Our children bad at maths? It just doesn't add up

It is difficult to switch on the television (or to open a newspaper) without encountering yet another survey reporting how dismally the English perform at mathematics. Are we really that bad? And if so, is the way forward to be more like the Swiss, the Germans or the Taiwanese?

From the furore over claims this week by Chris Woodhead, the Chief Inspector of Schools, that British children are years behind their foreign counterparts in maths, would you have guessed, for example, that English 13-year-olds were the only ones to beat Korea in 1988 (in logic and problem solving)? Or that the lowest 10 per cent of 13 year-olds in Taiwan had an average mathematics score below that of the lowest 10 per cent in England in 1992? Or that we usually come between fifth and tenth out of more than 40 countries in international maths olympiads?

There are relatively few international surveys that have produced reliable information on mathematics performance, in the sense that they have taken care over the design of their tests and have a randomly selected sample representative of the national population. Basically only three surveys meet these criteria: those carried out by the International Association for the Evaluation of Educational Achievement in 20 countries in 1981, and the two International Assessment of Educational Progress studies of 1988 and 1992, in six countries and 20 countries respectively.

In these studies the European, Australian and North American countries usually have very similar performances. For example, in 1981 at age 13, 12 such countries had a mean score in mathematics of between 45 and 52 per cent, and in 1992, 10 countries at age 13 scored between 55 and 64 per cent. England in both cases was slightly above average for these groups.

European countries only had higher scores in cases where there were real problems of comparison. For example, many European countries insist that pupils do not move up to the next class unless they have high enough results. This means that low-attaining pupils of the age studies are left behind and are therefore not in the classes surveyed, as in Hungary (which in the 1982 study appeared to have more than 60 per cent of pupils outside the main year group), and in Germany and Switzerland. In other countries relatively high proportions of low-attaining pupils were omitted because they were in special or vocational schools, so that for example 17 per cent of low-scoring Dutch pupils were left out, as were 12 per cent in France and 8 per cent in Switzerland. However even in these countries mean scores were not more than 10 per cent higher than the English core.

What is more interesting than the averages is the distribution of scores for each country, as reported in the 1992 study. It is clear that for both ages nine and 13, the lowest tenth score very similarly in every country, as do the top tenth, and in most countries the range of marks goes from about 20 per cent to 95 per cent. In other words the differences between countries are very small compared with the range within each.

Within these results, England has built up particular patterns of attainment, doing well on statistics and geometry, less well on measurement (not really surprising given our ambivalence about metric measures) and less well on number. However, many of the number questions reflect procedures that we no longer emphasise for most children at these ages, for example adding fractions other than halves and quarters. In cases where pupils are required to apply number to problems we do well, as in the 1989 study when we were top of six countries in problem-solving, and ahead of the Koreans.

It cannot be denied that the Pacific Rim countries like Korea, Japan and Taiwan do generally produce better performances than in Europe and North America, but it is difficult to be sure of the reasons for this. Most pupils in East Asian countries work about 40 extra days a year, as they attend school on Saturdays and have on average two or three times as much homework. A recent report indicates that more than 60 per cent of Japanese pupils also attend private coaching in the evenings, on average for three hours a week, in order to keep up with mathematics lessons. Taking all this into account, the average Japanese pupil is likely to spend more than twice as much time on mathematics as an English pupil, so it is perhaps not surprising that the mean score in Japan is about 15 per cent higher.

Although teaching methods are more formal on the Pacific rim, surprisingly the 1989 study suggests that England and Korea have rather similar patterns of teacher-pupil interaction, with pupils in England listening to the teacher at the front in more lessons than do Korean pupils, and also seeking more teacher support (Korean pupils help each other rather than asking the teacher). All other countries spent much longer listening to the teacher, even in countries that scored very low.

The 1981 international study undertook a detailed comparison of teaching methods over time in different schools and across different countries, even at the level of different approaches to different topics, but ended up in desperation showing no perceptible effects. The only significant determinants of attainment seemed to be pupil prior attainment and the proportion of the curriculum covered for all pupils.

Thus we should take care before implementing widespread changes in teaching methods.

The Cockcroft committee reported in 1982, and the national curriculum was introduced in 1989, both with the aims of increasing our standards of mathematical attainment through a wider range of teaching methods and a more rigorous curriculum. There is evidence that both affected positively the work of schools. National testing of mental arithmetic is increasing the amount of more formal teaching in primary schools, although most teachers are sensibly trying to maintain a variety of class, group and individual teaching.

Meanwhile the Japanese have recently decided they need a more individually- oriented problem- solving curriculum to match the more positive attitudes to mathematics and the creativity shown by pupils in England and other Western countries. Perhaps this convergence will ensure that we meet somewhere in the middle.

The writer is Professor of Mathematics Education and Head of the School of Education at King's College, University of London.