Power of logic

Gifted students have their own special needs, and a Kent school is taking a novel approach to meeting them

Schools are legally required to cater for the full ability range of their pupils, including the exceptionally able. But not all of them go to the lengths of schools in Kent to meet the requirements of the gifted. Although under no obligation to do so, Kent includes the exceptionally able in the special educational needs (SEN) category. It estimates that around 23,000 of its pupils are "very able and talented", of which some 4,600 are "exceptional".

Because the law does not require separate education for the exceptionally able, many schools rely on their examinations programmes to do the necessary. But when youngsters don't just pass examinations but surpass them, it becomes apparent that a complementary policy of fitting the course to the pupil, rather than the other way around, has a lot to commend it.

This is the view taken by Kent LEA, which offers start-up grants for initiatives aimed at assisting the exceptionally able in both the primary and secondary sectors, and includes sports and the performing arts in the remit.

I have been using one such grant to generate one timetabled period of teaching time per week, plus a nod to preparation time. I'm no dancer or footballer, but I do have an interest in logic. So, since good thinking is a fundamental skill always in demand, I have set up a course in it for a group of gifted lower sixth-formers from across the A-level range of disciplines. The journey was always going to be more important than the arrival, limited time precluding finished expertise. But accurate conceptualisation, logical ordering and forms of proof were certainly within reach, so I decided to go for those.

We warmed up with some modest conundrums that called for considerations of method. Here's an example.

Politicians never tell the truth and non-politicians always tell the truth. A stranger meets three individuals and asks the first, "Are you a politician?" The first answers, and the second reports that the first denied being a politician. The third says that the first is a politician. How many politicians are there?

(The answer is "one": the first must deny being a politician; the second is truthful; so either the first or the third is a liar.) we then moved on to St Anselm's ontogolical proof of God (indispensable, modern linguists will know, to Descartes), to Zeno's puzzle of Achilles and the tortoise, and to the dilemma of Epimenides the Cretan, who said that all Cretans were liars. This last one exemplifies a difficulty that famously ambushed Bertrand Russell. Try it in this form: On one side of a piece of paper is written: "The statement on the other side is false." On the other side, it says: "The statement on the other side is true." Reconcile these statements.

In addition to raising issues of logic, this puzzle usefully asks whether propositions which appear equivalent in isolation remain equivalent when taken together, thereby allowing a dip into linguistics as well.

We have also established that ethics has no single foundation and have considered architecture, science fiction and the single European currency. This term, we are looking at deduction and categorical propositions, the syllogism, classical and pop music, and painting (the entire National Gallery is now available on CD-Rom). Symbolic logic, too, I hope.

They may seem unconnected, but mastery of ordered abstraction is a defining characteristic of man. Lord Annan once said that intelligence was the ability to make unusual associations. Our class is doing just that.

I see nothing but good coming from this exercise: it benefits everyone, including me, if only because it frees me from the down-dumbing of the national curriculum. The national curriculum is an expensive, major error made plausible by minor successes, and one of its several evils is its stultifying prescriptivism.

But what do the people on the receiving end think? One participant told me: "I like the course. It makes me use a different part of my brain." Another, glimpsing the restlessness often inseparable from high achievement, said (of Epimenides's dilemma): "It seemed trivial at first. Then I had to keep at it." Anecdotal stuff, of course, and I wouldn't hide the bafflement, nor the fact that, predictably, some fare better than others. But the consensus is that the course is "interesting" and, given the quality of the takers, I'll settle for that.

Assignments are not only discussed, they are also written up, and I can see what has clicked and what hasn't. For all the ups and downs, what impresses me when I read what these people write is how far and how fast they have travelled. Two terms ago, they were just about taking their GCSEs, and it's simple maths to work out that 30 minutes a week since last September comes to a mere handful of hours. Yet here they are, still attending an "unofficial" class, hanging in there and ready for more.

Catering for the exceptionally able on their own terms is an eye-opener for pupil and teacher alike, and there is evidence that, in schools where such teaching is fostered, standards rise. If practised on a national scale through the primary and secondary phases, a lot of additional talent would be brought on; and our understanding of what is possible in schools would be transformed.

* Able children, Kent CC's ring-binder s available from Mrs D Kelly at KCC Education, Springfield, Maidstone ME14 2LJ (01622 671 411). Pounds 17.50, incl. pp

* Colin Butler's foundation text is C Cohen and I Copi, Introduction to Logic, Macmillan Pounds 25.95

* The National Centre for Able and Talented Children is at Park Campus, Boughton Green Road, Northampton NN2 7AL (01604 710 308)

* Useful CD-Roms include:

Microsoft Art Gallery (041-026) Pounds 34. The Ultimate Frank Lloyd Wright (051-562) Pounds 25

The Trinity Apocalypse (SE7 20800 1) Pounds 75

A Brief History of Time (SE7 359001) Pounds 34.02

The Ultimate Einstein (SE7 359008) Pounds 34.03

Challenge of the Universe (SE7 140027)

* Those at their wits' end can write to Dr Butler at the address below

Dr Colin Butler is senior English teacher at Borden Grammar School, Sittingbourne, Kent ME10 4DB

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