Familiar problems on the international scene prompt to pose some solutions. Four thousand maths teachers and lecturers from over 100 countries attended the Eighth International Congress on Mathematical Education in Seville in July.
Seville was an appropriate place for this global meeting. During the Middle Ages, Andalusia was one of the main centres for cultural and scientific exchanges between the ArabicIslamic and EuropeanChristian cultures. The city's cathedral is built on the site of an old mosque with its minaret preserved, the Giralda, and the region's architecture still exhibits an eastern influence. It is believed that our numerals and arithmetic operations were diffused into Europe from this region; and the teaching of number was a main focus for the congress.
At ICME-8 it became clear that the current problem of low maths achievement is not restricted to the UK - Spain itself and many other countries are especially concerned about maths at primary level. Worldwide dissatisfaction with standards appears primarily focused on the acquisition of number skills (including fractions) and number knowledge, and on associated teaching methods. The teaching of algebra at primary level was also raised as a problem. But handling data and geometry were not often raised as concerns.
If you are over 30 years old, try to look back on your own primary school maths - did you even do "mathematics", or was it simple arithmetic, one hour a day, five days a week? This was my experience, and I hated it. Since then, increasing demands have been made of primary teachers to teach a much wider range of maths and use a wider range of styles. The new syllabuses are certainly an improvement on the maths I suffered - at least on paper.
One national policy-producer at ICME-8 let slip a revealing comment: "It's easier for us to write the plans than to get the teachers to deliver them. "
We must not aim low, but when "plans" contain unrealistic statements, or require new teaching methods without appropriate training, they inevitably produce a failure to match expectation and create disaffection among teachers required to deliver them. And of course it is not just the maths curriculum that has increased - most primary teachers have to cope with the expansion of all subjects.
A lot of the required maths is new to primary teachers themselves. The first algebra I ever saw was in the second year of secondary school, and probability was not even included in my O-level syllabus; now both elements are introduced at junior level. Yet the time and resources allowed for maths teaching is roughly the same, or less.
This situation is the same throughout the world. The need for adequate mathematics in-service training has been stated in official reports for decades, and was frequently repeated throughout ICME-8. Some countries take the matter seriously and have developed national programmes for extended training. Several are considering an increase in specialised maths teaching, particularly in the upper primary years.
The possibility of a global maths curriculum was discussed and was considered feasible. Such a curriculum would make international comparisons easier, and there could be spin-offs in resource production. But there would also be a danger that such a document would create a monolithic block on further development. It would be more useful for each country to put its curriculum documents on the Internet.
International comparisons of class management and teaching styles are increasingly cited within the UK. Not long ago, Germany was being promoted as the country of success in maths education. A few statistics then appeared which did not suit the political case, (for example, average primary school teacher to pupil ratio in Germany is 1:14, for the UK 1:20). Now statistics comparing us to Taiwan, or the Pacific Rim in general, are being used against teachers.
Statistics do not reveal that in the Pacific Rim teachers enjoy high status and good discipline is expected rather than demanded, nor that teachers in the UK are trying to do too much. Yet international studies do raise important points. The soft option is to blame the teachers.
Who allowed the national curriculum to become overloaded and imposed it on schools? Where have all those people gone who demanded and bullied teachers into using the teaching methods now considered unsuitable? How many teachers were condemned by school advisers when we used textbooks, or failed to use "discovery" methods? (I certainly was after one lesson, and despite excellent school results - by a person who is now an OFSTED inspector.) Will additional funding be provided for additional training - or is the cheaper method of constant criticism to be the Government's only solution to its mathematics education problems?
At ICME-8 the need for balance between formally learning and practising the "standard rules" of arithmetic and heuristic development of personal strategies for problem solving and mathematical investigation was discussed once more. l had a sense of deja vu. Must it be eitheror? Surely we need both.
While it may be true that many people cannot easily see the beauty of pattern and process in maths, that does not mean they are wrong to insist on their children being able to manage the "basics". It verges on arrogance to assume that the demands of millions of parents, employers, and a large percentage of teachers do not have the best interests of their pupils at heart.
The tedious debate over the use of calculators in primary schools continued. I would throw them all out together with the computers in primary school. I have seen that IT is often a distraction from the more important, exciting, stimulating and practical things young children should be learning to do. The use of calculators all too often restricts the use of the mind.
Try the following questions with a class who regularly use calculators: 1 + 2 + 3 + 4 + 5 =?
1 x 2 x 3 x 4 x 5 x 0 =?
36 divided by 0 = ?
12,345,678 x 12,345,678 =?
1 divided by 2 =?
There is of course no chance that my Luddite wishes will come true, there is too much investment and sponsorship from IT companies for that to happen, (Casio was a major sponsor at ICME-8).
Finally, two proposals. First: scrap HMI. "In arithmetic . . . worse results than ever before have been obtained . . . the failures are almost invariably traceable to radically imperfect teaching." (HMI 1876.) If in over 100 years the Inspectorate has not managed to influence the teaching of maths and is still saying the same old thing, what is the point of having it?
Second, instead of looking East, why not look again at Mathematics Counts, the Cockcroft Report of 1982. As its sponsors, Sir Keith Joseph and Sir Nicholas Soames (both Tory MPs) wrote: "Few subjects in the school curriculum are as important to the future of the nation as mathematics; and few have been the subject of more comment and criticism in recent years. This report tackles that criticism head on. It offers constructive and original proposals for change. "
ICME-9 will be held in Japan in August, 2000 Malcolm Sanders teaches at Gunter Primary School, Birmingham. He has been responsible for maths for 18 years and is a founder member of the European Primary Schools Association