One of the main reasons behind the introduction of tiers for the GCSE mathematics examination was the wish to make sure pupils did not end up facing unsuitable papers. Unfortunately, many problems have become apparent with the system over the years.

The first difficulty is deciding in which tier pupils should be placed. This causes arguments between pupils, parents and teachers. On the whole, teachers get it right, but not always. Anyway such decisions should be unnecessary.

It is also a difficult structure to understand when you meet it for the first time. Parents often ask: “Why does it have to be so complicated?” The third problem is the need (as a safety measure) for an overlap between the tiers. As a consequence, the wide spread of grades needed means papers are less tightly targeted than originally intended.

The assessment framework of next summer’s exam is like this: Tier Grades available

Higher U C B A A*

Intermediate U E D C B

Foundation U G F E D

A second consequence of the overlap is that some grades can be achieved by more than one route. The grade causing most concern is the all-important C, which can be obtained by the top and middle tier. Much debate centres on which is easier. (Anecdotal evidence suggests those who know about these things ask at what tier the C was obtained.) But it is clear that a grade C in the intermediate level is obtained in a different academic way from the grade C at the higher level. The former represents a good performance on a limited syllabus. However, the latter shows a rather poor performance on substantially more difficult content and questions.

A third consequence is that candidates entered at the foundation level have no chance of obtaining that all-important C - it is rather like taking an examination you can never pass.

An alternative way of determining grades without ambiguity is to have all candidates take the same papers - at least as far as they are able. One possibility is to have three papers:

Paper Grades available

Paper 1 U G F E

Paper 2 D C

Paper 3 B A A*

Paper 1 would be taken by all candidates. Those who gained an E could take paper 2. Paper 3 could be taken by anyone taking paper 2, but they would have to achieve a C in that paper if they were to be awarded one of the paper 3 grades. There would be no penalty (except the entry fee) for failing to get a grade from paper 3.

Because the C from paper 2 is only a conditional grade needed for paper 3 and not a bar to taking it (as anything below an E is for paper 2) teachers would be expected to provide guidance as to the suitability of candidates for paper 3.

One problem is immediately apparent. Within the time scale of the normal GCSE examinations there would be insufficient time for paper 1 to be marked and graded to decide who is to take paper 2. So paper 1 would normally be taken in Year 10. This is the year before the examination year for the group concerned and the test would be fitted in during the usual examination period of the Year 11 pupils, preferably at the beginning. This would leave adequate time for the marking and grading process for paper 1, and even time for a re-sit in NovemberDecember for those who wish to get the necessary E grade - or perhaps to improve on any of the other grades.

This system would have several advantages: * It is simpler to understand, with a clear and logical progression.

* All ambiguity about grades would be avoided - there is only one way of achieving each grade.

* The system would be entirely “open”, with the grades awarded purely on results, with no bars imposed by the level of entry.

* Papers would be written for a small and specific target-range.

* Less able pupils would not have to suffer the morale-shattering experience of staring at a list of questions that mean nothing to them - it needs only one paper to establish grade E, F or G.

* The gradation obvious in the process could prove a considerable motivation in Year 11, especially for the less able.

* Higher grade candidates would necessarily be examined in aspects of the syllabus which they are expected to know but which they do not usually get questioned about. Some small-scale testing in this aspect has revealed a few surprising gaps.

No doubt there are other ways of achieving these worthwhile objectives. But whatever we do we should be making sure the GCSE examination in mathematics is transparently fair to all.

Professor David Burghes is director of the Centre for Innovation in Mathematics Teaching at the University of Exeter. Frank Tapson is a research fellow at the centre