Maths must end in tiers

Ron Allpress says maths is crying out for change.

Given the limits on the number of A-level syllabuses examination boards can provide, it is little surprise they are likely to offer only modular courses. Allowed to sell only two products, each board will choose those that maximise its market share. In fact the growth in popularity of modular maths and the decline in the number of A-level candidates choosing terminally examined syllabuses would seem to make the boards' choice of two modular syllabuses inevitable.

The style of examination, though, is too important to be left to market forces. Many teachers have resisted the drift to "easier" modular courses because they believe the integrity and coherence of mathematics courses are worth preserving and the assessment scheme should reflect this.

A group of such teachers has already devised a structured tier of syllabuses with related terminal examination papers that cater for the full range of abilities, covering the range from AS Mathematics to A-level Further Mathematics.

Anne Kitchen (The TES March 7, 1997) finds Colin Goldsmith's appeal (The TES, February 14, 1997) for tiered papers unhelpful, but this terminal-assessment model is a viable alternative to a modular scheme and has none of the disadvantages of traditional or modular examinations. By using tiered papers targeted at certain grades, examination boards can judge students' abilities, but without having some candidates miss out the difficult parts of questions, as often happens with modular papers. The number of students of all abilities choosing the (tiered) Oxford and Cambridge maths A-level is rising and we have no difficulty motivating and retaining our students.

In terms of teaching and administration, the scheme is a delight. It preserves the unity of the subject. It is an integrated course covering both main applications (statistics and mechanics). But the examination allows a candidate to achieve a grade A without necessarily having to answer questions on both.

Decisions about the level of entry can be deferred, and timetabling constraints are fewer than with a modular course. The cost to schools is a fraction of adopting a modular scheme. Regular internal progress tests are much less disruptive than module examinations.

Deferring assessment until the end of the course makes sense. By this time candidates should have the maturity and confidence to answer questions of interrelated components of the course. It is important that some of the new schemes of assessment are of this type. Entering candidates for a modular examination at the end of the course is not what is wanted.

Market forces alone are unlikely to preserve the required diversity in the form of assessment, but two changes in the School Curriculum Assessment Authority's rules would ensure this. First SCAA could seize the initiative by instructing at least one board to prepare such a scheme for its approval, with other boards later being required to make it available in addition to their own approved offerings (subject to some form of inter-board financial arrangement).

My second proposed change concerns SCAA's requirement that each A-level has a non-calculator paper (which will also apply to further maths). This will have a much more restrictive effect on a terminally examined maths assessment scheme than on a modular one. This requirement should be relaxed for traditional, non-modular schemes so that only a part of one of the papers has to be completed without a calculator. Adopting these simple suggestions would satisfy Education and Employment Secretary Gillian Shephard's promise that a non-modular exam would continue to be offered and allow all schools a real choice.

Ron Allpress is head of mathematics at Norwich High School

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