IT can’t be fun being an exam-taking adolescent. First, there is the sheer
misery of sweating through the papers themselves, knowing that Your Whole Future
rests on the outcome. Then there’s the sticky weeks of waiting to see the
results posted on a cruelly visible school noticeboard. And the final nightmare
of Having Done Really Badly.
Or curiously, even worse, of Having Done Really Well. These days exam success
is increasingly likely to attract unpleasantness from so-called adults. Perhaps
you’ve heard the “standards are falling” line which tends to end with “in my day
they had proper exams”.
Such people tend to argue thus: recently, the proportion of school students
getting high scores in their year 11 and 13 exams has risen year by year, in
many subjects. Therefore the exams must be getting easier.
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Clearly, if these adults ever learned anything about correlation or
statistical significance, they forgot it ten minutes after the relevant exam.
Possibly, they’re comparing how hard they found the exams then with what they
think they know now. That, as you may still remember, is error number one in
considering correlation.
To test this in Britain at least, let’s compare the exams set 25 years ago
with today’s. Not surprisingly, a call to one of the examination boards produces
some consternation. It also produces a paper by Helen Patrick of the University
of Cambridge Local Examinations Syndicate on the difficulties of comparing exam
results over time. “We’re not assessing the same thing,” she concludes, “we’re
not assessing it by the same methods, and even if we were we would be doing so
in quite a different context, which of itself would change the very thing we
were assessing.”
She has a point. A quarter of a century ago, for example, when I was a keen
but rebellious pupil, my eye was inevitably drawn to the heading “Pathological
Forms” on an article which described a mathematical curiosity known as
Sierpinski’s Gasket. I enthused. Forget it, said my teacher. Too obscure. Now
resource lists for mathematics teachers are full of such fractals.
Or take next year’s Institute of Physics syllabus for 16 to 18 year olds,
developed as part of its “Advancing Physics” initiative. It includes a 70-minute
paper entitled “Rise and Fall of the Clockwork Universe”. The content is largely
classical, non-chaotic, mechanics. But the critical approach of the title would
have confused many teachers in 1975.
The institute’s syllabus requires pupils to be familiar with “storage of
images in a computer as a series of numbers”. Think back. In 1975, computers
featured as a tiny part of any mathematics course anywhere. I well remember
excursions to see The Computer.
It seems that everything in the 1975 exam is still in the syllabus, except
for detailed knowledge of thermionic diodes (remember them?). In simple terms,
the exams are probably harder if anything. The subject as a whole is certainly
bigger, and the standard of adult general knowledge a lot higher. As Patrick
also says, careful comparisons can illuminate differences between schools,
between examination boards and between subjects—but not between
generations.
So, listen to Uncle Mike and cheer up. You live in a more complicated world
than many of the adults around you recognise. And, even more important, you
probably are, statistically, smarter than they are. So there.
