Many students flunked even basic questions on fractions in the test set by the education ministry.

The results fly in the face of the country’s top international ranking in those subjects. In 2001 15-year-olds in Japan came top in maths and second in science, beating their peers in 31 countries. The UK came eighth and fourth respectively in the survey by the Organisation for Economic Co-operation and Development and Programme for International Student Assessment.

In November 2002, around 105,000 of Japan’s high-school seniors took part in the national tests that covered seven subjects - an unprecedented 8 per cent of all third-year high-school students.

Nearly 50 per cent of students failed the maths test, with 60 per cent not even attempting to answer questions on trigonometry. For other science subjects, students scored similar results. Participants scored 49.4 per cent in geology, 50.2 per cent in physics and 48.1 per cent in chemistry.

Pass scores in Japanese and English were unexpectedly higher: 71.5 per cent and 59.3 per cent respectively. Students were also asked if they enjoyed studying - 80 per cent said no.

Following the publication of the ministry test results, pundits and officials alike have been quick to lay the blame on the newly-liberalised education system. Since the early 1990s, Japan has opted for a shorter school week, down from six days to five, and for a 30 per cent lighter curriculum. There has also been less cramming for the all-important university entrance exams.

The results, say the new system’s critics, demonstrate a collapse in students’ academic abilities. They also say that such poorly-trained young people will ultimately lead to economic collapse because the country depends on retaining an edge over competitors in technology and science.

The leading right-wing Sankei newspaper referred to the results as “the tragic consequences of relaxed education”.

But Michio Nitta, professor of education at the Institute of Social Science, Tokyo university, warned against reading too much into the test results.

Professor Nitta said:“It is generally believed that Japanese schools teach higher levels of maths earlier. Thus, if the international competition is made at the same age, Japanese children score better.”

He added that the content of the international and national tests was not the same, so marks were not comparable.

“The national survey follows the ministry of education guidelines which some scholars criticise as less meaningful. The international tests may be focusing on more fundamental skills in which Japanese children still excel,” he said.