Last year, Oxford University extended the length its mathematics exams from 90 to 105 minutes. Why? So that female students would perform better, relative to male students. According to the University, the problem with shorter exams is that “female candidates might be more likely to be adversely affected by time pressure”.

Hmm.

There’s good reason to be unhappy with the low percentage of female mathematics students, particularly at advanced levels. So, Oxford’s decision is in response to a genuine issue and is undoubtedly well-intentioned. Their decision, however also appears to be dumb, and it smells of dishonesty.

There are many suggestions as to why women are underrepresented in mathematics, and there’s plenty of room for thoughtful disagreement. (Of course there is also no shortage of pseudoscientific clowns and feminist nitwits.) Unfortunately, Oxford’s decision appears to be more in the nature of statistical manipulation than meaningful change.

Without more information, and the University has not been particularly forthcoming, it is difficult to know the effects of this decision. Reportedly, the percentage of female first class mathematics degrees awarded by Oxford increased from 21% in 2016 to 39% last year, while male firsts increased marginally to 47%. Oxford is presumably pleased, but without detailed information about score distributions and grade cut-offs it is impossible to understand what is underlying those percentages. Even if otherwise justified, however, Oxford’s decision constitutes deliberate grade inflation, and correspondingly its first class degree has been devalued.

The reported defences of Oxford’s decision tend only to undermine the decision. It seems that when the change was instituted last (Northern) summer, Oxford provided no rationale to the public. It was only last month, after *The Times* gained access to University documents under FOI, that the true reasons became known publicly. It’s a great way to sell a policy, of course, to be legally hounded into exposing your reasons.

Sarah Hart, a mathematician at the University of London, is quoted by *The Times* in support of longer exams: *“Male students were quicker to answer questions, she said, but were more likely to get the answer wrong”*. And, um, so we conclude what, exactly?

John Banzhaf, a prominent public interest lawyer, is reported as doubting Oxford’s decision could be regarded as “sexist”, since the extension of time was identical for male and female candidates. This is hilariously legalistic from such a politically wise fellow (who has some genuine mathematical nous).

The world is full of policies consciously designed to hurt one group or help another, and *many* of these policies are poorly camouflaged by fatuous “treating all people equally” nonsense. Any such policy can be good or bad, and well-intentioned or otherwise, but such crude attempts at camouflage are never honest or smart. The stated purpose of Oxford’s policy is to disproportionally assist female candidates; there are arguments for Oxford’s decision and one need not agree with the pejorative connotations of the word, but the policy is blatantly sexist.

Finally, there is the fundamental question of whether extending the exams makes them better exams. There is no way that someone unfamiliar with the exams and the students can know for sure, but there’s reasons to be sceptical. It is in the nature of most exams that there is time pressure. That’s not perfect, and there are very good arguments for other forms of assessment in mathematics. But all assessment forms are artificial and/or problematic in some significant way. And an exam is an exam. Presumably the maths exams were previously 90 minutes for some reason, and in the public debate no one has provided any proper consideration or critique of any such reasons.

*The Times* quotes Oxford’s internal document in support of the policy: *“It is thought that this [change in exam length] might mitigate the . . . gender gap that has arisen in recent years, and in any case the exam should be a demonstration of mathematical understanding and not a time trial.” *

This quote pretty much settles the question. No one has ever followed “and in any case” with a sincere argument.

A NON-HILARIOUS REPLY FROM JOHN BANZHAF

The author of this piece says that my doubt that this extension of time for both genders is “sexist” is “hilariously legalistic.”

I doubt that the author has the qualifications to determine whether something is “sexist,” at least from a “legalistic” point of view, and/or whether someone who may disagree with him is not just incorrect by “hilariously” so.

I, unlike the author, have won more than 100 legal actions against sexist policies. I also forced major organizations to change sexist policies of only admitting members who were male, and got the first woman admitted to a state school where its sexist policy initially limited applicants to males.

On the issue of mathematics, as a graduate of MIT and an inventor with two U.S. patents, I created the “Banzhaf Index of Voting Power” which is widely taught in math classes at both universities and high schools.

I was able to persuade New York’s highest court that my mathematical analysis of weighted voting was correct, and numerous scholars that my mathematical analysis of the Electoral College disproved long-held but erroneous beliefs.

I’ve spoken on mathematical topics before two different congressional committees, and more than a dozen courts, as well as on the BBC and in other media.

So perhaps my math and mathematical analysis (see below) is at least as well informed and valid as that of the anonymous author who does not appear to have provided much to prove that he has similar – much less substantially better – mathematical qualifications.

HERE’S MORE BACKGROUND AND EXPLANATION

Oxford University, one of the most prestigious universities in the world, is concerned that its female students are doing far less well than its male students on math and computer science exams, and has adopted a novel remedy which critics have reportedly slammed “as ‘sexist’ as they believe it suggests that women are the weaker sex.”

Since it involves nothing more than extending the time for students to take such exams, and the extension applies equally to male and female students alike, it is hard to see how it could reasonably be characterized as “sexist,” says public interest law professor John Banzhaf, who nevertheless suggests that the change might do little to eliminate the disparity because of what may be called tail differences.

