world. So did Williams-Bolar lose her freedom for something that would have little effect on her daughters’ chances in life?

According to Stephen Gorard, professor of education research at the University of Birmingham, it could be even worse than that - he thinks that the studies have failed to prove any school effect at all. “You have got 10 per cent left - what could explain it?” he asks. “One of the biggest components will be error. When we do a calculation for school effectiveness, half the cases will have one or more missing values on key variables - either attainment or free school meals or ethnicity or special educational needs.

“So the 10 per cent begins to dwindle and we have got almost nothing left that could be a school effect. My view is that the error component is so large it takes all the rest of the cake.”

So maybe Abrams is right, maybe teachers who think they make a difference believe a “lie”.

“I don’t believe it is a lie,” counters Tapper. “It is the reality in our school.”

Of course, a school such as Stockwell Park would not necessarily show up in the data-crunching exercises used to calculate school effect, because they are based on averages.

As Rebecca Allen, senior lecturer in economics of education at the University of London’s Institute of Education, argues: “Lots of schools on average happen to be fairly similar to each other. But it doesn’t mean that there aren’t outliers and people who are running schools in very different ways and doing really, really amazing things.”

But why should we be surprised that there is so little variation in the impact of most schools anyway? After all, as Gorard points out, this is “state-funded, compulsory, universal, per capita-funded, quality-assured, Ofsted-inspected, Sats-tested, national curriculum-delivered education”.

“We have deliberately, since 1944, tried to engineer a system of state- maintained education where it shouldn’t matter where you go to school,” he explains. “It is odd that nobody seems to want to consider the possibility of it being reasonably successful at doing that.”

But in a country where inequality has ballooned, social mobility stalled and state intervention shrunk, politicians of all parties now demand that some schools must make a difference. They view state education as their only real means of levelling the playing field, of “narrowing the gap”. So can it possibly deliver? Abrams is sceptical. “The sad truth is that not all schools can be straight-A schools - and not all kids can be straight-A kids,” her analysis concluded.

She is probably right - that kind of perfection would be virtually impossible. But her view that the “difference schools make is very small indeed” has riled some academics.

“It is a very dangerous message to start going down that route,” warns Allen. “Almost by saying schools don’t matter, you are saying that the schooling system doesn’t matter and then you start saying, `Well, teachers don’t matter’ and then you start telling teachers, `You can’t actually make a difference to people’s lives,’ which is completely false.”

That very pessimistic outlook is also limited in two important respects. First, it is built on analysis of the present, which by its very nature takes no account of the possibility of change. Second, it is based on averages, when perhaps attention would be better focused on schools at the margins.

As Tim Oates, group director of assessment research and development at the international exams group Cambridge Assessment, says: “If you look at the mass of things you might say: `Oh, well, schools don’t make a difference.’ But if you look at a couple of outliers and see how they have really turned themselves around, you think: `Well, it is possible.’

“We need to get inside those schools and understand what it is that enabled that change to take place.”

Gorard, despite arguing that there is no proven school effect, agrees. He believes that if error is eliminated in the future then such an effect might be statistically demonstrable.

But, he says, that is missing the point: “School effectiveness and improvement is stuck in a cycle of dredging through large datasets. I think we need to rethink the design and say that if we are at a stage where we think we know what might work, we need to try it out in practice.”

Learning from the outliers

So where are these outliers, these glimmers of hope showing that schools really can take on social disadvantage and win?

Cook’s study provides a clue. In a final chart (graph 2), it plots the average GCSE performance that each state secondary achieves with its pupils from the most deprived postcodes. The resulting pink line ought to “haunt” school reformers, according to Cook, because it shows that “poor children do badly in the majority of England’s schools”.

But it might also provide some inspiration for them, because it shows that there are a minority of schools where poor pupils do not do badly. There are even a few schools where poor pupils achieve GCSE results well above the national average.

So are they the examples we should try to get other schools to emulate? Possibly, except that what the graph does not tell us is how many pupils from poor areas there are in each school. It could well be that those with the best GCSE results for “poor” pupils have very few of those pupils, making their job much easier owing to the peer effect.

There would be little point in taking the solutions used by a school where 1 per cent of pupils are disadvantaged and expecting them to work in a school where more than 90 per cent are in that category.

Allen believes that she has found another glimmer of hope through an analysis that shows that schools judged “outstanding” by Ofsted are “pretty good social levellers”. That is to say that their results are “much better than the average school for poor children”, but “only moderately better than the average school for rich children”.

