Many students find A-level maths difficult but others find it straightforward. It was therefore recognised right from the start that two qualifications are required, standard A-level maths as a general qualification and A-level further maths, targeted at more able students and those intending to study degrees with a strong mathematical content, such as engineering, sciences, computing and maths itself.
But the high cost of small classes and a shortage of skilled staff have resulted in many sixth-forms no longer offering further maths. Student numbers have fallen from around 15,000 in 1980 to about 6,000 now, and many are unable to fulfil their potential. This means universities cannot specify further maths as an entry requirement, despite their concerns at the lack of mathematical knowledge and fluency among students with the single A-level. The QCA has sought to address this problem as part of the GCE maths reforms. From September 2004, ASA further maths qualifications are changing. These changes should improve access to further maths dramatically.
Currently, AS further maths may include only one AS-level unit. The other two units must be A2. In addition, it must include an A2 further pure maths unit which assumes knowledge of pure maths from the second year of the A-level maths course. The current AS further maths is thus more difficult than any other AS-level and is seen as a qualification for the elite only.
Further maths, with its dependence on A-level maths, has also been difficult to timetable, making it is awkward to teach the two in parallel.
The September changes introduce a new-style AS further maths, consisting of a compulsory "further pure 1" unit, designed to be taught alongside the maths core, and two other units, which may also be of AS standard. This will make AS further maths a true AS-level. Timetabling problems will be greatly reduced because it will be natural for further maths students to be taught ASA maths in the same classes as students not taking further maths.
Studying further maths boosts students' performance in A-level simply because they do more maths. And since the new further pure 1 unit introduces fundamental topics not included in A-level maths, such as complex numbers and matrices, it will give students a better base for degree studies.
The new AS further maths is a broadening qualification, useful to all who intend to study for a degree with a strong maths content. The full A-level further maths is deepening - crucial for the most able students - and broadening.
Last summer 38.9 per cent of students completing A-level maths achieved grade A, despite the fact that the ASA level course has one of the highest failure and drop-out rates. With such a high proportion achieving the top grade in the subject, it is vital that the most able can access a more demanding qualification, to stretch and inspire them.
The bad news is that some awarding bodies have shunned the opportunity to offer the new qualifications. Fortunately, two of the three English awarding bodies will be offering them and it is possible to do standard maths with one awarding body and further maths with another.
The changes mean that, from September this year, there will be no excuse for any school or college not to offer ASA further maths, taught either in-house or via distance-learning or local consortium arrangements such as the Gatsby-funded MEI Enabling Access to Further Maths project.
Once further maths is again widely available, universities will be able to specify it in their offers. Then we will see a real increase in the standard of post-16 maths education.
Charlie Stripp is further maths project co-ordinator for Mathematics in Education and Industry, and chair of the Mathematical Association's teaching committee