The Netherlands and Sweden were the top-performing countries in mathematics and science in the final year of secondary school, according to the latest report of the Third International Mathematics and Science Study (TIMSS). France led in advanced mathematics and Norway and Sweden in advanced physics.

The surprise finding, though, was the dismal performance of the United States, at 18th ahead of only Lithuania, Cyprus and South Africa in maths and science. It also came 15th out of 16 countries in advanced maths and 16th out of 16 in advanced science. France and Germany were 12th and 13th respectively.

TIMSS is the largest international study of student achievement, covering more than 40 countries and half a million students at five grade levels. The latest results cover 21 countries at grade 12 (equivalent to Year 13 in the UK). But they do not include the high-performing Far Eastern countries or the UK. Seventh and eighth grade (Year 8 and Year 9) figures released in the past two years have put Singapore, Korea and Japan in the top four performing countries in science.

Ingvar Persson, of the Swedish ministry of education, said the country’s top rankings follow substantial efforts to improve performance in mathematics and science since a similar survey carried out in 1980 put Sweden at the bottom of the mathematics league. Expanded in-service training had increased teachers’ knowledge in the sciences. There was also more interest among pupils in the subjects in Sweden than, for example, Denmark or Norway. Sixteen per cent of pupils take physics at advanced level compared with 3.8 per cent in Denmark and 8 per cent in Norway.

In addition to the Netherlands and Sweden, countries performing above the average in science and maths in the study were Iceland, Norway, Switzerland, Denmark, Canada, New Zealand and Austria. Below-average performers included Hungary, the Russian Federation and Italy. The tests were designed to measure how well students can use their knowledge in addressing real-world problems.

In all but one of the 21 countries boys outperformed girls. In the advanced subjects, boys did better than girls in 15 out of 16 countries in mathematics, but in physics boys outperformed girls in 11 of 16 countries.

To find out which educational methods were getting results, TIMSS researchers also asked advanced maths and physics students about the way they learned and how they were taught. The researchers found that indicators associated with high mathematics achievement included frequently solving equations, doing reasoning tasks and using a calculator.

“Most final-year students reported considerable use of calculators, whether at home, school, or work, and this was especially true of the students having taken advanced mathematics or physics,” said Michael Martin, TIMSS’s international deputy study director. “On all three tests, students who reported using calculators daily performed well above those who rarely or never used them.”

Researchers in the United States said the country’s curriculum was weaker than other countries - American middle-school children are said to spend less time on algebra, geometry, chemistry and physics than in northern Europe and Asia - and children spent less time completing their homework. Across the international sample, students reported spending two to three hours a day studying. However, the countries where more than a quarter of students said they worked in a job for three hours or more a day included Iceland, the Netherlands and Norway - three of the four highest performers in maths and science - as well as the United States.

Tjeerd Plomp, chairman of the International Association for the Evaluation of Educational Achievement, which sponsors TIMSS, said the study provided “a unique opportunity for countries to examine the content and rigour of what is being taught and learned in science and mathematics classrooms throughout primary and secondary schooling”.