In retrospect, it should have been easy to forecast the disastrous slump in the numbers of candidates taking GCE Mathematics examinations in June. It started the year before when 29% of the AS entries in June 2001 failed to achieve a useful grade leaving them with nothing to carry forward. This figure was double the average ‘failure’ rate for AS Level as a whole. The consequence was that thousands of candidates went for a new set of options and the entry for the full A Level examination slumped from around 66,000 to under 54,000. This outcome has since reverberated through mathematics degree courses and degree courses where mathematics is a requirement. There were seventeen hundred mathematics courses with vacancies in late August!

What went wrong? The first difficulty was that the 2001 problem was intractable. Even if that award was unduly severe there was no way of undoing the damage. Changing the standard in 2002 would have benefited candidates who took up the resit option but would have been clearly unfair to those people who took their AS Level out of the system in 2001. It would also have been unfair to those who carried their grades forward without re-sitting. Worse still, this severe award at AS was bound to impact on the 2002 A Level outcomes because it brought half the marks to those awards. And, that was not the end. If the A2 standard was lowered to compensate for the severe AS result then that would have to be readjusted in 2003. Schools realised this and saw that the awarding bodies would not be able to compensate so they voted with their feet and moved to other subjects.

Severity where an examination award is concerned can mean a number of things. The first thing to note is that it could be the case that the award is fair but the candidates are less able than previous cohorts or have been badly taught. However, if an AS award is not fair, the problem can lie in too difficult a specification in the sense that it makes demands that are unfair on candidates who only achieved GCSE a year earlier. It can also link to harsh marking and the imposition of a severe standard at the awarding meeting after the examination.

It may prove impossible to unravel the factors in this case but the most likely scenario is that the 2001 Specifications and AS papers were set too high for pupils who had only had a single year of specialist teaching beyond the GCSE threshold. Add to that, teacher unfamiliarity with a new examination and the increasing use of non-specialists in schools, plus a significant increase in workload with the introduction of the modular structure and it is easy to see that things could go wrong in locating a new AS standard.

Part of the problem, and a contributory factor in this case, is that mathematics examinations have always been notoriously difficult. What this means in practice is that candidates perceive that they have done badly but the pass rate is kept at a reasonable level by reducing the grade boundaries. In an ideal mathematics test, you would expect to score say over 80% of the marks to get an A grade, over 70% to get a B, over 60% to get a C and so on. However, there have been apocryphal tales for many years – and they include key stage testing – where the ‘average’ candidates received their ‘average’ grades for scoring fewer than 30% of the marks. The much-publicised downturn in results at key stage 2 in 2002 was also thought by many to have resulted from a difficult paper rather than from any decline in standards.

One undesirable outcome is that around 50% of sixteen-year-olds get no meaningful description of their ability in mathematics after two years of GCSE study. A hurdle at age 16 that less than half of the population can cross is of no help to the educational ambitions of the government and, eventually, people are going to start criticising the hurdle rather than the candidates or their teachers. This low figure immediately limits access to AS courses as well.

There has been government anxiety about poor pupil performance in mathematics for a number of years. The Numeracy Strategy and the framework at key stage 3 are one kind of response but there have also been attempts to map skills more effectively, to introduce new courses and to address the subject’s terminology. There have even been lengthy celebrations such as the Mathematics Year 2000 to encourage pupils to enjoy the subject and to raise its profile.

In the longer term, it is hard to see what can be done. Curriculum review leads to argument but not improvement. There are enthusiastic supporters for algebra and geometry who believe that the subject went off the rails when these essential items were displaced but there are plenty of teachers to say that they are as important as they have ever been. There have been absurd debates about calculator use, trumped by the fact that in Singapore, where they are used most, mathematics results are excellent and, currently, the government is trying to turn back the clock with more mental arithmetic as if greengrocer mathematics holds the key to success. As always the truth lies somewhere in between but, at the moment, it is the education system that is driving mathematics down not committed teachers or their students.