Constrained by rules
This September sees the start of new GCSE courses. Superficially, mathematics look much like its predecessors. Although the Qualifications and Curriculum Authority had considered moving from three tiers of entry to two, this proposal was rejected by Government. I am glad; too many students would have found themselves misfits, being forced to do work that they found either trivial or impossibly hard.
The impression of little change is, however, misleading. All the new GCSE specifications have the same content and it encapsulates a significant shift in emphasis. At each tier there is more formality and more algebra. Thus foundation tier students are now required to do simple algebraic factorisation, to solve linear inequalities and to be able to prove that the angle sum of a triangle is 180o.
There are similar changes in the other tiers. Higher tier students will now be required to solve simultaneous equations, one of which is non-linear, and to prove the circle theorems.
Let no one say that GCSE maths is getting easier. While we would all like to see students starting AS-level more fluent in algebra, I fear we may now be witnessing overkill. The examining principle "Do not look beyond a right answer" is being replaced by "All mistakes in algebra must be penalised". So imagine a question where the right answer is x2 + x; a candidate gets this but then goes on to write x3. Traditionally such a candidate would have been given full marks; now there will be a penalty. It is disturbing that a long-held principle can be abandoned so easily. I am not sure that it is for the good. I would prefer students to try to simplify algebraic expressions rather than to leave them unsimplified for fear of being penalised.
Another major area of change is in the statistics and here I think QCA is to be congratulated. The syllabus requirements are now embedded in the language of statistical investigations. Statistics is no longer described as a set of isolated techniques for summarising or displaying data; rather these are now the things you would dobecause you have carried out an investigation and need to analyse and report on your findings. As part of the same rethink, all students will be required to carry out a piece of statistics coursework. While welcoming this, I just hope that everyone concerned realise that it will take a lot of in-service training, as well as patient interaction between moderators and teachers, before the statistics in most students' coursework reaches a good standard. Inappropriate use of ICT must not be condoned.
There are also a number of new topics in the statistics: time series, moving averages, trend and seasonality; stem and leaf diagrams; box and whisker diagrams. However, standard deviation is no longer required so that students will meet this difficult concept for the first time at AS-level. The assessment requirements of all the new GCSE specifications include 20 per cent coursework, 10 per cent each for Using and Applying Mathematics and Data Handling. The coursework may be marked by a centre or board. The remaining 80 per cent of the assessment is by exam. QCA rules require that at least 50 per cent must be at the end, leaving 30 per cent that may be taken early. This has given rise to two patterns. In the linear specifications all the exams are taken at the end, typically two papers of 40 per cent each. In the modular specifications 30 per cent may be taken early, for example at the end of the first year (the pattern we have adopted for the MEI specification).
Syllabus developers were constrained by rules and as a direct consequence the new specifications cannot address either of the two major problems of the present GCSE. Foundation students will continue to be dubbed failures before they have even started, and Intermediate students will not reach the starting point for AS-level. We really needed a much more radical rethink, looking at the needs of students. I would have liked to see maths joining English and science as a double-subject GCSE, one for everyone and a second for the more talented.
Roger Porkess is project leader of the MEI (Mathematics in Education and Industry) and Industry syllabus examined by OCR