When the GCSE results are plotted pupil by pupil on a chart, similar to Cook’s method, the much flatter gradient does indeed look encouraging. But before anyone gets too excited, it is important to note that, like the Financial Times analysis, this takes no account of schools’ overall social mix. As Allen admits: “Schools that fail their Ofsted are (on average) far more deprived (in intake) than schools that don’t. And schools that are outstanding are on the whole fairly affluent schools.”

So “outstanding” schools may be doing better with disadvantaged pupils simply because they have fewer of them. And that, as we have said, does not offer much of a solution for the system as a whole.

Nevertheless, Allen remains confident that “we can find hundreds of individual examples of outstanding schools that truly appear to transform the lives of children from deprived neighbourhoods”.

To bolster her case, she has produced another graph for a Hackney comprehensive, where 40 per cent of last year’s GCSE cohort qualified for free school meals, and where three-quarters of “disadvantaged” pupils achieved five A*-C GCSEs or equivalent including English and maths, together with 62 per cent of its pupils with low prior attainment. Its almost flat graph is profoundly impressive, revealing that pupils from areas with every level of deprivation achieved an average of at least eight B-grade GCSEs or equivalent.

It is, of course, the much-lauded Mossbourne Community Academy. But where are the other conquerors of disadvantage? Allen compiled a “by no means exhaustive” shortlist of 17 of the best, including Stockwell Park. They were selected for having a high proportion of pupils hitting the main GCSE benchmark, despite having large numbers of pupils eligible for free school meals and with low primary attainment. They achieved good GCSE performance across English and maths for the low primary attainers and good value- added scores across English, maths and science.

In other words, they have as formidable records in overcoming poverty as you can find. But even here, some of the lustre can start to rub off when you examine the figures closely. It could be that entries in English Baccalaureate (EBac) subjects are very low, or that impressive GCSE point scores drop considerably when equivalent subjects are removed. Even Mossbourne gave only 9 per cent of its pupils with below-expected primary test results a chance to gain the EBac GCSEs that ministers believe all pupils should have.

That is not a criticism of an unquestionably good school. Low prior attainment is not always simply a proxy for social disadvantage and maybe the 40 pupils that were not entered would never have passed those GCSEs anyway. Also, ministers only announced the EBac in September 2010 - less than a year before this cohort sat their exams.

But it is worth mentioning because it suggests that there are no easy ways for even the very best schools to get all pupils up to the standard that everyone would like.

That is not to say that there are not valuable lessons that can be learned from these outliers, which would make a difference if adopted by the vast majority of schools.

But Allen admits “it isn’t easy” and that education “can never fix all of society’s problems”.

And Gorard warns that working out exactly what is making the difference can be a huge challenge in itself (see panel, right). It also might be, he points out, not something a school as a whole is doing that proves key, but something within a school - a single department or “one or two really inspired teachers”.

The UK has one of the highest levels of variation in pupil outcomes in the developed world. Results from the Programme for International Student Assessment (Pisa) published in 2002 showed that as much as 80 per cent of that variation occurs within schools rather than between them.

The government knows this, which is why it has begun a drive to improve the quality of individual teachers. Yet it still views school improvement as central. While this remains the case, the evidence suggests that threatening schools that fail to achieve the miracle of overcoming social disadvantage may be less productive than learning from what is happening in the small minority of schools that do.

The Financial Times analysis can be found at http:on.ft.comxwcrp3

CORRELATION NOT CAUSE

Identifying schools that really do overcome social disadvantage can be less than half the battle, Stephen Gorard warns.

Pinpointing exactly what it is they do that makes a difference and then working out whether it can be successfully introduced to other schools are huge challenges in themselves.

Numerous reports, some of them by Ofsted, have been produced identifying qualities shared by outstanding schools. Their implication is that, by adopting them, other schools can replicate their success.

But Gorard, who advises the US federal government on education policy research, cautions that correlation is different from cause and effect. He argues that those who act on that basis might as well be buying thousands of pot plants on the basis that every good school has one in their foyer.

Without controlled trials and proper work to identify the real “active ingredient”, money on large-scale implementation could be wasted, the professor of education research at the University of Birmingham says.

It is not about declaring “Here is a whizzo idea, let’s have free schools or let’s have foundation schools or let’s have specialist schools,” he says.

Instead, he argues that new ideas should be subjected to “rigorous evaluation” by sceptics before any large-scale implementation. “It is a cycle of research that we haven’t really got the hang of here,” he adds.