With its real and rightful concern to raise standards and to ensure that able pupils are stimulated and challenged, the Government, through its gifted and talented policies, is encouraging schools to enter more pupils early for GCSE. This is backed up by targets for schools within the Excellence in Cities programme and encouraged by recent widely reported remarks by David Hargreaves, the departing head of the Qualifications and Curriculum Authority, on the 14 to 19 curriculum.
Mathematics is in the unfortunate position of being in the front line of these initiatives because it has traditionally been a subject where some pupils have taken public examinations a year early. This policy is only practicable in schools where a full class can be entered early and, most importantly, where proper provision can be made for further study of maths in Year 11.
Able pupils need to become fluent with number and algebra, to acquire deep understanding of key mathematical ideas and, above all else, to learn to think for themselves through the frequent challenge of problem solving without detailed step-by-step instructions. The pressure for measurable results, which lies behind the early GCSE policy, will lead to a yet narrower focus on test requirements, which place a high premium on remembered routines and offer pupils little opportunity to solve demanding problems based on the same content. Neglecting wider aims damages pupils’ attitudes and their long-term learning.
The early entry policy is proceeding despite unanimous expert opinion across the often divided world of mathematicians, maths educators and experienced teachers. It is incredible that the very serious problems for maths, and other subjects, caused recently by Curriculum 2000, have not made policy-makers proceed with much greater caution by giving more forethought to the possible consequences of policy changes.
This is all part of the folly of giving excessive emphasis to testing. As a teacher trainer, I find that secondary PGCE maths students are often weak at solving elementary mathematical problems. Their experience of maths at school was invariably a matter of remembering routines, without the challenge of real problems to solve.
Teachers understandably do not emphasise such crucial things when all the pressures are on a short-term goal, important though GCSE may be when kept in proper perspective.
The key stage 3 national strategy is having some very beneficial effects on the teaching of maths, but its long-term effects on pupils’ attitudes and learning will be undermined if the demand for early success in exams is not abated.
Many teachers have a wealth of experience in working with able pupils. Initiatives which run counter to their wisdom and experience lead to frustration and disillusion. Acceleration through early GCSE entry is not the answer.
Getting maths “out of the way” early is not appropriate for the vast majority of able pupils, because it gives the impression that maths is something to be done and dispensed with rather than explored deeply for the challenges to curiosity and creative thinking that it offers.
Able pupils, and indeed all pupils, need more encouragement to think hard and make better sense of what they are learning, rather than more and more content.
It would make much better sense to recast or extend GCSE, and also the tests at KS2 and 3, so that there is a much stronger problem-solving element and questions which assess deeper understanding without adding extra content. This would be a much more manageable option whereby all schools could provide for their able pupils.
Doug French is a lecturer in education at the University of Hull and is chair of the Mathematical Association’s Teaching Committee. E-mail: d.w.french@hull.ac.uk
