A maths problem solved

Are the poor mathematical skills of students entering university the result of progressive teaching methods at school? No, says Ann Kitchen
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There seems to be a widespread view among the university fraternity that the standard of A-level mathematics has dropped over the past 15 years. This has led to a call for the return to the standard and style of teaching that was common in the early Eighties. No time or effort has been put into seeing whether the facts support the suppositions. Research suggests that, contrary to perceived wisdom, traditional methods of teaching are not as successful as many of the more progressive methods at GCSE.

This may well be true at A-level as well.

There are three major reasons for the fact that the mathematical background of students entering universities to study mathematics, physics and engineering is often inadequate. They are:

The significant proportion of students who are accepted with either low A-level grades or no A-levels at all.

The drop in the number of students who study double mathematics or further mathematics at A-level and therefore, in effect, have had four years of mathematics in the sixth form as opposed to two.

The pure mathematics syllabus content common to all mathematics A-levels has fallen from 40 per cent to 30 per cent, and hence there is a wider variability in the knowledge base of their students.

The Universities and Colleges Admission Service statistics are very revealing. Only 38 per cent of entrants with double mathematics at A-level chose to study degree courses in mathematics, physics or engineering in 1995. Of these, 7 per cent went into mathematically related subjects such as computing but the rest, 55 per cent, went into other science or non-science subjects and 11 per cent went into medicine or medically related subjects.

Looking at the figures for engineering we see that a staggering 10,413 students, or 59 per cent of all engineering entrants, did not have a qualification in A-level mathematics.

What did they have? Some 2,299 students had A-levels other than mathematics. They may have studied for mathematics but failed, or not studied A-level mathematics at all. A further 3,679 had BTEC or GNVQ qualifications, 1,546 had Scottish Highers, 450 came via access courses, 1,432 had other qualifications and 1,017 were listed as "none" or "unidentified".

Of all these qualifications, most would agree that an A or B at mathematics A-level was more demanding mathematically. Most school teachers I have spoken to would accept that an A or B at single mathematics or any double mathematics award would be a reasonable qualification for a mathematically related degree. Looking at the figures it is clear that only 24 per cent of the engineering students accepted fell into this category.

It is plain, therefore, that any shortcomings in undergraduates may well be due not to falling standards in A-level mathematics, but rather to a lowering of entry requirements by the universities and shortcomings in the other qualifications accepted.

Why has this occurred? First, the numbers of students taking double mathematics A-level is almost half that of 15 years ago, although it is now beginning to rise again with the introduction of AS-level, the so called half-A-level, in further mathematics. Yet the numbers admitted to university maths degrees has risen over the same period from 2,800 to 3,585.

How has this affected the level of knowledge of the entrants to a mathematics degree course? In 1995, 15 per cent of those doing double mathematics went on to read mathematics at university. If we assume that around the same proportion of double mathematics students went on to read mathematics in previous years, then 64 per cent of entrants to mathematics degrees had double mathematics in 1985, as opposed to 38 per cent in 1995. In addition, a B grade at A-level in single mathematics was the absolute minimum in 1985, and most had more. As a teacher at that time, I can't recall a single student being admitted to read mathematics with less than a B.

What has caused this drop in students studying for two mathematics A- levels? Most students are now encouraged to widen their choice of studies at A-level. This has had a great effect on their choices. While in 1985, 28.8 per cent of students chose only mathematics and/or science subjects at A-level, by 1995 this figure had dropped to only 16.6 per cent.

Another major cause is financial. With fewer students choosing to specialise, further mathematics is often not a viable subject for schools. Very few schools can afford to run groups of less than 10.

One way forward is certainly to increase the common maths core at A-level. The present compulsory pure core is 30 per cent of the A-level. I see no reason why 50 per cent of the content should not be pure maths and common to all A-levels. This mark should be reported separately. If the content of the other 50 per cent of the A-level is to vary, then I think it only right that the universities should know how well students perform on the content that they will take as the base for all students.

My major worry is that all the criticism from the universities will make well-qualified students feel that they would be better off choosing a non-mathematical subject to study.

Making A-level mathematics harder is certainly not the way forward. We have just started to increase the numbers taking mathematics at A-level. The students we get are well motivated and enjoy the subject. However, students go into the sixth form realising that their point score is all important for successful entry to university, and if it were seen to be much harder to get a good grade in mathematics than in most other subjects, the numbers studying it would plummet.

Universities must appraise the other qualifications that lead into university and not blame everything on A-levels. More guidance on what is expected from our students must be given. A clear specification of the content that is expected as basic knowledge for all entrants to a mathematics degree would leave the students able to decide whether they fulfilled those requirements n

The writer is a research fellow at the Centre for Mathematics Education, University of Manchester.