To talk about genes and their links to IQ and educational achievement is to risk accusations of elitism, fascism and racism. When the American professor Arthur Jensen published a paper in 1969 concluding that 80% of variance in IQ scores was attributable to genes, not environment – and attempts to boost African-American scores through pre-school intervention were therefore bound to fail – angry students besieged his office in California. The renowned psychologist Hans Eysenck, who backed Jensen, was punched on the nose while lecturing at the London School of Economics.

The controversy exploded again in the 1990s when the Harvard psychology professor Richard Herrnstein and political scientist Charles Murray published their book The Bell Curve, which stated that US blacks had an average IQ of 85 against 103 for whites and that, once this was taken into account, many racial differences in educational attainment and career achievement disappeared. Welfare polices that encouraged poor women to have babies, the book argued, risked lowering average American IQ.

Behind all such controversies lay the shadow of Nazi attempts to breed a master race. And teachers have always been suspicious of supporters of nature against nurture because they seem to imply that a child's fate is predetermined and anything schools do is pointless.

When Michael Gove's former adviser, Dominic Cummings, claimed in a 250-page paper leaked last year that genes accounted for more of the variation between GCSE scores than schools, teachers, neighbourhoods or even families, another row ensued, particularly when, shortly afterwards, Boris Johnson observed that human beings were "very far from equal in raw ability".

Genetics today, however, presents a kinder, more compassionate face. Cummings based his claims about GCSE scores on a paper written, with several colleagues, by Robert Plomin, research professor in behavioural genetics at King's College Institute of Psychiatry in London. Based on comparisons of more than 11,000 identical and non-identical twins, it reported that genes account for just over 50% of the variations in GCSE scores overall and 60% in science subjects. Plomin was repeatedly cited in Cummings's rambling paper, which proposed genetic screening to identify those capable of the scientific innovation needed to compete economically against rising Asian powers.

Born in Chicago but a UK resident since 1994, Plomin recently gave five lectures at the Department for Education, one of them attended by Gove. But, he tells me, "I'm very much on the left side of things" and adds that he's a Labour party member: "I shouldn't be because I'm not a British citizen, but they still take my money".

In a newly published book, G is for Genes, he and Kathryn Asbury, an educational psychology lecturer at York University, propose "a wish list" of 11 policy ideas. Several should raise cheers from Guardian-reading teachers: free, high-quality pre-school education for disadvantaged children from age two; a reduced national curriculum; more freedom for teachers; an individual education plan for every child; free or subsidised horse-riding, piano or ballet lessons for children from poor homes. The book also suggests, at least implicitly, that Plomin opposes grammar schools and externally imposed targets. And if schools alone don't make much difference, all the fuss about identifying "failing" schools and turning them into academies hardly sounds worth it. Moreover, as Plomin puts it, "why mortgage your house to pay those private school fees?"

All in all, Plomin, charming and fast-talking, sounds terribly child-centred and not at all Goveian. "Children differ in how they learn," he says. "The teacher standing in front of the class and lecturing to kids and getting them to chant their times tables – all that goes against what we suggest."

How does this square with his belief that genes account for most of the differences between children? Plomin turns the usual way of looking at such things on its head. It's not that environment doesn't matter, he says; it matters a lot. But the more successful we are at equalising environments, the more genes account for the differences between us. Genes don't explain so much variation in cognitive ability or test scores when children are very young, because their environments differ so widely. But as they go through school, where environments are to some extent equalised, genes count for more and more. If we could somehow put children through identical schooling – sending them all to Eton or, conversely, to an inner-city "sink" school – the contribution of genes might approach 100%. "In this light," Plomin and Asbury write, "causing an increase in heritability … can reasonably be seen as an achievement of which teachers and parents should be proud, rather than a sign of determinism to be mistrusted and feared."

As for differences between races and social classes in IQ and achievement, Plomin steers clear, arguing that differences between groups are small compared to differences between individuals within them. Besides, he says, "within a group, genes may explain a lot but the difference between that group and another could be wholly down to environment if one of them is discriminated against or kept in poverty."