Many claim the females do as well in math as males, and there is considerable data to back up that claim. However, for least 40 years, boys have consistently earned significantly higher math scores on the SATs, and almost twice as many boys continue to land in the 700 to 800 SAT score range (800 is perfect).

This large gap between the genders has been documented for many math tests, including the AP calculus test, the mathematics SAT, and the quantitative portion of the Graduate Record Exam (GRE).

One explanation, says Banzhaf – the mathematician who invented the “Banzhaf Index” – and one reason why simple fixes such as more time to complete exams is not likely to eliminate these big differences, is that although both genders have about the same average (mean) grade, males do better at the very high end of the performance curve, just as they do worse than females at the lower end of the curve.

In mathematical terms, the mean math grades for both genders may be about the same, but the standard deviation for males is substantially higher, suggests Banzhaf.

To understand this, picture two graphs of math grades, one for females and one for males. They may both be centered at the same point because the mean or average is about the same, but the curve for males is substantially wider; i.e. it has a greater standard deviation.

As a result, when you get to the very highest levels of performance (e.g., the top 5%), there are far more males than female. By the same token, when one looks at the very poorest levels of performance (e.g., the bottom 5%), males also predominate over females.

For example, studies have shown that the ratio of males to females who score in the top 5% in high school math has remained constant at 2 to 1 for the past 20 years. The same appears to be true for the students who scored 800 on the math SAT in 2007.

While there are many reasons being offered to explain this very high but also very persistent gender difference, one could simply be the difference in the distribution of the math grades as represented by two different curves: the one for female grades being significantly narrower (having a smaller standard deviation) than the one for males. This refers to what mathematicians call the “tails.”

For example two researchers “found that the gender gap widens dramatically when examining the right tail of the performance for students who participate in the American Mathematics Competition.”

Although a federal judge once found that awards based upon SAT scores unlawfully discriminated against females because they didn’t perform as well in math as males, the underlying cause – that males have longer tails than females – may not be easily changed.

JOHN F. BANZHAF III, B.S.E.E., J.D., Sc.D.

Professor of Public Interest Law

George Washington University Law School,

FAMRI Dr. William Cahan Distinguished Professor,

Fellow, World Technology Network,

Founder, Action on Smoking and Health (ASH),

http://banzhaf.net/ jbanzhaf3ATgmail.com @profbanzhaf

John, thank you for your patience. Here is my response.

To begin, THERE”S NO NEED TO SHOUT, and there’s no need to puff yourself up. Perhaps a little less “I” and “me” and “my”. If you had read my post with sufficient care, you would have noted that I referred to you as a “politically wise fellow” with “genuine mathematical nous”, and that I linked to an article on the Banzhof Power Index that you (re)discovered.

Secondly, as to my identity and qualifications, I am only anonymous to someone who can’t be bothered to click a link or two, and I consider my mathematical and legal qualifications to be irrelevant. I do not hide my identity, but I downplay it because I prefer arguments, and I specifically try to avoid appeals to authority, particularly to my own. Are you a greater legal scholar than me? Undoubtedly. Are you mathematically more adept? Possibly. So what?

Now, to the substantial matter of my post. You dispute that Oxford’s new policy is “sexist”, and you are annoyed that I referred to your approach as “legalistic”. Specifically, the issue is around a statement of yours, which you quote in your comment:

Since [the policy] involves nothing more than extending the time for students to take such exams, and the extension applies equally to male and female students alike, it is hard to see how it could reasonably be characterized as “sexist,”At the outset, I hope we can avoid silly word games. I used the word “sexist” because, as I wrote, Oxford’s clear purpose was “to disproportionally assist female candidates”. I noted, without approving of them, the pejorative connotations of the word, and at no time did I suggest that Oxford’s conduct amounted to some manner of legal sexual discrimination. I also used the word “legalistic”, which has a commonly accepted non-legal meaning. What you John, mean when you use these words, and what you understand when you read these words, only you can say.

But let’s consider the substance of your statement. To generalise, you appear to be claiming that if a policy applies “equally” to two groups then “it is hard to see how” that policy could reasonably be characterised as discrimination of one group or the other.

Really? The “equal” treatment is of course not prima facie evidence of discrimination. Do you honestly consider, however, that it is difficult or unreasonable to imagine some “equality” of treatment being consistent with discrimination, either in fact or intent?

John, do you really want to choose that hill to die on? I could have sworn you spent your life fighting such nonsense.

Finally, John, your comment raises a controversial aspect of this debate, an aspect which I had carefully avoided. You refer to the “tails” of score distributions, and to the fact that male math scores consistently tend to have longer tails than female. You note that there are many suggestions as to the reason for this, without discussing or evaluating the reasons. Given, however that Honours level mathematics is very much an activity undertaken by people who are at the right tail, it is clearly a highly relevant question. I am not sure it is an aspect of the debate which, on the available evidence, supports Oxford’s policy or your arguments in support of them.

No, John, I think you’re wrong. Your reply was pretty damn funny.

I will respond in detail when I get the chance.

The more we learn about cognitive science and psychrometry, the more generally true is the old generalization that “speed is skill”.