In the middle of August The Irish Times carried comment about the chief examiner's report on Junior Cert higher-level mathematics. The article, like the report, expressed concern about declining standards. This is a matter which should be considered seriously - particularly because, as Andy Pollak, your education correspondent, pointed out, mathematics is a key subject for opportunities in high-tech industry.
There has been a fall in the proportion of candidates achieving honours, from 80 per cent in 1994 to 66.1 per cent in 1996. In light of the very large numbers taking the exam, such changes are spectacular.
There are two ways to explain a major shift in the results profile of a public exam. It might be due to changes in the set of candidates or it might be due to changes in examining.
The chief examiner's report indicated a presumption that there has been a significant decline in candidate standards. This presumption should be questioned.
Movements in the true level of student achievement normally take place very slowly. They can be caused by changes in participation levels, or by a culture shift. There is no obvious reason to suggest that there has been a change in the type of student attempting higher-level mathematics in very recent years. The chief examiner's report implies that the explanation is cultural - the fault is in student preparation.
There is no external evidence to support a view that students have suddenly started working less hard or less effectively. Nor is there any reason to believe that a withdrawal of student effort should focus on mathematics. Furthermore, the rate of change is implausibly large for such an explanation.
This should lead us to consider whether the change has happened in the exam rather than in the candidates. The Department of Education takes its responsibilities as an examining body very seriously. Irish public examinations are conducted with commendable care and thoroughness. The Department's inspectors regard examining as the most important of their functions, and devote a great deal of time and attention to it.
All those who assist in examining as administrators, as supervisors, as examiners or as advising examiners will testify that all aspects of the work are subject to rigorous safeguards to ensure fairness.
A candidate's result is determined by that candidate's knowledge and skills and the examining process. There are two important variables in the examining process - the setting of papers and the marking of scripts.
Regular readers of The Irish Times during the certificate examinations are aware that perceptions of the difficulty of papers vary, sometimes quite considerably. It frequently happens that, when a paper is perceived as difficult, the result profiles do not differ greatly from other years. This is because of the second examining variable: the marking scheme is adapted to take account of the difficulty of questions.
The chief examiner is responsible for both setting papers and controlling marking schemes. This is a fundamental flaw in the system - each exam depends entirely on the judgment of an individual.
Even with the best of intentions, the type of exam that we traditionally conduct in Ireland does not, and cannot, have an absolute assurance on standards. In general, chief examiners aspire to achieve consistency in standards. This is much easier said than done.
The difficulty of exam items is a very complex issue. A difference in presenting a question might appear negligible, but results in real differences in answers. For example, a candidate who could deal with the question "17 x 3 = ?" might not be able to deal with "3 x 17 = ?". From the point of view of the examiner, the skill might be considered to be the same; the candidate might see a difference between multiplying by three and multiplying by 17.
Have there been cases where the goalposts have been moved intentionally? In the 1991 exam in Leaving Cert higher-level mathematics, for example, 66.5 per cent of candidates were awarded grade C or higher. By 1996 the percentage had risen to 82. This has not been generally heralded as an improvement in candidate standards. Where it has been commented on at all, it has been acknowledged as an adjustment in examining standards.
The scale of public exams in Ireland is enormous. If we combine Junior Cert and Leaving Cert, about 120,000 candidates submit about 1,400,000 scripts or pieces of work in about 140 separate examinations. Each one of those exams depends upon the judgement of its chief examiner. The mechanisms for achieving consistency of standards between subjects, or in the one subject from year to year, are informal and perhaps weak.
Public exams, particularly the Leaving Cert, are crucially important in determining an individual's life chances.
Irish society is becoming increasingly litigious. It seems only a matter of time before a disappointed candidate with access to financial resources brings a court challenge, and requires the Department of Education to justify its procedures. The outcome might be interesting.
Dr Padraig Breathnach teaches in the Patrician High School, Carrickmacross, Co Monaghan. He has carried out academic research in the areas of curriculum and examination.
