The debate on A-level standards is riddled with dilemmas and contradictions. It is the point of confluence between the bottom-up and top-down approaches to curriculum and assessment design. And confluences can be turbulent events. We have a national curriculum, with its associated assessment arrangements, designed as an entitlement for all, meeting with an assessment regime designed for university entrance for some.
We have diversity in the post-16 intentions of learners. Some wish to extend their mathematical tool kit, or pursue lines of interest, and assure a general preparation for higher education. Others wish to pursue an in-depth study of a particular subject area and prepare for higher education in specific subjects, including maths. In short, there is a need to accommodate the mathematical needs of the majority with the mathematical needs of the minority. We encourage more students to study maths post-16, while encountering increasingly acute teacher supply difficulties. We are trapped by an English approach, characterised by:
* the idea that however complex the problem, there exists a single solution
* an assumption that things were better in the past
* the construction of jargons which allow exclusive groups to argue over such issues as the relative merits of accessibility and facility of questions
* a barricade approach to open discussion between mathematicians and maths educators - derived from the single solution standpoint
* political correctness fears about admitting differential provision patterns to meet differential needs, albeit in a framework of equal opportunity P> * the notion that "value" is determined by scarcity: the more people who have something the less its value.
It is time to move the thinking on from an "either ... or" consideration to a "both ... and" consideration. Surely, this is at the heart of "inclusion" thinking.
All students are entitled to continue their study of maths post-16, but there will be differences in the balance between breadth and depth. There will also be differences in areas of application and modelling. Determining this complex pattern of provision requires and deserves extensive debate and proper trialling. What a novelty it would be to have a curriculum and assessment structure based on evidence rather than dogma.
The reality is that pupils are entering secondary school with more confidence in basic numeracy skills. More pupils in secondary schools are displaying positive attitudes to maths. We owe it to these pupils to provide opportunities post-16 to continue with their maths. Calls to make A-level maths harder add little value to the debate. It is already harder than most subjects.
The focus of Government attention should shift towards issues of teacher supply, assessing the impact of changing funding arrangements on school sixth forms, and opening a proper enquiry on GCSE and GCE A-level exams in maths. The alternative is bleak: skill levels of the majority will remain unrealised and the supply of home-grown mathematicians will continue to dwindle.
Peter Lacey is chair of the general council of the Association of Teachers of Mathematics and deputy director of education in north-east Lincolnshire