Comment is sacred, but facts are free?

Scene: a second-year Mechanics tutorial, fairly recently.

Me: … so we just need to know how long the body takes to go round the earth. The body in question is the moon, so we know that its period is roughly… anyone?


[Embarrassed shufflings and avoidance of eye contact.]


Student: Twelve hours?

And Galileo never said "Elementary, my dear Watson" either.

“”Eppur si muove”, Holmes”, I remarked testily.

I think I handled the situation reasonably well, or at least without apparent mockery: I explained the difference between the period of the tides and that of the moon; I talked about phases; I mentioned the entwined etymologies of “month” and “moon”, and I noted, by way of lightening the mood, that Mr Sherlock Holmes would probably have thought this information as unimportant as did most of the class. (This last may have been a tactical mistake, since I’m not sure on reflection how many of them have heard of Baker Street’s most celebrated consulting detective.) Any gibbering that I needed to do, I kept for the privacy of my own office.

Gibbering aside, I think there’s a serious point lurking behind the incident, which is something to do with prior knowledge. I’m prepared to believe that nowhere in the chain of prerequisites for this Mechanics course is there a syllabus containing the statement “the orbital period of the Moon is approximately one month”. Technically, then, one could argue that I shouldn’t expect it to form part of my students’ prior knowledge, any more than I should expect them to have heard of Sherlock Holmes.

The trouble is that it’s practically impossible to teach any applied subject — perhaps impossible to teach any subject that consists of anything except narrow technicalities — without assuming a shared hinterland containing this kind of basic information. The moon incident makes me wonder what else they’ve found completely incomprehensible. When we covered orbital mechanics a few weeks ago, how many of them (pace Holmes) knew that the planets go round the sun? How many of them had heard of Halley’s comet? (I’m sure from the reaction that very few of them had heard of the Bayeaux tapestry, of which I always show the relevant portion at this stage.) For how many of them did the names of Newton, or Galileo, or Archimedes, carry any associations whatsoever? On the more mundane side, how many knew what a pendulum was before they saw the picture in the lecture notes (or the demonstration I gave with an old yoyo)? If I talked about a distance as being roughly as far as from Glasgow to London, or from Glasgow to New York, how many of them had the faintest idea of what that meant?

Maybe this problem is the result of asinine “progressive” educational approaches in which definite knowledge of any kind is sneered at and it is presumed that one can learn to think perfectly well when one is uncluttered by facts or learned procedures. This is certainly a popular heresy, which the interested reader can find being dealt with robustly on Harry “Substance” Webb’s blog — for example, in this recent post or this slightly older one. (Indeed, Holmes, who was rather wiser than most educationalists, knew perfectly well the impossibility of letting the brain work without sufficient material.) I’m inclined to seek the root of today’s incident somewhere deeper still, however, because what my students lack isn’t formal education so much as the everyday informal education that a curious mind happily constructs for itself from whatever it comes across — the caddis casing of the intellect.

Once upon a time, my more wizened colleagues tell me, one could assume that university students were more than functionally literate: in their spare time they occasionally read newspapers, or even books, and as a consequence they had stocked their minds with all sorts of information that would never explicitly be examined, but which provided a context for anything else they might learn. I even seem to remember something of the sort from my own days on Roke Island, or wherever it was. We might not understand every reference that our teachers threw at us — indeed, there were quite a few we didn’t get — but we knew enough to start forming connections between the known and the unknown, and we expected to have to pick up a lot as we went along. For the students in my Mechanics tutorial, and for a lot of others I’ve met, this simply doesn’t seem to be the case.

I know there are vocations within teaching where this sort of thing is your bread and butter. Friends who teach primary-school kids tell me poignant little stories about the ones who wouldn’t believe that milk came from cows, or who didn’t know that Christmas happened in other villages at the same time that it happened in theirs. Friends who teach in inner-city schools where there are twenty first languages in a class of thirty students tell me how careful they have to be not to navigate using the cultural landmarks of the white and middle-class and educated. But… I teach, by and large, native Scots with English as their native language, who are supposed to have come through at least thirteen years of education before they reached me, and I’m supposed to be able to introduce them to non-trivial helpings of the common intellectual wealth of the human species. And they don’t know how long it takes for the Moon to go round the Earth; and, to judge by their reaction when told, they feel no shame in not having know this, and they will forget it again as soon as possible.

There are commentors on education who criticise students (occasionally) and teachers (frequently) for allegedly reducing learning to a process of memorising disconnected facts, and since such a process clearly isn’t the same thing as genuine learning — whatever that means — these commentors conclude that learning facts is unimportant. I’m sure there are plenty out there who’d tell me that it doesn’t matter that my students don’t know how long it takes for the Moon to orbit the Earth, because they can find this information on Wikipedia at the tap of a touchscreen. The reason it does matter is that disconnected facts may be valueless but connected facts are knowledge; and what make the connections between facts, generally, are other facts. Scattered “names and dates and battles”, to take the classic example, can be rote-learned like a somewhat baroque shopping list: I’m sure that someone could memorise “Dunbar 1296, Stirling Bridge 1297, Falkirk 1298, Bannockburn 1314, Declaration of Arbroath 1320” without knowing whether they described historical events or phone numbers. But what starts to put these in context is knowing about the deaths of Alexander III in 1286 and Margaret of Norway in 1290, the election of John Balliol in 1292, the death of Edward I of England in 1307… Add more facts until the solution supersaturates and they will crystallise into a story, and that remarkable document of Arbroath and its consequences may start to come into focus. (Of course, it also helps to have some idea what a king was, what a battle was, where Scotland and England are and were; without this kind of prior knowledge, you’re in the position of somebody interrupting the story of Goldilocks every five seconds to ask “What’s a bear?” “What’s a bed?” “What’s porridge?”)

Higher education, on the whole, is designed around the assumption that our students don’t reach us with entirely empty minds. We expect that our job is, yes, to give them new information, but also to help nucleate the crystallisation of what they already know into systematic, organised knowledge. But when the solution has to be resaturated from scratch at the start of every class, it’s like dealing with the narratrix of S. J. Watson’s splendid Before I Go To Sleep, who wakes up every morning with her memory swept clean, and who must communicate with herself from one day to the next through little notes to herself and hidden diary entries — a process not unlike our students in September trying to prepare themselves for a new academic year equipped only with the revision notes they made last May.

I can’t see a remedy that lies within my power. If somebody chooses to look at any syllabus, however well designed, and see in it nothing but disconnected facts and algorithms, then I can’t prevent them from doing so; and even if I went all constructively-aligned about it and started demanding breadth of prior knowledge in the exam, it would probably be ten years too late to stop the rot. I can’t insist that nobody should enter any degree course, whether it be in mathematics or any other subject, unless they have made a habit of reading a good newspaper, or an informative blog, or anything of that nature, a couple of times a week. But I’m sure that unless students have acquired such prior knowledge, any education we attempt to provide for them will degenerate into either meaningless memorisation or — equally meaningless and still more irritating — endless “discussion” and “debate” carried out in the total absence of relevant information.

And for many of my students, the sad fact is that this is exactly what has happened.

This entry was posted in Teaching, Undergrad. Adv. Math. and tagged . Bookmark the permalink.

3 Responses to Comment is sacred, but facts are free?

  1. Pingback: Maths teaching and technology: a dead language or a pickled fish? | New-cleckit dominie

  2. Pingback: On the banks of denial: the Higher Maths “crocodile” question | New-cleckit dominie

  3. Pingback: Curious cosmologies and killer rabbits | New-cleckit dominie

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