Plomin knows he's playing with fire. In the wake of The Bell Curve row, he signed, with 51 other leading researchers including Eysenck and Jensen, a statement in the Wall Street Journal that largely endorsed the data in the book, though not the authors' conclusions. He says he doesn't regret signing. As he wrote in 1996, genes gave him a stubborn nature, while family nurture "gave me a strong dose of self-esteem", allowing him to "take the heat".

He was born in 1948 in a one-bedroom, rented flat. His father worked on the assembly line at a car factory, later becoming a layout engineer. "Neither parent went to college and there were no books in our house." But his parents encouraged him to go to the public library where, aged 10, he found an illustrated book on evolution. When he produced it during a science lesson at his Catholic school, he was suspended, turning him almost overnight into an atheist.

For most of his formative years, he spent more time earning than studying. He delivered chickens, shovelled snow and, eventually, because he could type, assisted the research director of an educational association. He went to college only because he was paid to go. After trying philosophy, where the lecturer kept talking about the essence of "deskness", he wanted something more empirical, so he chose psychology. His interest in behavioural genetics developed at graduate school in Texas, then a leading centre for the subject. After completing a PhD, for which he began studying twins, and working at universities in Colorado and Pennsylvania, he moved to England with his third wife, a British-born developmental psychologist and now also a King's College professor.

Though he is rated among the world's top psychologists, Plomin, until recently, was little known outside academia. Now he's on a mission. The education world, he thinks, doesn't take enough notice of genes. Learning about genetics should be part of teacher training, he says, so that teachers understand how to draw out individual talents. His big idea is personalised learning. He's against all labels: dyslexia, attention deficit disorder, gifted and so on. Every child has special needs, he argues. Schools should therefore offer the widest possible choice of subjects and extra-curricular activities, even if it means them being very large.

Eventually, Plomin says, DNA analysis will give each child a Learning Chip (his capitals) as "a reliable genetic predictor" of strengths and weaknesses. "It's wholly accepted that preventative medicine is the way to go," he says. "Why not preventative education? We wait for problems such as reading disability to develop. Children go to school, they fail, they get diagnosed, they're given special resources but by then it's too late. They've only ever experienced failure and it's like putting Humpty Dumpty back together. Once you have the genes, you could predict difficulties and hopefully prevent them."

This is where Plomin's work runs back into controversy. That's not only because it recalls the dystopia of the late Michael Young's The Rise of the Meritocracy – where biennial IQ tests put children on different occupational tracks – but also because many scientists say a learning chip isn't possible. Specific genes that explain anything have mostly proved elusive. Geneticists call it the "missing heritability" problem. Oliver James, a London-based psychologist, author and broadcaster, says: "It's been shown again and again that DNA cannot explain more than a small proportion of the differences between people." Steve Jones, emeritus professor of genetics at University College London, says: "Hundreds of different genes have been found behind the variation in height. But put them all together and you still explain only a fifth of the variation. There's no way you can make a gene-chip for height. So how the hell can you make one for IQ?"

Plomin doesn't deny the problem. "I've been looking for these genes for 15 years and I don't have any," he says. The best he and other researchers can do is look at variations in gene sequences. These, he claims, do explain differences in ability and achievement, but only about half of what twin studies show. So it looks as though heritability, after all, explains only 20% to 40% of variance, putting environment back in the driving seat. Plomin thinks this is because the studies include only the most common genes. If rare variants can be included, he believes, the missing heritability problem will disappear.

Others are sceptical. "They're looking at patterns in tea-leaves," says James. "They can find correlations, but they can't prove that specific genes cause anything."

Moreover, some geneticists argue that twin studies are flawed because they assume that non-identical twins share an environment in the same way that identical twins do. But that, the critics say, isn't true: the environment for monozygotic twins is a distinct one, even before birth when they share a placenta. Even close relatives often can't tell them apart and they tend to develop strong emotional bonds and sometimes identity confusion. "If one goes to the library all the time," says Jones, "the other will. How you get that out of the equation I just don't understand." In other words, researchers tend to attribute to twins' genes what ought to be attributed to their peculiar shared environment.

But Plomin won't easily give up his faith in twin studies, to which he has devoted most of his life. He says he has no intention of retiring. "It's such an exciting time in genetics. I want to be there to find out whether we win or lose." And what if the genes he's looking for are never found? There is only slight hesitation. "I will still believe that heritability is true." Whether it's nature or nurture, he's certainly stubborn.