Elegy onthe death of practical problems
Many teachers will say good riddance to maths coursework! No more haranguing students to hand it in, or wrestling with assessment schemes, or judgments about levels. Has she "carried through a substantial task and solved quite complex problems by breaking them down into smaller, more manageable tasks?" (level 4). Have they reached level 5 and "starting from problems or contexts that have been presented to them, introduced questions of their own, which generate fuller solutions?" (I think I'll go and put the kettle on.) Many a student (more likely a "him" rather than a "her") will be pleased, too: one less project deadline to meet. But not all will be - especially those who freeze up in exams and write notes on their scripts. As an examiner I get to read these pathetic pleas for mercy: "To whoever marks this exam: I'm sorry to waste your time. It's all pants, I know, but my cat died this morning." At least coursework can be completed in the privacy of the bedroom and, who knows, that internet connection might come in handy.
As a teacher, I have mixed feelings. In the past few years I have become cynical about the whole enterprise. How much "help" should I give? Students came to my sixth-form college thoroughly versed in the GCSE coursework game -teachers are there not to assess what students can do, but to maximise their marks.
I remember a few years ago going to a sociology open evening at a local college touting to take my daughter, at which the teacher proudly announced: "We make sure all students pass their coursework." But if that's the case, what's the point of them doing it?
Besides, my salary may depend on exam success: the better students do in their coursework, the more likely it is that I will get a pay rise. Of course, I'm not really that cynical, but there's certainly plenty of pressure to produce results. If they fail, it's your fault.
Rather than take the not unreasonable responsibility for assessing their students, teachers' authority has been eroded. They have been manoeuvered into a game in which they fight for their students against the exam boards and their external examiners. Awarding low marks for their coursework would be like friendly fire, or a self-inflicted wound.
Yet I look back to the 1990s, when I was designing coursework. I worked for the School Mathematics Project and spent many hours discussing with fellow teachers what tasks to set and how to mark them. Our "bible" was Cockroft 243, the alluring mantra from Mathematics Counts, the 1982 Cockroft report which said maths should include - among traditional matters such as exposition -problem-solving, applying maths to everyday situations and investigative work.
Most maths teachers accepted the Cockroft vision as a chance to re-vitalise maths. I remember how one working group, presided over by the late John Hersee, a former Cockroft member, came up with a fantastic kitchen-sink scheme that involved not only open investigations and practical work, but also one-to-one maths "orals" and mental tests. The only problem was that it was not practical for teachers to administer: they did not have enough time or energy to run it.
Even so, it was an exciting time. The idea was that the then new GCSE, might reflect good teaching practice, rather than encourage the time-honoured misconception (held by politicians fixated on the 3Rs) that maths is entirely about being able to solve artificially constructed 10-minute problems in an exam hall.
So where did it all go wrong? And what are the lessons we can learn for the future? Maths coursework foundered on one of the overriding principles of our education system. To paraphrase an army motto: if it moves, measure it.
It is becoming an increasingly accepted viewpoint that our education system is totally dominated by assessment. It matters little what our children learn from education, as long as it is measurable. And a fundamental law of educational assessment, which I shall self-indulgently call "Little's law of assessment", is that the educational validity of what is being assessed is inversely proportional (a bit of GCSE maths here) to the accuracy by which it can be measured.
In mathematical terms, investigating an open problem can give a student a valid, albeit fleeting, notion about what doing maths is about. But it is a damn sight harder to agree how many marks the result should get. We can readily agree that a correct answer to a short, artificial problem on inverse proportion (say, how long it takes workers to dig a ditch) is worth three marks, but it tells us nothing about what maths, or for that matter digging ditches, is really about.
I would like to adapt the army motto further: if it moves, measure it, then certificate it. Why are we so obsessed with labelling children's achievements and measuring their worth by the number of A*s and As they get? Does getting 12 A*s in a GCSE make you a better person?
And why are we even more obsessed with the "fairness" of these results? It is unfortunate that the August silly season for journalists coincides with the publication of GCSE, AS and A-level results. This may explain the lurid detail in which they are dissected. But are blemishes in our external exam system (assumed to be faultless, unlike other human enterprises such as journalism) treated as public disasters?
So, GCSE maths coursework, rest in peace. The forces of provable educational "progress" have triumphed over the idealists. Ditch those investigations and stick to exam questions about digging ditches.
Chris Little is principal examiner in A-level maths. Until recently he was teaching at St Vincent College, in Gosport. He was formerly chief executive of the School Mathematics Project