CONCERNS ABOUT NUMBERS

Funding mechanisms now encourage HE institutions at 18+, and schools and colleges at 16--19, to `fill places' in numerate disciplines as best they can. Though numbers have increased, there are nevertheless clear grounds for concern at the number of adequately prepared students taking courses in mathematics at 16-19, and the number of suitably qualified applicants wishing to specialise in mathematics, science or engineering at 18+.

We recognise that such concerns are not new: the ``relative decline in [the number of students undertaking] the study of science and technology'' was explicitly addressed in Dainton (1968) [5]. When considering the nature of our present difficulties at 16--19 and at 18+, it is important to understand some of the changes that have occurred within the English and Welsh educational systems since the Dainton committee began its work in 1965. This section highlights some of the more dramatic changes.

In the thirty years since 1965 the country's educational systems have been extensively reorganised, and the school-leaving age has been raised to 16. In 1995 most 11-16 year old students attend comprehensive schools, and a much larger proportion of the age cohort (72% according to some estimates) now continues in full-time education beyond the age of 16.

Since 1965 the total number of A-levels taken each year has doubled, but this increase is far from uniform. For example, the number of students entering for physics A-level fell by almost a fifth between 1965 and 1995. Part of this drop in numbers may be attributable to demographic trends. However, it is easy to misinterpret this crude statistic. For example, the demographic change among the social groups providing the bulk of undergraduates has been relatively modest. Moreover, as the number of students staying on after the age of 16 has expanded, some subjects have apparently flourished. For example, over the period of demographic decline since 1965, numbers taking English A-level have more than doubled.

The changes over the same period in numbers taking mathematics A-level have been both more modest and more complicated. Appendix C shows an increase of one third in single mathematics entries (with a corresponding two thirds increase in single mathematics passes), and a two thirds decline in double mathematics entries. Overall there has been a significant increase in participation since 1965; but there has also been a substantial reduction in the number who study the subject in greater depth. More serious is the fact that, in the last decade, there has been a dramatic decline on both fronts (see Appendix D). The sequence of expansion followed by decline means that, when compared with 1965, the number of male A-level mathematics entries is now no different from what it was; any growth can be attributed to the welcome increase in the number of female candidates from 6,400 in 1965 to 20,400 in 1995 (see also DfE (1994) [8]).

One change which deserves more serious attention is the dramatic trend away from students combining mathematics and science A-levels as constituents of a coherent course of study leading to higher level courses in engineering, science and technology. In 1965 38% of A-level students studied only science and mathematics; in 1993 the percentage had dropped to 16%. (Indeed, DFEE data suggest that in 1994 less than 9% of 17 year-old A-level students studied only science and mathematics.) This change has profound implications.

Increasing numbers of students choose, and are often encouraged to choose, a `more balanced' A-level course, including subjects drawn from both sides of the Arts-Science divide: 14% in 1965, 40% in 1991. This desire to seek a broadly based education creates severe problems when most students take only two or three main subjects. For example, the mutual support which mathematics and physics traditionally provided for each other can no longer be assumed. Moreover, where able students taking a fourth A-level used to take further mathematics, they are now often required to take general studies. The position has recently been further exacerbated in sixth form colleges by the funding policies of the FEFC. As a result of these various pressures, many students are effectively dissuaded from taking a second mathematics A-level (the number doing so has decreased by over 60% since 1965).

One significant change to patterns of university entrance since 1965 is the marked increase in the percentage of entrants who do not come straight from school, or who have qualifications other than A-levels. The number of such students entering degrees in mathematics and physics may still be small; but the number of `non A-level' students entering engineering courses has increased substantially. Teaching mathematics to such students has created additional serious problems, which have mostly been tackled ad hoc.

We shall refer to these changes again in Section 12. Meanwhile, we shall concentrate our attention on concerns affecting A-level, starting with the mathematical preparation underpinning A-level mathematics courses.