When the results of an international mathematics and science test were made public last week, showing American 12th-graders near the bottom of the industrialized world, leaders reacted with well-rehearsed alarm. They warned that Americans would not be able "to continue to be global competitors in the new knowledge economy," as Education Secretary Richard Riley put it.

But with the United States standing today as the world's unchallenged technological powerhouse, top scientists and educators are wondering whether the country is succeeding despite loose educational practices or, at least in part, because of them.Larry Cuban, a professor of education at Stanford University, said, "American ingenuity and innovation seem to be so nimble in responding to difficult problems that one could speculate that the progressivism that so many critics claim has seized American schools is the very fountainhead for that creativity and innovation."

Nearly all educators agreed that American schooling required improvement, but many said the links between its problems and the country's economic performance were apparently far less direct than had been supposed.

American 12th-graders were outperformed in mathematics and science literacy by their counterparts in 12 countries out of 20 and did better than students in just two, Cyprus and South Africa. In advanced mathematics and physics, no country performed more poorly.

In the late 1950s when the Soviet Union put a rocket in space ahead of the United States, and in the '70s and '80s when Japanese cars and computers were leaving U.S. products behind, the gaps in students' mathematics and science scores were seen as damning evidence of an imminent national decline.

But today Asian and European educators are coming for visits to see what they might learn from the American system.

"I remember," said Gerald Bracey, a researcher and writer on education, "when the education minister of Singapore came here, and people said: `What are you looking here for? Your kids consistently score on top of all international tests.' And he said something like, `All that our kids can do is take tests.' He understood that we are nurturing more creativity here."