THE A-LEVEL STRUCTURE

We referred in Section 8 to a `relaxation' of standards and to attempts to make mathematics more `accessible'. We also pointed out in Sections 6 and 7 how mathematics at A-level is no longer attracting the same percentage of those with high grades in mathematics at GCSE. Are these two facts connected? Are the needs of the mathematical high-flyers being met as well as they were in the past? If not, how can the situation be improved?

Though the problems have their roots in pupils' experience of mathematics at age 5--16, many argue that the inflexibility of the A-level structure presents additional problems at the 16-19 stage. If we adopt the assumptions of the 1988 TGAT `levels' model, then an A* student at GCSE would be four or five years in advance of a Grade C student in terms of mathematical knowledge and attainment. Yet both are expected to be examined on the same A-level papers only two years later. (We have remarked in Section 9 on the likely consequences for the student with a Grade C.) Hence, in addition to the need to revise the 5--16 mathematics structure, there is also a need for more flexible 16--19 courses with time allocations and subsequent qualifications geared more to specific needs, and ensuring adequate differentiation.

Traditionally the double subject qualification (in mathematics and further mathematics, or in pure mathematics and applied mathematics) provided a challenging goal for the mathematical high-attainer. As noted in Section 5, the number of candidates has dropped considerably in recent years; in addition, the current funding policies of government and its agencies now make this qualification a far from attractive option for schools and sixth form colleges. In 1965 over one third of all mathematics A-level candidates attempted double subject mathematics; by 1994 the corresponding figure was about 10% . There are signs that the flexibility of modular schemes may bring with them some improvement in the position (mainly because students can now take `one-and-a-half' mathematics A-levels, leading to both an A and an AS qualification --- a welcome, but unplanned spin-off of the introduction of AS-levels

We recall that there have been many previous proposals for changes at this level. Dainton (1968) [5] recommended a revised sixth form curriculum which would provide students with a more broadly-based education that could still contain, as a significant part, a coherent mathematics and science component; Higginson (1988) [13] called for slightly different changes; more recently, the Royal Society (e.g. 1991) [25] has echoed the demands of Dainton. These proposals deserve renewed consideration. The position relating to science and technology has, by most measures, deteriorated since Dainton's day. As was indicated in Section 10, we can no longer claim that our A-level mathematics students begin university better prepared than their peers in countries in which students follow more broadly-based courses.

We welcome the commitment in .5 of the Interim Report of the current review of the 16--19 qualifications (Dearing (1995) [7]) that specific attention will be paid to the particular problems encountered in mathematics (see also Section 13). However, consultations will need to be carried out in an open and collaborative fashion. Moreover, while we acknowledge the need for a review of provision at the 16--19 level, such changes must not preempt a revision of the mathematics curriculum for ages 5--16. We need to work towards a position in which the foundation laid at 5--16 allows for a range of provision at 16--19 comparable with that in other EU countries.