Here’s a question that’s been puzzling me for some time. If we believe our own publicity, maths graduates are still among the more employable ones out there. We tend to attribute this to the abilities that a maths degree develops: careful logical thinking; the ability to analyse problems; fluency with abstract reasoning; a toolkit of technical skills; and so on. The problem is that, as far as I can see, a lot of maths students don’t in fact develop these abilities. At the top end of the scale, of course, we have some who do, and because these tend to be the students who become our postgrads and then our colleagues they tend to bias our perception. At the bottom end of the scale, there are some students on whom the course leaves no appreciable intellectual mark: whether these students ought to graduate with a maths degree is an important question, but a different one. Between these extremes, though, we have the swathe of students who learn how to pass maths exams with reasonable efficiency but who never show much sign of learning to think like mathematicians. Yet, for the statistics to hold up, these students have to be fairly attractive to employers. What’s going on?
I can think of three possible answers. First: more of our students than we realise are developing the abilities we want. Second: the standard of graduates has fallen but either employers haven’t yet realised this or the standards in other disciplines have fallen further; sooner or later there will be a reckoning. Third: the abilities that make our graduates attractive aren’t the ones we think they are.
The first answer is hard to disprove, and my main argument against it is that I don’t believe I — and many of my colleagues — can be quite as hopeless as that at spotting thought processes in our students. I can believe that we underestimate them somewhat, but can there really be so much high-level intellectual activity going on that never shows up in homework, or exams, or project meetings?
The second answer is the popular apocalyptic one, and I suspect it has an element of truth in it. The problem with it is that it presupposes a great deal of blindness on the part of employers. We do hear them complain about lack of “transferable skills”, meaning apparently that they find it irritating to have to train staff to give a Powerpoint talk or write an email to a customer without making half a dozen embarrassing errors. We don’t, though, seem to hear them complain much about a lack of the high-level abilities about which we talk so much but which we detect in our students so infrequently. Can we really be getting away with the long grift so successfully?
The third answer is one I’ve only recently started taking seriously, partly prompted by Steven Brint’s excellent article on “educational heresies” in the LA Review of Books, which puts the case that American education is better adapted to American society than it realises. I don’t suggest that there’s a conspiracy between teachers, students and employers to provide training in one thing and present it as another; but suppose that, empirically, employers find that maths graduates function well in their jobs and so keep on employing them. Nobody then has any real incentive to ask what it is that makes these people an attractive proposition, and both employers and teachers can satisfy themselves with an answer that is vaguely flattering to all concerned.
Let’s try to look in a positive way, then, at what a mediocre maths student actually learns. He or she spends three or four years essentially adrift in a foreign country. If there are underlying principles to the tasks he or she is asked to do, these are generally invisible. The language is often opaque and the demands arbitrary. What the student learns, though, is not to panic in this situation. He or she learns to infer what the “key” requirements are; to perform apparently artificial tasks reasonably effectively; to learn, at some level, without worrying about the deeper structure of what he or she is learning. It’s a bit like a gap year spent wandering round Europe doing bar work to make ends meet: one never engages deeply with the cultures or languages in which one’s immersed, but one learns enough phrases to operate in them, and one learns, above all, to cope with being perpetually slightly lost.
Looked at in this way, I think we can see what might make a maths graduate a useful employee. Introduced to an unfamiliar corporate environment and given tasks to carry out without a detailed sense of their context or purpose, such graduates won’t panic. They’ll work out what they actually need to do to keep people off their backs; they’ll make as much sense of things as they need to and no more; and they’ll get on with things without asking awkward questions.
Of course, none of this is peculiar to maths, but I think a plausible case can be made that maths trains students in this manner better than most subjects do. The advantage we have is that much of our subject matter is thoroughly alien to our students’ lives and expressed in an alien language and notation: this positively encourages students to find ways to operate within the discipline without becoming part of it. Our assessment practices, which tend to reward the mechanical application of poorly-understood rules, undoubtedly also help. In contrast, students in, say, history or English literature are working in a dialect of their own language to start with, and are continually running across concepts they can’t help but relate to their own lives: the skills they acquire are unlikely to be those required for an obedient and alienated existence.
This argument does lead to some rather perverse conclusions. If we want to serve our students and their future employers, it suggests, we should be wary of attempting to make our courses more relevant or applicable, or to make our students think critically and engage with maths in the way that “real” mathematicians do. Instead, we should offer more courses in subjects like analysis and group theory, where the professional notation and terminology is as intimidating as possible and the weaker students are forced to learn a handful of techniques to perform and facts to regurgitate to scrape their 50% passes in exams We should also continue to talk loudly about the superb education maths provides in high-level thought processes, because this provides a convenient cover story for everyone — students, teachers and employers — who’d rather not admit that in our society knowing how to fake higher-level abilities is practically as valuable as having the abilities themselves, and causes everybody a deal less trouble.
With any luck I’m wrong about all this, and I’m being led astray by my native cynicism and the usual side-effects of reaching this stage of term. The horrible thing is that it makes more sense than any other argument I can come up with. Further proof, perhaps, that having a mathematical training and doing one’s job without getting tangled up in doubts about it are not terribly compatible?