The Mathematics Crisis in Britain
Stephen Bush and Michael Robinson
The view is now commonplace in universities and among many business people that the advent of GCSE in particular has brought about a steep decline in the educational standards of 18 year-olds preparing to enter university. As well as mathematics, the decline applies to a wide range of subjects – English language and literature, foreign languages, geography and the sciences. This is the view of the customers of school education. The producers – the schools, the examining boards and increasingly the government – contest this view. They say that the rising pass rates, as witnessed by this year’s A-level results, and specifically the numbers graded A or B – are indicative of improving standards and it is mean and unfair to pupils and producers alike for the customers to complain.
Our evidence, arising from direct professional experience, is that the decline in mathematics standards at A-level is dramatic and irrefutable. We have concentrated on mathematics because of its absolutely central role in the sciences and in professional engineering. Without adequate mathematics these subjects, on which modern industry depends, simply cannot be studied and applied. For this reason the mathematics crisis is a national issue of concern to everyone in the country and not merely to those in education.
We not only have objective data from our own country, but also external data from Hong Kong and Singapore. Both of these countries are situated in the Pacific Rim region which competes industrially with us and both derive their school education systems directly from the traditional English ‘O’ and ‘A’ level examinations. Moreover, because considerable numbers of students from these countries are admitted to our engineering courses in UMIST, we are able not only to compare their performance on course with that of their British contemporaries, but also to make an objective comparison of the value of their A-level grades with those of British students.
First a summary of the internal evidence. Virtually every engineering and science department in the traditional universities, which are responsible for about three quarters of all science and engineering graduates, have established or are establishing four year instead of three year courses in order to cope with the reduction in entry standards at 18+. The recent discovery of a 1981 London O-level question appearing in a specimen 1996 A-level paper is a grim portent.
As members of one of the largest engineering departments in the country we can measure the effects of grade inflation. Since the mid-1980s the average science A-level scores of the British students admitted to our courses have risen. Despite extensive remedial action, the first year fail rate has more than doubled over the same 10-year period while despite this rise in average A-level scores and some expansion of our intake, the absolute number of British students gaining first class honours on our courses has fallen. At what we believe are constant exit standards, the number of students from overseas, principally the Pacific Rim countries, gaining first class honours has risen disproportionately.
Evidence from Singapore and Hong Kong
Singapore students take O and A-level papers set by the University of Cambridge Local Examinations Syndicate (UCLES) in the style and at the standard applying in England up to the mid-80s. Anyone doubting the poor, one might say demeaning, quality of GCSE maths papers (or indeed any other subject) should compare them with the O-level papers set by UCLES or the University of London Examination Board (ULEAC) which also sets O-levels exclusively for overseas candidates. Being able to take a real mathematics course leading to O-level rather than GCSE prepares pupils for the A-level papers which UCLES sets its Singapore candidates. More than ten percent of the whole Singapore age group obtained an A-grade in A-level mathematics, about the same proportion as gained any sort of pass on the easier papers set by UCLES and the other boards for our own students.
The Hong Kong Certificate of Education (O and A-levels) is administered by the Hong Kong Examination Authority. By analysing the actual exam papers we conclude that both levels are at least equal to the O and A-level standards in England fifteen or more years ago. In particular the Hong Kong A-level Pure Maths papers correspond at least to our present day Further Maths papers, for which last year there were only 5,000 candidates in the whole of Britain (ie about 0.7% of the age group). In contrast around 7,000, about 9% of the Hong Kong age group, took their A-level Pure Mathematics.
Solving the Crisis
The starting point is to accept that the mathematics required for professional engineering and science is something only a small minority of our population, or any population, wish to and can do. No country’s economy will ever require more than a small minority of its workforce to be professonal engineers and scientists. But the quality of this small minority is absolutely critical to any country’s industrial success. The evidence is not just of a marginal but a huge decline in top-end standards. All the bluster and self-deception of the examining boards and teachers’ organizations will not alter the facts that in science and engineering we have to meet standards set not by the boards, but by our international competitors.
We propose that a self selecting cohort of pupils 14+ should be able to pursue a higher level maths course than the present GCSE-A-level one. The new course, suitably christened and administered by one authority only, would essentially follow the O and A-level syllabuses set by UCLES for Singapore.
Perhaps 3-4% of the age-group would take the course, but this would more than provide the nation with all the professional engineers and scientists it needs. It would also serve to pull up the maths standards for the rest of the population. As an incentive for pupils to take the more demanding maths course, and for schools to teach it, we propose that students passing the course should be able to go into the second year of the new four-year courses in science or engineering and the grades would count double for the school league tables. The taxpayer would be saved about £10,000 per student thereby. There is no need for any more enquiries, or long-winded committees agonising over nuances of syllabuses: they are there – ready and paid for.
18 August 1996
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