Occasional reflections on Life, the World, and Mathematics

Oxford admissions

One of the genuinely unique features of Oxbridge is the admissions procedure. To judge by the news reporting, there is no issue in education that interests the British as much as admission to the “Ancient Universities”. The only countries with comparable concerns (that I am aware of) are the US, France, and Japan. I know almost nothing about Japanese university admissions. France, famously, has a parallel system of Grandes Écoles of fairly modern (mostly post-Revolution) vintage, while the traditional universities are completely unselective in admissions, though of course some courses ruthlessly prune students through mid-course exams. The Grandes Écoles are a broad pallette of fairly small and specialised institutions, relying on special preparatory classes and rigid admissions exams. While the ENS in Paris as the primus inter pares for academic subjects, the specialisation means that aspiring business or political or civil-engineering leaders have their own, equally exclusive institutions.

An American trying to understand the significance of Oxbridge admissions should imagine the frenzy over Ivy League and comparable universities, reduced to two elite universities, of which students are permitted to apply to only one. For all the frenzy in the US over getting children into Harvard, it is well understood that there are fine gradations of quality and prestige, and at least half a dozen institutions whose diplomas will do you exactly as much good in climbing the socioeconomic ladder, as well as several dozen more that will count you among the elite.

The UK is blessed with a large number of truly excellent universities, world-class in research and truly dedicated to teaching their students. But why should anyone care how brilliant your instructors were (unless you are one of the small minority who go on to a research career, and even then, only if the brilliant instructor has worked closely enough with you to be able to make a meaningful recommendation, and that brilliant instructor is one of that small subset who are not only brilliant themselves, but capable and willing to recognise brilliance in others)? University admissions in a stratified educational system is as much about exclusion as education. The “return” that universities provide to most of their undergraduates, from the coarse economic perspective, is largely conditioned on exclusivity. It’s rather like a hyper-expensive resort that provides reasonable comfort, but offers above all the opportunity to be secluded with other phenomenally wealthy vacationers. The price becomes part of the service, rather than being a trade-off. Universities don’t exclude by wealth primarily (particularly not in the UK), but by academic performance. There is a widespread perception that a certain amount of academic brilliance is the right qualification for many of the most desireable jobs in the modern economy, enough to make a place among the academic elite seem immensely desireable. Bankers pay £20,000 a year or more to send their children to “independent schools” (or “public schools”), the primary measure of whose success (it would be unfair to say it is their overriding educational goal) is the number of students they place in Oxford and Cambridge.

The universities could probably do more to exclude the striving sons and daughters of the haute-bourgeois, in favour of the enthusiastic poor or not-so-poor scholars, but then society at large would stop caring about us, and would stop supporting us in the style to which we have become accustomed. On the other hand, if the moneyed classes were too  It’s a delicate balance, which recurs in many aspects of the university. For instance, there is considerable pressure to put business people onto boards of universities, to align the universities more closely with business interests. But of course, if the business community knew how to achieve their interests in selection, training, and research, they wouldn’t be mucking about with universities at all. They want to bend the universities more to their interests, but too much capitalist gleichschaltung leaves universities like the internal research departments that they already have too much of. Academics are a bit like yeast, going about our own metabolic processes, whose effluvium (in this case intellectually sharp employees, leaders, and future captains of industry — no offense intended) turns out to be of great value to others, for reasons that we tiny yeast cells can no more than dimly recognise, while we are mainly striving to reproduce ourselves (in the academic sense, by seducing the rare brilliant student into a life of cogitation). As a machine for selecting and training the upper class, universities seem obviously inefficient, since they are intentionally pursuing quite different goals. Like the brewer’s yeast, though, academics work cheap (by the standards of private industry); furthermore, the system is entrenched and well tested, and the rigour with which academics enforce intellectual standards and is far enough superior (or, at least, complementary) to the soft-soap appraisals of business and government to compensate for the frequent disjunctions and not infrequent contradictions between them. Even if universities were supposed to serve no other purposes than those of business, for business leaders to streamline the university in their own image would be like trying to augment honey production by steam-cleaning the beehive.

On what basis are some individuals judged “worthy” of an Oxford education? The obvious answer is, those who are most talented, and have the most potential to learn and achieve notable scholarship, in their chosen fields. But why? There is some feeling that the brightest students will make the best use of an excellent education. And yet, this is far from the usual principles for allocating scarce resources. We do not insist that the finest automobiles go to the best drivers, nor do we insist on providing top-notch kitchen utensils to good chefs. (There is some effort to match exceptional music instruments to exceptional musicians, though.) When the market solution is rejected, it is typically for egalitarian reasons. But on an egalitarian basis, one might argue for providing the best post-secondary education to the most ignorant students, to balance things out. For an alternative justification, we might jump to the argument that the education at an elite university differs not in quality but in kind. This is especially true in the UK, where Oxford and Cambridge rely largely on the tutorial system. By leaving students very much to their own devices, but providing close contact and frequent interaction with leading senior scholars, this puts a premium on students’ ability to organise and motivate their studies, and to ask probing questions. For someone incapable of this (or simply uninterested), a place at Oxford would not be a gift. Then there is the problem of competition and mutual assistance among fellow students: Clearly students all benefit from a certain amount of stratification by ability, simply to allow lectures to be targetted at a common pace.

