Marking A-level maths too hard only puts candidates off, argues Colin Goldsmith
It is some months since the study Standards in Public Education 1975 to 1995, popularly known as Standards over Time, was jointly published by the School Curriculum and Assessment Authority and the Office for Standards in Education. It is important to re-open discussion of some of the issues raised, in mathematics at 18-plus at least, because SCAA seems to have misunderstood the main message of this strand, judging by some of the proposals being forcefully advocated for immediate change to AS and A-level mathematics assessment. These proposals have raised widespread alarm among those responsible for teaching the subject in schools and colleges.
It is instructive to look first at the situation in 1975. In that year 44 per cent of the candidates in the mainstream mathematics A-levels covered in the study failed. Thousands of students were rejected by the system. How had this disastrous outcome been allowed to happen? In the previous five years a whole raft of new universities (York, Warwick, Essex etc) were building up to full strength and numbers in higher education doubled. This meant a broader spectrum of students wishing to apply for university entrance through the A-level system. The standard of questions set in mathematics A-level papers was rigorously maintained and the mark distribution was heavily skewed towards the lower end. Awarders were unwilling to set derisory passmarks and so the failure rate was excessive.
The mismatch between the standard of the candidates and the standard of the examination questions received negligible publicity then; it would surely be different nowadays. It was left to some university professors of engineering to start agitating. The Grade D students that they were taking on to their courses, faute de mieux, could not be relied on for any proficiency in, or even previous exposure to, many key areas of A-level mathematics.
The moral to this story is obvious: that any institution must adapt to altering circumstances. School assessment is no exception. When the clientele for A-level mathematics changed, the examinations had to change too. Courses should always be challenging, but tailored to the needs and abilities of the students for whom they are intended. This fosters motivation and leads to more effective teaching and learning. It maximises real attainment. Over-hard assessment merely discourages and shows up candidates' deficiencies; ideal assessment reveals accurately what students know and can do. No politician of any party has been brave enough to explain to the public that "lower standards" are often appropriate and highly desirable, leading to what are, in some important respects, higher standards. Just as economists do not now argue for rigid and immutable international currency exchange rates, so educationalists should not entertain the chimera of an A-level Gold Standard.
In the first half of this decade, the number of students in higher education has increased in percentage terms as dramatically as it did 20 years earlier. This time the system has coped sensitively and effectively with the flood of new students, weaker in ability and previous attainment.
Mathematics assessment at A-level has become more accessible to weaker students (that is, easier); the motivation of students has increased; passmarks have risen; and failure rates have been further reduced. These factors are all inter-related and it is unhelpful and irrelevant to try to sum them up in a crude statement such as "Standards have fallen".
Until GNVQs are fully developed and have earned comparable esteem, AS and A-level courses must continue to cater appropriately for the top 40 per cent of the ability spectrum. If the assessment is made to revert to the form it took in 1985 and earlier, the marks scored will drop, confidence will be eroded and numbers choosing what is still regarded as a hard subject will plummet again just when the prolonged fall of recent years has been halted.
I have made no reference, so far, to the higher grade candidates. About 5,000 were awarded grade A in 1975 and 16,000 in 1995. It would not be surprising if some students with grade A now have less academic potential than their counterparts of 20 years ago. What is important is that they are given appropriate challenges throughout the course. There is evidence to suggest that this has not been the case in general during the last five years or so. There is a need to re-think the provision for the better candidates without affecting the demands on those now embarking on 16 to 19 courses with a background of grades B and C at GCSE. The ability range is enormous at GCSE and common examination papers in mathematics would be ridiculous. Many students who took only the intermediate tier at GCSE now go on to A-level. There is a wide attainment range on entry and by the end of two years of specialised education this has spread substantially. In a subject such as mathematics it might be deemed impossible to provide properly for the range of ability without tiered courses and assessment. A higher tier course can include more content, problem-solving and proof, the whole presented in a more rigorous way. A lower tier course would give greater emphasis to straightforward applications of core material with a more structured development.
An understanding of the past should be a pre-requisite of decision making. Now that educational decisions are more centralised and their effects more pervasive, it is important to make sure that they are based on wide-ranging consultation which is given proper consideration. Can we try to ensure that party politics does not distort the evidence and dictate the outcome?
Colin Goldsmith is deputy chairman of the School Mathematics Project, chief examiner of the Oxford and Cambridge Schools Examination Board's non-modular A-level and was the co-ordinator of the maths at 18 section of the SCAAOFSTED report into Standards over Time