Enabling the most able
Recent events have highlighted the need for a national strategy for our brightest maths students. The National Numeracy and Literacy Strategies have been a response to the country's need for a higher minimum level of competence among its citizens. The Able Student strategy would address the country's need for a greater proportion of the population to have an advanced level of competence. At present, the national picture for able mathematicians is confused. While the Excellence in the Cities project is setting targets for early GCSE entry, the call for greater breadth at A-level may be reducing the number opting for Further Mathematics.
A national maths strategy for able students must address all ages and operate through normal classroom lessons, as enrichment activities only cater for a minority for a limited time. Masterclasses, maths challenges and the Cognitive Acceleration in Mathematics Education project demonstrate that many students can think more deeply, but early entry for examinations is not the answer. The Mathematical Association wants able students to cover topics in greater depth, aiming for complete mastery. They should be learning level 8 material in Year 9, covering the full GCSE higher syllabus by Year 11 and continuing maths in the sixth form. Those considering degree courses in numerate disciplines (like physics, engineering, maths and statistics) should be urged to take Further Maths.
The Institute of Education has recently reported on a "vicious circle" in maths teaching. Because too few take A-level, the pool of suitably qualified mathematicians is too small and, in any case, most are snapped up by business and industry. As a consequence, schools are forced to use teachers whose understanding of maths is limited. This results in some uninspiring teaching, which turns students off the subject, thereby reducing the pool still further. To break this circle we must convince our most able school students that maths is an exciting subject, worthy of study in the sixth form. Unfortunately, there are signs that the changes to key stage 3 and A-levels could have the opposite effect.
Regarding KS3, Anita Straker of the National Numeracy Stategy told the MA:
"Our first priority must be to secure higher standards of mathematics for the 85 per cent of pupils who at present achieve level 6 at best."
The MA fully supports the numeracy strategy's intention of raising standards, but we want this to apply to able students too. After all, these are the students we want to attract into maths teaching. Unfortunately the QCA has removed level 8 from KS3 and the Department for Education and Employment is insisting on using the term "Year 9 framework" for level 56 work aimed at average students. This gives the impression that topics such as Pythagoras and trigonometry are somehow "optional", despite Ms Straker's recognition that they are core material for the more able Year 9 pupils who will progress to higher level GCSE and A-levels.
Ideally, the vast majority of sixth-form students would take at least AS maths, yet many will have heard that the QCA has reduced the content of all AS subjects except maths. When I tackled Nick Tate, former chief executive of the QCA, he conceded: "I do not consider that A-level mathematics should be any harder than other A-levels", but said that the QCA had been swayed by university complaints and a report that AS maths was "too easy". Maths exams that are fair to weaker students do give "easy" A grades to able candidates.
The best solution for universities is to require able students to take Further Maths, which provides the wider coverage and deeper understanding that their "numerate" departments want.
In the meantime the DFEE should be promoting AS and A-level maths strongly to potential sixth-formers and countering the impression that it is a hard subject. The MA wants a wide-ranging review of the provision for able students, leading to a national strategy for the top 20 per cent. This should cover content, teaching approaches, expected progress, assessment and professional development needs. The strategy should advise on when (if ever) to accelerate students, the respective roles of A-level Maths and Further Maths, and the maths needed for various degree courses. We need to raise our game now. Our able students deserve a fair deal.
Steve Abbott is president of the Mathematical Association, 259 London Road, Leicester LE2 3BE. Tel: 0116 221 0013. Web: www.m-a.org.uk