It seemed to defy not just stereotypes but brain science when girls topped the state in every mathematics course in the NSW Higher School Certificate last year, even though more boys than girls studied maths.

A boy, Mischa Davenport, was the top performer in French extension, German extension, Italian continuers and Italian extension, even though girls outnumbered boys by two to one in language courses.

The idea that biological differences in male and female brains give rise to different behaviours, aptitudes and learning styles has recently become firmly lodged in the public brain, thanks to reams of research endorsed in scores of popular science books.

Only this week a new study from a British university purported to show that men really do suffer from ''man flu'' because their brains have more temperature receptors than women so they feel more heat from the fight against bad germs.

Students in years 7 to 9 who fronted up for the first week of term at the co-educational St Andrews Cathedral School in Sydney this week will be segregated by sex for English, maths and science.

''If we have single sex classes we can work with - rather than against - their learning styles,'' says the St Andrews head, Dr John Collier. He refers to ''a body of research'' suggesting boys' and girls' learning needs diverge at the beginning of adolescence, when boys become more kinisthetic and competitive in their learning, and girls more co-operative and social.

At Tintern Schools in Ringwood, Melbourne, ''parallel'' or sex-segregated learning is practised from prep until the start of year 10, though boys and girls are free to mix in the playground.

It ''allows you to do certain things that appeal more to one gender'', says the deputy principal, Peter Buckingham, citing ''plenty of evidence that gender is relevant to how people engage with learning and what kind of learning they best engage with''.

Yet the extent and effect of ''essential'' brain-based differences in learning and abilities between the sexes is hotly contested among scientists and social scientists.

Australia's most distinguished sociologist, Professor Raewyn Connell, says boxing boys and girls into different learning styles on the basis of supposed biological differences is ''educational nonsense'' and ''potentially harmful''.

The Melbourne Business School academic psychologist Dr Cordelia Fine in her book Delusions of Gender calls it ''sexism disguised in neuroscientific finery'', or ''neurosexism''.

The two least controversial biological differences between male and female brains are in size (about 10 per cent larger in males on average) and a small structure within the hypothalamus (which is about twice as large, on average, in males).

But, given the ''daunting complexity'' of brain function, which depends on distributed neural networks and a dizzying array of connections, synaptic functions and neurotransmitter systems, it is ''fantastically ambitious'' to try to relate any subtle brain differences to psychological function, Fine argues.

In the case for gendered difference in cognitive abilities, the test for mental rotation performance is Exhibit A. Subjects are shown the target, a three-dimensional shape made up of cubes, along with four other similar shapes.

Two of the four other shapes are the same as the target but have been rotated in three-dimensional space, and two are mirror images. When the task is to work out which two are the same as the target, about 75 per cent of people who score above average are male. This difference is claimed to be significant in explaining men's dominance in science, engineering and maths.

Exhibit B is the proposal that high levels of foetal testosterone experienced by males in the womb permanently ''masculinises'' the brain, leaving boys ''innately'' predisposed for typically male pursuits and interests.

The famous baby face and mobile study conducted by Simon Baron-Cohen of Cambridge University and graduate student Jennifer Connellan is a staple of popular science books in support of this idea.

''Presented with a face or mechanical mobile to look at, more newborn boys look for longer at the mobile, and more newborn girls [look for longer] at the face'', in the words of professor of psychology and psychiatry Baron-Cohen. This has been widely interpreted to mean girls are prewired to be more interested in the social world while boys have a prewired bias towards moving objects, with clear implications for career choices (physics, mechanics, engineering versus social work).

Fine points to ''a surprising number of gaps, assumptions, inconsistencies, poor methodologies and leaps of faith'' in scientific studies of male-female brain differences. Her criticism of the methodology and interpretation of the baby face and mobile study has drawn her into a coruscating public exchange with Baron-Cohen, who accuses her of ''extreme social determinism''. Later this month she is invited to speak to a meeting of the Central American Philosophical Association at an event ominously titled ''Author Meets Critics''.

Fine also asserts that the brain is not a ''tidily isolated data processor'', so test results are strongly influenced by social behaviour and attitudes, including stereotypes, and can be easily manipulated. For example, women have been found to do well at mental rotation when they are told the white lie in advance that their sex is usually the superior performer.

Connell, who holds a university chair at the University of Sydney and whose 1995 book Masculinities is among the most cited publications in the field of masculinity studies, says the assertion of fixed social differences resulting from biological differences between sexes in the brain is typical of the rhetorical misuse of scientific ''authority'' in the gender debate.

Connell notes that the biological mechanism held responsible for supposed gender-based cognitive differences keeps shifting ''according to what is fashionable science''.

But what has been historically called sex differences research should really be known as sex similarities research, says Connell. ''When you look at the whole body of research, the conclusion that leaps out at you is that the actual psychological differences between men as a group and women as a group are few and far between, and very small when they do appear.''

''This is one of the most important findings in the whole arena of gender research'', she says, citing a 2005 analysis by Janet Hyde which took in over 5000 research studies based on the psychological testing of 7 million people.

Hyde, one of America's leading academic psychologists, concluded that ''78 per cent of gender differences are small or close to zero''.

''When you think of it'', says Connell, ''all the biological-essentialist ideology depends on the idea there are natural bases - hormones, brains, genes, take your pick - that produce big mental differences between men and women, and these explain the social differences.

''If it is not true that there are big psychological differences, the whole argument that there is a fixed biological basis for the social differences collapses.''

So why, if the evidence is so thin, does the idea of a biological basis for difference in male and female abilities persist? No prizes for guessing Fine's answer: ''It helps to make the status quo seem fair, natural and inevitable. It's comforting to be able to look around at the considerable sex inequality that still exists and blame different brains, rather than sexism, socialisation and discrimination.''

Even if the evidence for biological brain differences between the sexes is inconclusive, stereotypes are persistent and powerful. ''The dynamics of gendered interactions'' are a real problem for schools, says Connell. For example, the choice of electives in senior secondary school is ''one of the most gendered areas of education'', along with discipline (boys are far more likely to fall foul of school authorities) and sport (participation in different sports cleaves along gender lines).

Subject choice statistics support stereotypes: in the 2012 HSC, only 31 per cent of candidates in hospitality were male, but in physics 78 per cent were male; in family and community studies, females comprised 92 per cent of candidates.

Collier, of St Andrews Cathedral School, says that ''when you discount for social and economic factors, there is really no significant difference in the results between single sex and co-ed''. But equally he says ''twinning is not going to be detrimental'', and the school and parent body are strongly supportive of it.

In class, it means ''boys are less likely to be quiet because they feel intellectually outclassed by boys, and girls are less likely to be quiet fearing that if they are seen as noisy or outgoing they will be rejected''.

The debate is a constant. In the 19th century it was feared teaching or secretarial roles might damage women's reproductive physiology. Until the late 1970s girls rather than boys were most likely to leave school early. In recent years females have come to dominate the study of law and biology, previously male domains.

''There are all sorts of ways in which social arrangements impact on bodies, and all sorts of ways in which bodies shape the possible characteristics of human society,'' Connell says. Eventually, research might tell us more about whether and how society's teaching of gender affects neurological processes.

Neurology, endocrinology, psychology, sociology, anthropology, history, ''none of these gives us the master key'' to understanding human life and development and the interplay between masculinity and femininity.

For that, ''we have to build the sciences together'', she says. But ''this is a slow and difficult process, and not what ideologues want, because they want quick and easy answers''.