Oxbridge discrimination, elite schools, and the Sutton Trust report

The public is clearly of two minds. It is opposed to “elitism” on principle, but wants to be respected in the world for its elites. There seems to be less hostility than in the US toward pointy-headed academics, but they want class distinctions to be erased in the allocation of resources. As long as genius blows whereThe fact that well-heeled parents are buying not only a posh accent with their school fees, but sharper minds, genuinely better prepared for a top university, cuts uncomfortably across these lines. To put it bluntly, while everyone could benefit from an Oxford degree, not everyone would benefit from an Oxford education. This discrepancy is what drives the headlines, though, since one feels that the valuable Oxford degrees, being partly funded by the taxpayers, should be spread around more broadly. In particular, there is the sense, expressed in articles such as this one, that  This article describes the Sutton Trust report, which found that out of about 3700 schools in the UK, there are 100 — 78 of them private — which provides Oxbridge with about 1/3 of their matriculants. What does that mean? It sounds to many like an indictment of the fairness of the admissions process. Some schools are receiving more than their “fair share” of Oxbridge places. Or are they? In principle, this pattern could be explained if the 100 top schools had twenty times as many pupils as the rest, on average. Of course, they do not, but the idea does not seem so absurd when we replace “pupils” by “highly motivated pupils with highly motivated families”. Wealth is a factor, that is, but so is the importance placed upon education. Furthermore, as long as there is a perception that elite schools are the necessary springboard to Oxbridge, those families who yearn for Oxbridge will, if at all possible, scrape together the money to send their little ones to an independent school. The less motivated — perhaps because they do not care about education, perhaps because they find Oxbridge pretensions insufferable — will be less well prepared for Oxbridge (though perhaps better prepared for something else), and may not even apply. Indeed, if we look at application statistics, we see that the state school pupils are drastically underrepresented among the Oxford applicants as well. Only 57.5% of Oxford applicants in 2005-7 came from state schools. Those who did apply did fairly well, as we see that 53.2% of the places went to applicants from state schools. (Worcester received only 46.4% of its applications from state schools, but 48.7% of those accepted were from this group.)

Even if we accepted the soundness of the statistical inference — some schools are unfairly (or, at least, unreasonably) advantaged in placing their graduates in elite universities — the logical conclusion is being twisted to a political agenda. Consider that we believe ourselves to have strong empirical evidence for the proposition:
1) Graduates of elite universities are more likely to get good jobs and be economically successful in their lives.
The socially conscious concludes that therefore
2) We need to widen access to this important Oxbridge benefit.
We are then confronted with strong empirical evidence for the proposition:
3) Graduates of elite schools are more likely to be admitted to elite universities, and be economically successful in their lives.
The same pattern of reasoning then would lead us to
4) We need to widen access to this important elite school benefit.
One might widen access by helping more children from a variety of backgrounds to be able to afford to attend the best schools. Or, one might widen access by improving the education provided in the state schools, copying the methods and the funding levels of the independent schools. But no, that is not feasible. You see, that would demand higher taxes, and the British public does not believe in being taxed the way other Europeans are. But then, it is hard to see why, if they believe that the wealthy should be allowed by right to keep the money they earn, they are surprised when the wealthy want to use the money to buy something valuable, like a good education. And yet, this is not the conclusion drawn by some newspaper columnists and government ministers. (with some notable exceptions such as this journalist and this anodyne ministerial comment)

The report clouds the issue by multiplying the meaningless statistics: Quite promininent is the information that “The proportion of university entrants going to Oxbridge from the top performing 30 independent schools was nearly twice that of the top performing 30 grammar schools — despite having very similar average A-level scores.” That sounds rather damning, unless you know that  Oxford is choosing only from the students who have the maximum possible score of three A grades in their A-level exams. These comprise fully 10% of all school leavers, while less than 1% will be able to find a place at Oxford or Cambridge. Thus, comparing average A-level grades would not be expected necessarily to have much relevance in predicting Oxbridge acceptance rates. It is rather as though one were to infer invidious discrimination from observing that the Royal Philharmonic was far more likely to hire graduates of a leading conservatory than university graduates in music pedagogy, despite the fact that both groups on average had learned to play the same number of scales.

While the UK gives students only one shot at the “elite”, at the very least the message of rejection is somewhat limited by the admissions criteria. Whereas UK universities seek out the students most capable for the particular course of study that they aspire to study, US universities nourish the fiction that they evaluate the whole person. So when Harvard or Yale or Stanford rejects you, it is not just your academic qualifications that they are judging inadequate. It is your life.

