People have missed the point of the London Mathematical Society's report Tackling the Mathematics Problem which was published last October. It appears to be assumed that the report's main concerns lie with that small proportion of maths A-level students who go on to study maths in universities, and that university lecturers are merely wanting a school system designed to make life easy for them, so that all their students have reached a certain level of proficiency before their university courses.
This is far from the truth. I was a member of the group that wrote the report, and although I am now a lecturer in higher education, I taught maths in schools for many years. The authors of the report genuinely want the best maths education for the whole ability and age range. We believe that the problems academics have with undergraduates are symptomatic of a wider problem for a large proportion of children, far more than the small number who go on to read mathematics or engineering at university.
This is the problem which the report highlights, not only from the authors' own perspectives, but also for the nation at large. Some of our brightest students display some of the problems to which we refer, which adds yet more weight to the points we are making.
In this article, I would like to look at the aims we have in teaching school maths, and to suggest just one improvement that we could make.
Cockcroft gives one aim as to enable "each pupil to develop, within his capabilities, the mathematical skills and understanding required for adult life, for employment and for further study and training" (Mathematics Counts, 1982).
We are patently not doing this because those of us concerned with maths education from 5 to 21-plus are not working together; schools do their own thing largely governed by the School Curriculum and Assessment Authority and the examination boards, and ignore the needs of furtherhigher education.
I believe that standards have gone down over the past 30 years. Examination boards have had to follow this trend otherwise they would be out of a job. Constant curriculum changes have not helped; nor has lack of consultation and constant deriding of teachers in the media. I do not think it is fair to blame teachers, who are under very great pressure and who have to work within the constraints of the system in which they teach. SCAA has not always received the best advice and in any case SCAA has nothing to do with teaching methods and with the way in which schools are organised - both of which contribute to the quality of the education.
The main recommendation made by the London Mathematical Society's report was that we need a standing committee to look after mathematics education across the full age range: a committee with power to implement change. Representatives of teachers of all age groups would need to be involved in this, from professors of mathematics and research mathematicians to teachers from primary, secondary and tertiary education.
We need to establish whether or not children are receiving a good maths education. This is not a simple matter as the situation ranges widely across the country. On average, though, I believe the situation is poor for too many children. To illustrate this, I want to examine two further aims: * developing numeracy and spatial awareness, and * teaching mathematics as a subject in its own right.
We certainly spend much time on the first of these, though I'm not too sure how effective we are. However, let us assume for the purposes of this article that this aim is successfully achieved by all pupils commensurate with their abilities.
It is the second of these aims that is not being achieved by many pupils, even those who could be expected to do well in maths, mainly because we do not even set out to teach it as a subject. The whole thrust of our teaching is concerned with using mathematics in context and with "real-life" problems: a lifeskills course; or applied mathematics.
This is probably appropriate in primary schools but in secondary schools, it is time to begin the process of teaching maths as a subject in itself with its rules of logic and its interconnecting ideas, as well as to continue to develop numeracy skills.
Perhaps this is the problem: that we are trying to tackle these two disparate aims at the same time, in the same course and with the same assessment procedures. The more mathematical part of our aims are at present not being achieved by many pupils could all benefit from learning maths, not just because it is useful in physics, biology, economics, etc while they are at school, but because it is educationally beneficial in itself and offers something that no other subject does.
If we had a standing committee we could work out set of solutions to some of our problems, but the Government has said no to the idea. So, in the absence of wider initiatives, let me tentatively suggest just one which idea would cost the nation nothing and every school is at liberty to do it.
Many schools operate on a basis of two double and one single lesson per week. I believe that this results in the equivalent of three single lessons per week in terms of the amount of learning. Double lessons may be 75 minutes long, good for a practical task but otherwise teachers know that this time is too long a stretch for most children. The result is that the pace of the lesson is slower and less focused than it would have been for a single lesson, and in addition the teacher has deliberately to allow for some "dead" time, usually at the end of the lesson. It seems that most weeks, the lessons amount to three single lessons' worth of learning time instead of five.
Even worse is the situation where the teacher, embedded in the usual situation of two doubles and a single, feels that "you can't do anything worthwhile in a single lesson" and so operates as if there are effectively only two lessons of maths per week.
The important point here may be the focusing power of single lessons for the teacher, as well as the attention span of the pupils. Thus we would achieve far more in lessons if we had five, well-focused single lessons per week (of 40 minutes each), one per day. Perhaps some teachers would prefer to have one double lesson because of the activities they do, in which case a sensible compromise would be three single and one double on four separate days. Would the bureaucrats complain about the difficulties of the timetable? Probably, but if it is good for learning, then it has to be done.
At all events, the issues raised in the London Mathematical Society's report must be heeded: it is highly relevant to school teachers and school teaching. And, while we await a standing committee, I would urge headteachers to think seriously about how time is used!
Dr J M Jagger is a lecturer at Trinity and All Saints University College, Leeds LS18 5HD. email: firstname.lastname@example.org