Why do women get fewer first class honours degrees than men - and fewer thirds? Gerard McCrum raises at least the first half of this hardy perennial on page 19 in relation to Oxbridge but it is a question that could be asked much more widely of higher education and that is far from being resolved.

Mr McCrum, however, has long been interested in arguing for single sex education for girls in state schools and has written extensively about how its decline is spoiling women's chances. This preoccupation colours his analysis of the Oxbridge figures so that he concludes his article with the assertion that the Oxbridge "gender deficit" of the past 20 years "is due to a weakening of the original high academic quality of women from state schools" as well as to "an operational bias towards men within the Oxford honour schools" (and his figures mainly relate to Oxford).

In his various writings about this matter in relation to schools, Mr McCrum has been made great use of by the single sex education lobby. His analyses - not set out here - however, fail to account for the rapid improvement nationally in women's academic achievement, particularly in sciences and maths but also in subjects like history, at A level as the proportion of girls attending single sex schools has declined.

There are many factors at work. Ambitious middle-class families who once sent their sons to expensive boarding schools and expected them to go on to university while their girls attended local, often state, single sex day schools, now pay for their daughters too, often sending them to mixed public school sixth forms. Over the period he is analysing, opportunities for women in higher education have increased dramatically. Much of the expansion, at least until recently, has been accounted for by the university-aspiring classes expecting their daughters as well as their sons to go on into higher education. Within the overall expansion, the rise in participation of women has been much more rapid than of men.

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As part of this increase in women's opportunities, many more women are now admitted to Oxbridge than was the case before the men's colleges went mixed. Yet both their A-level scores and degree results have improved. This is absolute success. A higher success rate over the same period for men could be because it is now harder for them to get in thanks to the competition from women. It is misleading to present all this as some sort of decline in women's attainment.

Such statistical juggling, however, allows the universities - and perhaps Oxford in particular - to duck the second part of Mr McCrum's conclusion: that there is a bias towards men.

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Conversations with state school pupils and teachers reveal that many do not find the idea of Oxford appealing. Girls, in particular, accustomed to co-education, are put off by seeping tales of sexual harassment (however discretely handled); by complaints about boys' dorm rumbustiousness or academic misogyny in some of the former mens' colleges. Oxford has a problem attracting state school pupils and a particular problem about state school girls.

Rather, then, than deflect debate onto whether or not state schools are failing girls, it would be better if Oxford, as part of its review now under way, were to examine the beam in its own eye by addressing apparent male bias, women's apparent under performance in some subjects once they reach the university, and their subsequent under-representation at every further step up the academic ladder.

But does the university honestly, sincerely, want to change? Women, for example, are known to do better when continuously assessed than when confronted with sudden-death exams. Recently we reported the not-very-radical demands of Oxford students for changes to the form of finals - and the unenthusiastic response. Changes in assessment might transform women's performance and also transform the atmosphere of the university. But long tolerance of discrimination by the Pall Mall Club that trades under their logos, suggests that neither Oxford nor Cambridge is likely to be energetic about change.