The problem was simple: the higher level maths paper was deemed to be too hard. Anybody who ever sat this exam will recall that it was scary enough to conjure up nightmares for years afterwards but, even by those standards, this one was supposed to be especially tough.
The most serious criticism initially appeared to be that the paper touched on matters outside the standard syllabus. If that were so, then it would indeed be hugely unfair. It would be the equivalent of studying a Leaving Cert history course that concentrated exclusively on Irish-related subjects and being set an exam question on a minor battle in the American civil war.
If that had been the problem last week then students and teachers would have had legitimate grounds for complaint. Mathematical problems, though, are not quite so straightforward. Whether a problem requires extraneous knowledge, or an exercise in the sort of lateral thinking and logical application that maths is meant to foster, may well be a matter of opinion.
As it transpired the real problem lay elsewhere. It wasn’t so much that students were expected to know about matters they hadn’t studied but that the questions themselves didn’t follow the usual format.
The structure of the problems had changed, and parts of questions that were usually easy (guaranteeing to deliver marks and settle nerves) had been beefed up considerably. To make matters worse, the so-called “banker” question in trigonometry caught everybody on the hop by being a lot tougher than usual.
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So those students who planned to land their higher maths result through tactical and strategic answering based on analysis of past papers and specific guidance by clued-in tutors got the shock of their young lives last Monday.
And you can guarantee that where there is a whiff of outrage and indignation, especially among young people who will be old enough to vote in the next election, politicians will follow with their noses in the air.
Sean Crowe, Sinn Fein’s education spokesman, described the paper as “outrageously difficult and full of tricks”, while Labour’s Jan O’Sullivan suggested that state exams are a chance for students to show off what they know, “not an occasion to expose gaps in their knowledge”.
Oddly enough, I always thought that exams were about serving both purposes at once, since the gaps in a student’s knowledge are of no small significance when they move on to higher study.
So what precisely was the nature of the trick played on the unsuspecting students? The Irish Times summarised it as follows: “Maths Paper Two was designed to put rote learners and those who had learned off grind-school notes at a disadvantage (compared with) those who can employ independent mathematical reasoning.” And that’s it.
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The paper was condemned as unfair because it required students to be ood at maths. It was deemed to be cunning because it demanded an aptitude to work out hard sums rather than a good memory for past papers. It required logic and lateral thinking, rather than a well-heeled parent who could afford grind-school fees during the Easter and Christmas holidays.
This infuriated maths teachers. They were cross because the paper demanded that the students apply what they had learned, rather than regurgitate what they had simply taken in. Which is understandable, of course, as teachers are under pressure from schools and parents to help their pupils acquire the points they need to secure the third-level courses they want.
What this row underscores is that, somewhere along the way, the notion of teaching skills and abilities that pupils might need later in life has been abandoned. We’ve suspected it for a while, but the maths paper furore makes it absolutely clear — the Leaving Certificate is not an education, it’s a production line.
For years employers, foreign investors and universities have been warning that our mathematical skills are in a steep decline. Much of our economic success derives from specialised industries in the high-tech, pharmaceutical and medical-devices sectors. These in turn depend on a regular supply of graduates with strong numerical skills. We can’t compete internationally in terms of labour costs, but we’ve always comforted ourselves with the mantra that our “highly skilled and well educated workforce” would see us through rough times ahead.
Now it seems our workforce is not quite as skilled as it ought to be. Students are not bothering to put the work into higher-level maths because the time required simply doesn’t repay them in terms of points — and that’s all that matters. They figure they’d be better off blagging ordinary-level maths with mindless rote learning, and doing two additional “easy” subjects in the time saved. And it’s hard to blame them.
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The problem with this rationale, a direct product of the competitive points system, is that mathematics is essential in countless walks of life. Maths teaches analytical skills and abstract reasoning, and if you’re planning a career in science, business or technology, you won’t get very far without it. In economic terms, intellectual skills in these specific areas are the country’s best chance of maintaining a competitive edge “going forward”, as thrusting business types are wont to say.
So-called “transferable skills”, such as problem solving, analytical thinking, project management and numeracy, are the most sought-after by employers and all of them are developed through the study of maths. Learning no more than just those answers required to get them through the Leaving Certificate simply doesn’t equip students with the fundamentals they need.
The universities have been saying for years that grade A maths students pursuing courses in the sciences often lack the most basic grip on the principles involved. That shouldn’t surprise us. As last week’s exam rumpus confirmed, not even maths teachers see the point of maths, other than as another points “banker” to be crammed in and spewed out regardless of understanding.
It has been argued that this year’s paper will dissuade students from attempting the higher- level exam in the future. If they reckon they’ll have to put in the time to acquire the necessary mathematical skills, rather than studying the subject by rote with the aim of getting a guaranteed result, they just won’t bother.
The solution, therefore, is to make it worth their while. The department of education should heed the pleas of business and third-level institutions and allot additional points for higher-level maths in next year’s exams. Up to 20 years ago there was a generous points premium for an A in honours maths so it’s no coincidence that performance in the subject in the interim has declined steadily.
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Genuine mathematical skill, rather than just savvy strategic mnemonics, has to be incentivised and those pupils who put in the effort have to be rewarded. Because we’re going to need them.