Teaching is the art of the testable

I've spent a few hours yesterday and today (and will add a couple more tomorrow morning) standing in the computer labs proving support for the students doing the Water Resources project [WARNING: PDF, 68Kb, the unit in question is on page 19; these things should be in HTML, natch]. As ever, an interesting experience. Working out what they get, and what they don't, trying to steer them to thinking about something without telling them, and so on. It's been a while since I've done any sort of teaching, and it's fun (but two half jobs and teaching doesn't work, before anyone in the department starts getting ideas :-).

When Dad was over in Bristol for the evening last week, one of the things we talked about was the way we (in the most general sense) teach kids (since this starts from a very early age) so effectively to answer exam questions. We've got ourselves stuck in this marvellous viscous cycle, where we try to dream up difficult questions, and the kids just get better at filtering out the crap. We ask,

Johnny has four apples, and he gives two to Mary. How many does he have left?

If Mary had three to begin with, how many does she end up with?

After being faced with a couple of these, our hypothetical child begins to see,

Johnny has four apples, and - he gives two to Mary. = How many does he have left?

If Mary had three to begin with, how many does she end up with? + 2 =

This has just put me in mind of Edsger Dijkstra's rant about mental crutches. Dijkstra's complaint was that, having learned to use the crutch, it is difficult to unlearn, and using the crutch results in an impoverished understanding.

Aside: Dijkstra, while I'm here, wrote short essays, duplicated them, and distributed them to computer science departments around the world. Collected, these essays constitute a weblog (observed by, among others, Sébastien Paquet at the time of Dijkstra's death), mostly written before the web. But then, to mangle a Dijkstra quote, "Weblogging is no more about the web than astronomy is about telescopes."

The problem is worse than that. Our pupils are systematically taught that the only important thing to know is how to separate the question from the crap. And that, thus winnowed, the question will be soluble by the application of arbitrary but memorisable rules.

Skip forward a few years, and our "model" has arrived at University, having chosen (against all the odds) to read Civil Engineering (our model pupil has parents of sufficient means that the idea of adding a several thousand pound a year tuition fee debt to the inevitable cost of being a student is not offputting, and has chosen to read, rather then study). She sits down in a class listed in her timetable as "Design", and is asked to follow the instructions in Extracts from British Standards for students of structural design. British Standards PP7312:2002.

Immediately, our student's well honed filtering skills jump into action. While the authors of the Standard may attempt to explain where the mandated equations come from, our student merrily processes them as if they were plucked from thin air. The assignment is completed, an impressive mark stored towards the hoped-for first class degree, and the filter, now even better honed than before, is deactivated. Exit design studio left, in direction of pub.

"Science is the art of the soluble," said Peter Medawar, modelling his comment on R. A. Butler's earlier assertion, "Politics is the art of the possible." [I don't know this stuff, by the way, it's all out there in the cloud.] Is teaching simply the art of the testable?

What, you may be asking, has this to do with the Water Resources Project? I found myself thinking about these things again as a result of a situation which sits uncomfortably between amusing and alarming. Bear in mind that the students on this course are third and fourth years (the fourth years are those who spent their third year abroad), along with some incoming Socrates students, and so are not straight from school (with or without gap year). They have already been through two or three years of University education; they should have learned to think.

One of the activities necessary in this project is the preparation of minimum runoff curves from a flow record, in order to calculate the storage necessary in a reservoir given three possible dam sites (chosen by the students), to ensure that a dam at that site would create a reservoir of sufficient size to supply a moderately sized new town development. The flow at the dam sites is estimated by adjusting a flow record at a downstream flow gauging station according to the size of the catchment feeding into the river at that site relative to the catchment supplying the river at the gauging station. The first step in the preparation of the minimum runoff diagram is very time consuming.

I was approached by a student (let's call him X) who had just realised that they had calculated the required storage for a reservoir created by a dam at the site of the flow gauging station (the numerous residents of the Welsh valley above this location would no doubt be nonplussed at this idea, although the presence of the station would make the calculations much easier). To his credit, X had spotted the error in his ways already, but wondered whether he need repeat the first stage three times, or whether he could apply the catchment size factor at a later stage in the proceedings, thus saving considerable effort.

In reply, I suggested (ever helpful) that X (and his team mates) might like to think about which of the steps were non-linear in the catchment area, since clearly everything after the first such step must be repeated, but everything before need not. I heard nothing more, and fondly imagined that X (and his team mates) had taken heed of my well intentioned advice.

I heard nothing, that is, until the end of the session, when I overheard Dawei Han explaining that the work which X had diligently replicated three times over the course of the hour or so since I had spoken to him had been a total waste of time, that the results of the first stage could be scaled by the relevant factors and fed, thusly scaled, into the second (and non-linear) stage of the process.

If X had thought about what he was doing, and had mistakenly come to the conclusion that this work was necessary, I would have had some sympathy. It turns out, however (and X freely admitted this), that after receiving my unedifying advice he had consulted one of the other teaching assistants the same question. And had been given a direct answer.

An answer which while direct was, unfortunately, also quite wrong.

So it goes.

Comments

[Hamish]

Perhaps I should add a couple of notes to this.

First, I've just had a half hour discussion about the fact that the students this year have all completed this first part of the project well within the time limit. There are a few reasons for the fact that they didn't take as long as before, but they also did this without asking many questions. An impressive performance.

Second, in previous years people have tied themselves in terrible knots around the structure of the spreadsheet required to prepare the minimum runoff diagram. There was little to no evidence of that this year, which suggests that these students have developed the ability to view problems in spreadsheet terms. Where this skill came from all of a sudden I don't know. I'm told that Excel is used in sixth form Physics and Chemistry work at school now. Perhaps extended exposure is helpful.

Of course, there remains the issue that the fact that they are competent users of Excel does not mean they are expert users of computers. A problem which the ubiquity of Excel and early exposure to it are only likely to exacerbate.