Researchers have produced some support for this hypothesis by testing the intuitive, or socially acquired, understanding of fractions displayed by five-year-olds in the United States and in the two Pacific Rim countries.

In Japan and Korea the fraction “one fourth” is expressed as “of four parts one”. In English, however, the fraction is more often explained as “one of the four equal parts”. The Californian researchers, Irene Miura and Chungson Kim, of San Jose State University, and Yukari Okamoto, of Santa Barbara University College, explored the significance of this difference by setting three tests for first-year elementary school pupils.

A Japanese school took part in the first of the tests but only Korean and American pupils were involved in the second and third tests. None of the schools included in the study had begun to teach the children about fractions. All the schools were in middle-class neighbourhoods.

The first test, which required the children to represent eight fractions by shading in the appropriate proportion of a circle, square or rectangle, involved 29 Japanese children, 44 Korean and 29 American. Twelve of the Japanese children identified all the fractions correctly, as did nine of the Koreans, but only four American infants obtained full marks. This finding was partly offset by the fact that only two American children answered five or more of the questions incorrectly, compared with eight of the Japanese and five of the Koreans. However, further testing revealed that Korean children had a far better grasp of complicated fractions than American children by the end of their first year in school.

In a follow-up test, five Korean children identified eight complex fractions correctly and four of their classmates had six or seven right answers. No American child was able to match this performance.