The report, Tackling the Mathematics Problem, written by leading maths dons has received wide attention. Like its authors, I desperately wish to see higher standards of mathematics in Britain and I do not believe we are doing as well as we could or should.
This report, which was commissioned by the London Mathematical Society and supported by the Institute of Mathematics and the Royal Statistical Society, can only make a limited contribution to improving the situation since its argument is occasionally flawed or based on incorrect data.
The report’s authors believe that new undergraduates are no longer as well prepared in mathematics as they used to be.
The evidence for this is anecdotal. There is nothing wrong with that, but it means that the comparison is being made over a reasonable memory span, say about l0 years. However, the discussion on A-level numbers uses 1965 as a base date. This use of inconsistent base dates hides what has actually been happening.
The number of students taking mathematics at A-level is similar now to what it was in 1965 (although the number of them taking further mathematics has fallen by about two-thirds). However, since 1965 the uptake of education post-16 and in higher education has substantially expanded. The numbers taking mathematics also rose in the 1960s and 1970s, reaching a peak in the early 1980s. Since then, they have been falling steadily, by 41 per cent since 1984, from roughly l00,000 to 60,000.
Consequently, universities have had to drop their entrance requirements in order to fill their places. Inevitably, the students coming to them are less well prepared in mathematics since many of them have lower grades.
Also, until recently almost all of those going on to read mathematics at university would have taken double A-levels in the subject. This is no longer the case. Not only have students done less mathematics, but their work has been at a less sophisticated level. Further mathematics has always been aimed at the best mathematicians, including those going on to university. By contrast, single-subject mathematics is aimed at a much broader range of students.
By choosing to compare present numbers with those of 30 years ago, the report’s authors have missed the point. There is a crisis in school mathematics: nowhere near enough students take the subject. We need to get numbers back up again and also encourage more of our best students to take further mathematics. The new modular A-levels do both.
The report expresses concern about the variability in students’ knowledge and attributes this to the number of syllabuses on offer. “The amount of material that is now common to all the boards has been reduced to the point where those in higher education can infer relatively little from the fact that a student has ‘mathematics’ A-level,” it says.
However, when you turn to the relevant table, you find it shows the non-core items in the pure mathematics parts of the various syllabuses. This is the 20 per cent of allowed variability.
No mention is made of the 80 per cent covering the core content, which is common to them all. Of the eight topics said to be missing from the compulsory part of our Mathematics in Education and Industry syllabus, four are actually required. Similar errors have been made in other syllabuses. When filled in correctly, the table shows a remarkable level of agreement on non-core topics.
The report goes on to claim that there are “obvious merits in cutting the number of different A-level syllabuses.” It is sad that the authors, who call for more emphasis on proof, should invoke such a false line of argument. Variability in students’ knowledge has less to do with the diversity of syllabuses on offer than with the general weakness of some students now being offered places.
The report emphasises the need for consultation. But it is clear that what the authors envisage is a one-way process in which universities tell schools what and how they should teach. That is a recipe for disaster. Whatever the imperfections in our school or university teaching, no improvements will be made without involving those doing the job in any proposed changes.
The report is diminished by a lack of consultation with those providing school syllabuses and those delivering them. It is essentially a wish-list from a group of university mathematicians.
Should it be taken seriously? The imprimatur of three learned societies means that action on the report is likely, and for that reason it is important that its limitations are understood.
On the other hand, much of it is valuable and well argued. The concerns of its authors are strongly felt. That does not, however, mean that their recommendations improve the situation. (My view is that some of them would have the opposite effect.) It would be wrong to take action on the basis of such a limited analysis.
By far the best outcome would be to take up the report’s suggestion that there should be a committee of inquiry. This would allow mature consideration of the issues, and for the views of teachers to be given proper weight.
Roger Porkess is project leader, Mathematics in Education and Industry, the Centre for Teaching Mathematics, University of Plymouth.
