Testing, testing;Subject of the week;Maths
The Government has decreed changes to mathematics in the national curriculum and at A-level. But instead of improving the teaching of mathematics, these changes will further disadvantage children learning mathematics in secondary schools.
For most students, GCSE mathematics is an endless sequence of memorising - and then forgetting - facts and procedures that make little sense to them. Although the same topics are taught and retaught year after year, the students do not necessarily learn them.
Unfortunately, the national curriculum proposals to divide GCSE into two tiers - foundation and higher - will repeat this vicious trend. Essentially, students who fail at key stage 3 will retake the same course at key stage 4. And if every examination board offers six-module A-level programmes, the "teach-test" philosophy of education will overshadow an approach towards thinking and reasoning.
Teachers and examiners have tried to contribute to discussions of change but this summer's national curriculum consultation was not encouraging. It seemed, once again, the Government preferred not to ask the educational community for its opinion of the actual curriculum, instead posing rather banal general questions which did not foster a wider debate. Can we assume that the Secretary of State believes that this time we have a "perfect" curriculum?
So where are we going? Pupils have the same potential to do as well in mathematics as at any time in history. At least 20 per cent are able to achieve the same breadth and depth of mathematics as 10, 20, or 30 years ago. We also have a well-trained teaching force capable of delivering such mathematics. Why then does the subject seem to be heading for the rocks?
I often meet parents of children who are bored with mathematics at key stage 4 because they feel they are being held back. Some of these children attend the Masterclass programme at venues around the country, including the University of Plymouth, and show considerable ability at going beyond their school mathematics. But it appears that schools are artificially holding back these talented young mathematicians.
Most large comprehensive schools will probably have about 30 children capable of achieving good grades at GCSE - and starting their advanced mathematics programmes - at least a year early. Yet they hold them back. Of course, early GCSEs do not show in the league tables.
Schools should be setting stretching, but realistic, targets for pupils to enrich mathematics up to and beyond GCSE.
Nearly every pupil enters secondary school mathematically healthy and enjoys the way they solve problems in methods that make sense to them. But most leave apprehensive and unsure about doing all but the most trivial of mathematical tasks.
In its submission to the consultation process, the Mathematical Association pointed out that the new key stage 3 and key stage 4 proposals of splitting the content instead of presenting a single core with extension material for more able pupils will aggravate the situation. Alternative approaches, often drawn from vocational aspects, for pupils who are likely to achieve below grade C in GCSE, will also find no place.
In common with every teacher, the Secretary of State is justifiably concerned about a national curriculum which is "failing to engage a significant minority of 14- to 16-year-olds, who were as a consequence becoming disaffected with learning". Mathematics has a very large "minority" of students who are disaffected and the solution is far from obvious.
The problem will be exacerbated if we go on with a key stage 4 study programme which is almost identical to that proposed for key stage 3, apart from a few modified statements and examples.
Such a repetition seems to imply that pupils would not have been successful at key stage 3 and does not provide any possibility for new ideas.
For those pupils who will achieve grade C and above in GCSE, separating the programmes of the two key stages also reduces the flexibility for teachers to meet their needs. For example, trigonometry does not appear until key stage 4, although there is an obvious value in able pupils encountering the topic earlier.
A single programme of study across both key stages would give teachers greater flexibility in developing their programmes for the "significant minority". Examples recognising and encouraging a variety of methods, including those related to real-life contexts for less-able pupils, would be appropriate.
On top of this, the oft-quoted "gold standard" of A-level now faces terminal decline with the new modular system of provision. The prevailing view is that mathematics is a set of procedures and that teaching means telling students how to perform those procedures. Teachers end up teaching "mindless mimicry" mathematics.
Splitting the A-level into small bites of single-term modules encourages the narrow "teach-test" philosophy, robbing students of the richness and opportunities that can be found in the subject.
At Plymouth we can spot those in the current intake of undergraduates who have studied a six-module A-level compared with other syllabuses. Generally, they are not capable of beginning a problem without structure and signposts. A-levels such as these undermine the preparedness of students for any course in higher education that requires mathematics.
As a subject, mathematics is first and foremost a form of reasoning and those who choose to study it beyond GCSE should be given opportunities to develop reasoning skills. External assessment every six months during a two-year course only goes to undermine these skills.
There is, however, a "gold standard" that would benefit students beyond GCSE, that develops depth and breadth and is suited to the needs of different pupils.
Schools with aspirations for their school-leavers should investigate the International Baccalaureate (IB). There are two main courses: one aimed at the continuation of mathematics for students who will move into science, engineering and mathematics in higher education and one for those aiming towards subjects such as economics, social sciences and business studies.
But how can such a programme continue at a "gold standard"? Perhaps because the politicians have not interfered and forced their narrow dogmatic views on to the curriculum.
John Berry is professor of mathematics education at the University of Plymouth and president of the Mathematical Association. He is writing here in a personal capacity