Speculations on a world of possibilities
The report, commissioned by the Office for Standards in Education, reviewed international surveys of educational achievement, which included England. In its conclusion, those of us involved in mathematics education are invited to "look beyond the immediate restriction of tradition and geography and use an open mind to see if other countries have ideas and practices which we can utilise, adapt and adopt". It would be foolish, and parochial to dismiss such a suggestion. The major difficulty, as I see it, is being able to keep an open mind while considering the evidence.
In attempting to explain the European and Pacific Rim's superior performance in these surveys, Professor David Reynolds, one of the authors of the report, offers a range of hypotheses and "speculations". He discusses some of the issues relating to the differing cultural climates and organisational systems, and describes others that are focused at the school and the classroom level. These need closer examination, particularly in view of the conflicting and contradictory messages emanating from recent OFSTED publications and governmental pronouncements.
Mixed ability teaching The report says that children in Taiwan are taught in mixed-ability classes throughout their junior years. Eighty-two per cent of 13-year-olds in Swiss schools are in mixed-ability groups for maths compared with only 8 per cent of English pupils. As Taiwanese and Swiss children consistently perform better than the English, it would appear that this form of classroom organisation should be favoured in our schools. Why, then, does the Government attack mixed-ability teaching, arguing for more setting, streaming and grammar schools, and introducing legislation to enable schools to select more of their pupils by ability?
Testing The frequency of testing is offered as a potential contributing factor to success. This is deemed important, not only for providing information for pupil, teacher and school, but also for developing pupils' ability to perform well in timed tests. But do we need more testing? Teachers already carry out frequent formal and informal assessments of their children - and many schools provide "training" in standard assessment task completion. Incidentally, fewer countries test more than they do in the United States, where weekly "quizzes" and fortnightly end-of-unit tests are the norm, yet US children fare worse than ours in international surveys.
Textbooks Reynolds points out that many of the more successful countries adopt a government-approved standard textbook, written by experts. But were we to adopt a similar strategy in this country, which experts would be invited to write these texts? Not, I am sure, any of those university lecturers who espouse Plowden-inspired theories, nor any of those practising teachers who were all trained by these self-same trendies.
Given the internecine battles that took place on the original national curriculum working party for mathematics, I doubt if you would even get agreement on what a standard textbook might look like. The textbooks that are used in most North American states, although written by different authors, are similar in structure and content, and could almost be a standard scheme. However, we know how well American children fare in international surveys.
Differentiation In Taiwanese schools, the same work is set for all the pupils in a class. Despite the groups being mixed ability, they are treated as homogeneous units. This way of operating stems from a belief that there need not be a "trailing edge" of low-attaining pupils: all of them are considered capable of assimilating the work and are taught accordingly. "Differentiation" - that important concept dear to the hearts of school inspectors - does not appear to enter into the equation.
Range of performance Related to differentiation is the idea of performance range. British children produced a greater range than any other country in the report - what the Independent called "the gap between the brightest and the dullest". One way of reducing this range, which is used in several countries, is to make children who fail to reach a minimum standard repeat the school year.
The Taiwanese teacher interviewed in Panorama criticised the English practice of setting by ability, and was concerned about the self-image of those children who were in the lower sets. However, she appeared to accept with equanimity a system that must dent children's self-image by making them repeat a year of their education.
Time in school The amount of time that children spend in school is another issue which is not clear cut. Children in Pacific Rim countries spend about 30 extra days a year in school in addition to the many hours doing work in "juku" (cramming schools) in the evening. The implication is that the greater the amount of time spent in school, the higher the standard of performance. However, we know that English children begin school a year or so earlier than those in most other countries, and, as a result, probably spend more time in formal education. Extra time in school does not seem to help us.
Calculators Pacific Rim and European countries introduce calculators at a much later stage for fear of damaging children's capacity to perform mental calculation. The implication is that calculators contribute to England's inferior performance. However, teachers have reason to feel confused over the calculator issue, particularly as a recent OFSTED publication, which was sent to every school, states that "calculators can improve performance and attitude". How are teachers to respond to this conflicting advice?
Whole-class teaching The main rationale for the Panorama programme which dealt with the findings of Worlds Apart? appeared to be to supply Chief Inspector Chris Woodhead with ammunition to fuel his argument that whole-class teaching should be used for 60 per cent of the time for teaching maths in junior school. He said that an important characteristic of the teaching in those countries that are performing better than us is whole-class teaching. What he failed to tell us is that this method also predominates in many of the countries that fare worse than us.
Whole-class teaching, which conjures up pictures of a teacher standing at the blackboard lecturing to a class of silent children, has been euphemistically renamed "interactive whole-class teaching" in order to dispel such negative connotations. This teaching style, we are told, involves the teacher starting with a problem and developing concepts and solutions through questions addressed to the whole class. On TV, it looks like what good maths teachers have been doing for years, namely, using some of the teaching strategies described 14 years ago in the Cockcroft Report: exposition, discussion between teacher and pupil, discussion between pupils and consolidation and practice.
If I were to reflect on Worlds Apart? with a closed mind, I could find evidence within the report to argue that: * mixed-ability teaching should be used more widely, and setting, streaming and selection by ability should be discouraged * moves to increase the use of differentiation, either by task or by outcome, should be curtailed because of the increase in the range of performance it appears to generate * all primary teachers should be given a third of their time out of the classroom - as in Taiwan - to enable them to develop their collaborative working skills * class size should be reduced so that it is the same as in Switzerland n more money should be spent on textbooks (England reported the highest proportion of schools with a textbook shortage at age 13).
But as I have read the document with an open mind, I shall not attempt to make such points.
Ian Thompson lectures in maths education at the University of Newcastle
HIGHER HOPE AT LOW LEVEL. A Mathematical Foundation, a paper from the Society of Education Officers, the Engineering Council and the Standing Conference on Schools' Science and Technology (August 96), calls for co-ordination in tackling the problem of low standards on entry into British universities in maths-related subjects. The report expresses concern that many difficulties at this advanced level stem from inadequate mastery of number and application of number at primary level.
Among many proposed objectives and actions which presuppose support by a number of agencies, the report calls for improved primary teacher training in maths and the teaching of maths; for more attention to continuing professional development for anyone who teaches maths; and for agreement in the key mathematical knowledge needed for maths-related and particularly engineering university degrees.
Further details from the Engineering Council, 10 Maltravers Street, London WC2R 3ER.Tel: 0171 240 7891