Myth of a golden age
This summer, GCSE candidates were asked to take part of their maths exam without the aid of a calculator. This change was part of the QCA's new policy on calculators, with no-calculator papers at key stage 3 and part of A-level restricted to scientific calculators only.
Students almost always suffer at times of change; the weaker ones usually come off worse. This particular cohort will have some reason to feel like guinea pigs. They were among the first to take KS2 SATs and some of them are also the first to take the new sixth-form curriculum, which began this month, leading to new A-levels in two years' time.
What are the effects of this new requirement? Examiners report that it made little difference to higher-tier candidates. There could be several reasons for this: these candidates are generally more competent and so on the whole can do the sums; the number section of the syllabus is lightly weighted in the higher-tier exam at 17 per cent; and this tier is more about ideas (like knowing that 6413 is the cube root of 64) and less about calculations.
In the intermediate and foundation exams, though, there is greater weighting for number (25 per cent and 33 per cent respectively) and the syllabus emphasis is more on routine calculations. Evidence from the scripts suggests that the weaker intermediate students found the non-calculator paper harder. They scored lower marks than in the paper where they used calculators. They knew what they wanted to do but were unable to do it; often in a percentage calculation the right numbers would be on the top and bottom but somehow the wrong answer would emerge.
Foundation students encountered similar problems but the effect was less marked; for many the difficulty lay further back within the questions, in knowing what to do in the first place, such as whether to add or to multiply in a given situation.
Given that many students find maths difficult, penalising weaker students seems a worrying outcome. It might perhaps prompt policy-makers to think closely about their aim. Is it to foster a sensible balance between the use of brain and button, to encourage students to recognise that it is much easier to do some calculations mentally than to go to the trouble of taking out a calculator? Or is it an attempt to return to some golden age of numerical competence?
Many people nterested in maths would support the former aim. Yet this year's GCSE exam was at odds with it. GCSE papers are very tightly regulated by having to meet the requirements of a document called Targets and Tariffs (originated by QCA). Worryingly, no changes were made to this before the introduction of the no-calculator papers. Calculations on the no-calculator paper ought logically to be restricted to those that would be better done mentally. Yet this year's papers were effectively the same papers as the year before: they were actually calculator papers to be taken without a calculator. Where the non-calculator method is more difficult or time-consuming, or a question requires repetitive calculations, candidates now have to work harder for the same marks.
This would seem to point to an intention to discipline students into being fluent at all calculations, whether or not they are better done on a calculator. Such ideas were current two or three years ago when, for example, it was planned to ban calculators completely from a significant part of A-level maths.
There never was a golden age when children got their sums right. Report after report, stretching back well over 100 years, bemoans the level of arithmetic in our schools. When I started teaching, calculators had not been invented and students spent forever getting their sums wrong using logarithms; to our exasperation, they would even use them to do things like 2 multiplied by 3 and 90 divided by 10.
The situation will be quite different for GCSE candidates as the National Numeracy Strategy takes effect. The difference is not that they will have had calculators banned (which they will not) but that all the way through their school career they will have been exposed to mental arithmetic and, crucially, to mental strategies. It will in future, for example, be quite alien to numeracy strategy students to use their calculators to find the cost of three CDs at pound;14.99 each. They will know that it is easier to do 3xpound;15 and then take away 3x1p.
However, the skills that this new generation of students are acquiring are not quite the same as those tested in the present non-calculator papers. This is the time to identify these skills. Exam boards need to start setting GCSE questions that reward them. As I believe QCA's maths team also holds this view, we can hope for new guidelines and more appropriate papers.
Roger Porkess is project leader for Mathematics in Education and Industry.