My own experience as a student going through the US university admissions mill certainly colours my experience. Being quite naive about the process, I applied only to four universities: Harvard, MIT, Yale, and Johns Hopkins (the last only because my brother was there). I had admissions interviews at the first two, and was accepted at the last two. As someone who has gone on to be a quite competent research mathematician, I find the rejection by MIT back then particularly telling. I was a top student in high school, winning a fair share of local and national prizes in mathematics. I have gone on to become a fairly successful research mathematician. And yet I was rejected by MIT, which is focused almost entirely on natural sciences, and accepted by Yale, with much broader interests and a football team to squeeze in. Why? I can only guess that, as a shy and introverted, math-obsessed and relatively young school pupil, I did not perform very well in an interview that had almost no academic content.

Discrimination, Legacies, and Development Cases

US universities are rather infamous for the many different ways they discriminate for or against certain applicants. The most notorious are the legacies — preference for childre, or occasionally other relatives, of alumni — and the “development cases”, a euphemism for children of the great and the good, whose patronage may be expected. For an excellent discussion of the open scandals of US university admissions, see Daniel Golden’s The Price of Admission. Oxford explicitly rejects the principle of considering family connections as a factor in admissions.

I was interested to notice that even stuffy, old, rich Trinity College rejected Euan Blair, son of the Prime Minister, despite the fact that the warden (head of the college) is himself a notoriously wealthy and nonacademic alumnus of the college, and apparently a friend of the Blair family. Given the public attention that his case received, it’s easy to suppose that they were making a show of scrupulousness in admissions, but even then, it is notable that they felt it to be important to show that they would not play favourites with the son of a prime minister. Certainly US universities feel no compunctions about competing for the children of the wealthy, famous, and powerful, vaulting them ahead of more conventionally qualified applicants. Blair would hardly have been a disastrous student here: He did receive a conditional acceptance, but failed to make the required A-level grades — apparently his school predicted two A’s and a B, and he in fact received a C in French — and went on to study ancient history successfully at Bristol. (It is hardly a unique case. A classics tutor in Worcester told me of having rejected the son of a wealthy alumnus who they had ranked sixth among their applicants, when there were only five places. )

Of course, this is an often overlooked reason to be worried about the wealth-differential between colleges

Mathematics admissions at Worcester College

I presume that mathematics admissions are similar in most of the colleges, although the mechanics surely differ between those colleges with large numbers of applicants, and those with only a few. For some years now Worcester College has received the largest number of applications for mathematics and connected subjects, and in fact, the largest number of applications overall. Consequently, we had to interview from early morning to late evening on two consecutive days. Each applicant was interviewed twice, once on a sheet of questions that they had already seen, once on unseen questions. As I mentioned above, the school grades were all at the maximum. They had taken a mathematics exam specifically for Oxford admission, which has some influence on decisions.

In the end, I was quite impressed with how much one could see in a half-hour interview to distinguish the student with a superficial test-taking expertise from the student with the seeds of real mathematical vision and sharp problem-solving intelligence. At the same time, there are obvious dangers. The interview is extremely convincing, because it is something you have seen with your own eyes, and it does tend to wipe out all other considerations — particularly since, as I have remarked, the school system fails to provide the exceptional pupils with very many possibilities to differentiate themselves from the mass of merely adequate contemporaries. And while the interviews seem to be a very good tool for finding the prospective students likely to thrive in the tutorial system, it is hard to escape the suspicion that there are the rare young people whose minds are profound but not necessarily quick, who would benefit greatly from this university, and contribute greatly as well, who never manage to show their true mettle in a half-hour interview. We give two interviews, and then a third if there is disagreement, but it’s clear that a real genius might be missed.

On the other hand, I think that the interviews (at least as applied in mathematics) are well crafted to avoid the obvious inequities that concern many people. In discussions of admissions I never heard anyone suggest any criterion for admission other than mathematical ability, or rather, mathematical potential. Peripheral factors — in particular, quality of a candidate’s school, or national origin and language difficulties — were discussed only to the extent that they would help in translating the ability shown in the interview into potential. The principle, of course, is that the seed that sprouted well on stony ground has more potential than the seed that has already shown what it can do in rich loam. A candidate who seemed exceptionally nervous, or who was struggling a bit with conversational English, might deserve another look if his or her performance at the interview seemed otherwise not quite at the level of another without these handicaps. In the end, though, as sedulous as we tried to be in adjusting our expectations for the obvious distortions of personality and background, there is no question that a bright young person would be best served by the training of an excellent school, which would allow his or her ability to be directly demonstrated in the interview, rather than relying on the hit or miss possibility of some interviewer descrying great potential as through a glass darkly.

It might seem that students should calculate to apply to the less popular colleges, to compete against a weaker field. The advantage to be gained from such a strategy is marginal, though, and it could be counterproductive. There is a pretty thorough system for making sure that colleges with too many excellent applicants pass some on to the colleges with too few. My own impression is that there were a few rejected applicants, but not a large number, who probably ought to have found a place somewhere in the university had resources been unlimited.

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