Curious cosmologies and killer rabbits

Another dissertation season has been and gone. For our weaker final-year students this season meant struggling gamely with the constraints on self-expression imposed by English grammar as their supervisors understand it; for me it meant struggling less gamely to  understand what these students had written and, if possible, why. It was an unusually rich season for puzzling statements, and two specimens in particular got me thinking.

The first specimen came from a student writing a dissertation on mathematical biology, in which a reference to “predators (rabbits)” prompted the following conversation.

NCD: Are rabbits really “predators”?
Student (confidently): Yes.
NCD: What do they prey on?
Student (happily): Birds!
The shade of General Woundwort passes across the stage.
Student: Er… no, that’s not right, is it?

The second specimen came from a student whose dissertation was on climate models. I’ve brought the grammar in line with modern English but have not altered the content (which she stood by when I brought it to her attention):

The Earth takes one day to complete a full rotation around the Sun and the Earth’s axis is tilted at an angle of 23.5 degrees. This explains why we experience day and night.

After a lengthy discussion and two more weeks of effort, this had been amended but had gained the comment that

The Northern hemisphere always faces towards space

— which is, at any rate, not wrong.

Although I stand by my position that sharing suitably anonymised jaw-droppers like this is a valid way for staff to cope with the horrors of marking, that isn’t the point at issue today. The question is how people who are smart enough to have reached the final year of a university degree can possibly come out with stuff like this, and what it might indicate about how their education has failed them.

I can offer three hypotheses, which aren’t mutually exclusive. The first is that these students genuinely don’t know, despite the Pythons’ efforts, that the Earth takes a year to orbit the sun, or that rabbits are herbivores; the second is that they “know” facts like these but fail to connect them with other facts and contexts; the third is that there is a serious disconnection between what these students know, in either sense, and what they write.

I resisted the first hypothesis for a while, but faced with evidence like Specimen 2 I’m forced to accept it, for at least some of my students some of the time. Such unexpected gaps in students’ knowledge are bound to affect how we can teach them, and indeed to make teaching them some subjects pretty tricky. I find it bizarre that in an age of almost unrestricted access to information somebody can reach their Honours year without knowing the astronomical difference between a year and a day, but apparently this is possible. What I don’t know is whether they’re stocking their minds with something other than this sort of common information, or whether they’re simply stocking them with nothing.

If my students are stocking their minds willingly with one subject but have chosen — presumably for employability’s sake — to spend four years grudgingly studying another, then I can only feel sorry for them. It’s easy to sneer at degrees in surfing or classes in pop lyrics, but if such courses let students experience the joy of learning something that they really care about then they may serve a noble purpose. If, alternatively, my students simply know nothing then I feel even sorrier for them. They’ve spent, by the end of their degrees, sixteen or seventeen years in education, and at no point have they discovered that learning is fun — and more than fun, “the only thing which the poor mind can never exhaust, never alienate, never be tortured by, never fear or distrust, and never dream of regretting”, to quote again from Merlin’s splendid speech in The Sword in the Stone. But I’ve no idea what to do but pity them.

For a while I suspected that the students who seemed to know nothing were the ones who simply didn’t read; it was largely through omnivorous reading in my early years that I learned about the Earth’s rotation or the diet of rabbits. Only about half our undergraduates have a C or better at Higher English, which at first seemed like a reasonable proxy for the kind of higher-level literacy that I’d associate with general knowledge. The trouble is that I can find no correlation between whether or not students have Higher English and how well or badly they do in later years, even in classes in modelling or dissertation-writing where one might expect background knowledge to help. It’s possible that I overestimate what Higher English tells us about literacy, but for now I’ve parked this theory for lack of evidence.

The second hypothesis seems more productive. Students may acquire pieces of knowledge but fail to connect them, either with “adjacent” facts or with more distant constellations of information; in an extreme case, some students may assign facts to distinct magisteria so that a rabbit in theorem and a rabbit in a lettuce patch need have no properties in common. This seems more plausible than that they think the rabbit in the lettuce patch eats birds. If this is what’s going on, the students who suffer from it are simply not trying to make sense of new information: given two thematically related statements, they don’t try to assemble them into a coherent whole, but are happy to dump them side-by-side in a mental lumber-room. It would also explain how my student recovered her position when prompted: sometimes a rhetorical prod can stir the brain into sense-making activity. But is it really necessary, by the final year of a degree, to supply such prods? If the sense-making habit hasn’t formed by now — if the habit hasn’t formed by some point in primary school — I have a nasty suspicion that there’s not much anyone can do about it.

That leaves my third hypothesis, which may be the most cynical but also offers a way forward: my students know this stuff well enough, but “what you write for class” and “what you know outside class” exist in different social worlds. The separation between these worlds is marked by the local dialects: colloquialisms and bullet points place one in the “real” world, where maths is of course irrelevant; paragraphs of formal English (or worse, formal mathematics) locate one firmly in Laputa where to show awareness of quotidian affairs renders one “extremely contemptible”. It would be a serious solecism to speak the language of one world within another.

I can see two ways to end this separation. One is to break down the barrier of dialects and try to teach in the dialects that students encounter in their “real world”. I’d do this more if I believed that these dialects were suited to express complicated ideas, but the reason that formal English and scientific jargon exist is precisely that they’re not. The problem can be illustrated by considering Newtonian mechanics, where the teacher would like the students to bring into the classroom their intuition and experience of forces and motion, but to leave at the door the everyday usage in which force, energy, and power are effective synonyms. And that’s to ignore the fact that many of my students’ preferred dialects are even less suited to mathematics than standard informal English. Edward Tufte cured me some years ago of believing that technical material could be reduced to bullet-pointed shrapnel in the manner for which my students lobby me, and although I relish colloquial Glaswegian I’m not convinced it has the vocabulary or the syntactic flexibility for advanced mathematics. A direct collision between Laputa and a surface town was liable to injure both.

The other way to end the separation between class and world is to equip students to break down the barrier from the other side — and indeed this should help under my second hypothesis too. What our students lack seems to be the mental control mechanism that one painfully learns to apply to one’s statements and arguments. Under hypothesis 3, the control mechanism doesn’t draw on general knowledge when it’s applied in academic contexts; under hypothesis 2, the control mechanism barely exists at all. The idea is to make the sanity check an essential part of our students’ routine: at the end of every calculation or every paragraph, go back and ask yourself “does it make sense?” If we could drill this one question into them then I’d cheerfully accept a little less fluency in solving ODEs or inverting Laplace transforms; hell, if I could be sure I’d never see another “when π = 2”, I could accept dumbing-down elsewhere with equanimity.

The catch? The drilling-in would not be pretty. Few students really mind being corrected if they can be persuaded that the correction is a recondite technical matter; corrected in this manner they tend to blink solemnly and file the new fact away in that mental lumber-room. In contrast, practically all of us mind being called stupid, but the essence of a failed sanity check is that — for a moment at least — that’s exactly what we are. One can leaven it with humour and a touch of tact, but if we can never force this realisation on our students then we’ll see more killer rabbits and more cosmologies of which Kepler never dreamed. And not just in dissertation season.

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