From time to time we read of the sensationally disappointing results of arithmetical performance among young school-leavers. I am concerned here with the subject of arithmetic only, but it would be possible (and I personally think useful) to extend my scheme to algebra and perhaps other subjects as well. However arithmetic is the outstanding example as far as feasibility is concerned. This system would make it possible to avoid the cumbersome process of our normal public examinations which for many is a single and disastrous experience.
Such a test should be open to all (children included), but I am thinking particularly of the young innumerate school-leaver. The existence of the examination would give the young (and indeed the older) unemployed person a structured goal and produce a real rise in performance.
When I say 'performance', I do mean just that, for I am convinced that many, sadly perhaps most, school-leavers are under-achievers, sometimes to an absurd or tragic degree.
I write as someone who has coached dozens of young people who have not been given good mathematics instruction in their formative years. The main fault that I have found with the teaching they have already received (apart from not knowing the tables) is that it has been at far too high a level for the baffled pupil, who quite naturally simply gives up. I have taught a child for instance who did not understand decimals, yet had been taught arithmetic 'to other bases.' She had no idea what the normal base was. Hence my emphasis on an elementary syllabus, assuredly related to 'real life', together with a very good performance.
The use of computers for setting papers would be a simple way of maintaining a constant standard of variable questions. The computer would be programmed to print questions on (say) fractions, decimals, simple interest, hire-purchase agreements, speed/distance and time, areas/volumes, unitary method, averages, percentages and ratio. Calculators would not be allowed, but 'heavy' arithmetic would be avoided.
Candidates would pay for this examination, even if only a non-economic fee, to discourage frivolous use.
Books of sample papers and worked examples should also be available.
May I emphasise the entirely practical advantages of my suggestion: the low cost once the computers and fax machines were installed; the fairness; the availability to all; and above all the rapidity with which the results could be produced and the frequency with which the test could be taken. Several groups of people could take the examination in the same room at different times in one day, with no difficulty in supplying different papers for each group - or even each candidate.
Incidentally at the modest level I am considering, there would be no shortage of teachers, though of course it would be possible to have more than one level of examination.
I will finish with the comment that while it is not necessary for a nurse to have passed GCSE mathematics, it may be positively dangerous for her not to understand decimals: indeed I understand that so-called 'metrication deaths' are not unknown.
Ed: Perhaps the computer program could also offer the examinee a chance to go back over mistakes in the examination, offering coaching on those particular points, using good graphics, humour and real life or science fiction examples, making it all as much like an exciting computer game as possible - to help make up for any deficiencies in their regular teacher.
Alison Crawshaw, 13a Porchester Terrace, London W2 3TH (tel 071 262 6012).