INTERNATIONAL COMPARISONS

One way of highlighting possible weaknesses in our current systems is to ask how our students, our curricula, our assessment procedures, and the support we give to our teachers compare with those in other countries --- especially other European ones. It was disappointing, therefore, that the DfE (1994) [8] report included no comparative data. Again, comparisons will centre on two issues: quantity (the percentage of students opting for mathematical studies once it is no longer compulsory) and quality.

Considerable attention has been paid to quality in numerous international studies (e.g. Robitaille and Garden (1989) [24], IAEP (1989) [15], Prais (1994) [23]) and the messages are consistently discouraging: pre-16 we lag behind many European and Asian countries. One apparent success is reported in Fitz-Gibbon and Vincent (1994) [10]: ``in international comparisons ... [England's] mathematics achievement at A-level was ahead of most countries''. However, this was based on a misconception, since it failed to note that what were compared were the average marks of all 17 year-olds specialising in mathematics --- and that, among the countries surveyed, England and Hong Kong had the smallest percentages of the age cohort doing this. When the marks of the top 1% or the top 5% were compared, England sank to its usual middle-of-the-table position (Robitaille and Garden (1989) [24] p.151, McKnight et al (1987) [19] p.26). Regrettably, England is not taking part in that section of the current Third International Study which is comparing the attainments of 17 year-olds specialising in mathematics and which is also studying general numeracy amongst all 17 year-olds.

The failure over the last decade and more to expand significantly the percentage of 16--19 year-olds opting to study mathematics is a serious one. To argue, as in DfE (1994) [8], that A-level mathematics is, by its nature, only suitable for a select few ignores the fact that in England we are now recruiting A-level mathematics students from a broader intellectual range than formerly (and that A-level mathematics entries almost trebled in the decade 1955-1965). Such a view also ignores experiences elsewhere. In Metropolitan France, for example, the number of students obtaining the Series C Mathematics and Physical Sciences Baccalauréat has mushroomed from 21,443 in 1970 to 66,438 in 1993. (In the same period, the numbers admitted to all sections of the Arts Baccalauréat increased only from 64,502 to 74,431 - a striking contrast with changes in numbers at A-level). The data for the 1994 Baccalauréat were:

(Other streams lay less emphasis on mathematics)

(Regarding hours per week, it should be noted (see, e.g. (Dearing (1995) [7]) that French students have considerably more time-tabled hours per week than do English and Welsh sixth-formers.)

If we compare these figures with those for A-level mathematics in 1994 --- roughly, 57,000 attempted `single-subject' A-level (4--5 hours per week in Years 12 and 13) of whom 5,400 took `double subject' (about 9 hours per week) --- the contrast in the figures, as well as in the changes since 1970, is quite stark.

The working group was also able to study examination papers from elsewhere in the EU. These indicated, for example, that in one country 20% of the 18 year-old age cohort were studying integral calculus at a standard comparable with that of A-level as opposed to about 7% in England and Wales (Dearing (1995) [7]).

Many countries are concerned about recruitment to science and to mathematics undergraduate courses. However, it would appear that the important aim of sending mathematically competent students to university to study quantitative subjects is being more satisfactorily met elsewhere than it is in the UK.

It is essential that our national aims and objectives for education in mathematics should take full account of what is being achieved in other countries.