Before the mid-Eighties, our pupils took 0-grade courses at 16, at the end of S4 or Year 11 (secondary education starts at the end of Primary 7). The 0-grade courses were broadly similar to 0-levels in other parts of the UK. In maths, there was Mathematics, Arithmetic and also Statistics. Approximately 30-35 per cent of the year group sat 0-grade maths and 60-65 per cent sat arithmetic. Statistics was taken in some schools as an extra subject. So it was possible to find "mathematical pupils" collecting three 0-grades.
Then came Standard Grade. This was an extensive reform - and the effect on maths was dramatic. Away went Arithmetic, Statistics withered, and virtually everyone took standard grade Mathematics at one of its three levels (Foundation, General, Credit), a universality which is in contrast to GCSE.
It was not normal for pupils in S5 to try to improve on their standard grade performance and maths departments generally opted for "modules" for pupils who were not attempting higher maths. Modules are certificated by the Scottish Council for Vocational Education. They are internally assessed and in many cases pupils follow a pathway through resources with the teacher acting as a tutor - whole class teaching is not appropriate.
The higher grade course covers, in one year, basic post-16 maths; introductions to calculus and to vectors; more co-ordinate geometry; sequences via recurrence relations; trigonometry (angle formulae) and so on. The assessment is in two parts: an "investigation" (worth 10 per cent) and end of course exam papers - all handled by the Scottish Examination Board. After S5, our pupils can do more from the range of modules, repeat (or take for the first time) higher grade or, for those who have passed higher grade , there is a range of Certificate of Sixth Year Studies courses. There are five of these - General Mathematics, Pure Mathematics, Statistics, Numerical Analysis, Mechanics - and they can be taken more or less independently. Pupils who take two of these will have a qualification which is broadly equivalent to a single A-level in maths and some schools are able to offer pupils more than two.
From August 1998, this fairly complicated structure is to be replaced by a more integrated series of packages. The structure can be illustrated by outlining the format of the proposed higher grade course. The course content is to be split into three chunks, officially designated as "units". Each unit will be assessed internally and successful completion will be recorded on a student's certificate. So, in taking the course, a student will complete three units.
In order to assess an overall, graded award, there is to be an end of course exam which will result in grades A-E (A, B and C being passes). In the higher grade course, the first two units are to be compulsory but the third will allow a choice of either another unit of "mathematics" or a unit of statistics. A student who takes the three maths units and the exam will obtain a qualification identical to the present higher, just differently packaged.
For those not aspiring to higher grade, the existing SCOTVEC modules are to be realigned and converted into units. As with higher, three appropriate units will comprise a course. For S6 pupils, a similar structure is to be used with virtually all the existing CSYS material being incorporated into one unit or another. Three units will comprise a course and it will be possible for candidates to take two courses which will move their maths beyond the standard of a single A-level and approaching further mathematics in content and difficulty. As more than six units are on offer at this level, to be known as "advanced higher", it will be possible for a pupil to complete extra units on an internally assessed basis and have these recorded on their certificate.
Schools have already had an opportunity to comment on the framework. The consultation on the content of units and courses will begin in June. It is crucial that the opportunity to take part is used to the full. If it isn't, then schools and colleges may have to operate with a system that they may not feel a part of.
Bill Richardson is principal teacher of maths at Elgin Academy and president of the Mathematical Association