Asia's rising economic success has helped China's hi-tech corridor to take a clear lead in the latest OECD international education rankings.

The results of the OECD's programme for international student assessment – a triennial exam for 15-year-olds known as Pisa – show that China's Shanghai region easily tops the rest of the world in maths, reading and science.

Singapore, Hong Kong, Taiwan and South Korea made up the rest of the top five for maths, followed by the Chinese island of Macao.

Elsewhere, Pisa results were a further disappointment for the US, which saw its maths rank fall to 36th place overall, worse than its 2009 performance, which President Obama dubbed a "Sputnik moment" for American education. In reading, the US fell seven places, to 24th, and in science the country came in 28th, down five.

Australia saw a precipitous fall in its maths ranking, from 15th in 2009 to 19th in 2012, as it was overtaken by Poland and the new entrant, Vietnam, which appears in the OECD tables for the first time. Australia's reading score was little changed but its performance in science slipped from 10th to 16th, tied with Macao.

Finland was the highest placed European country, with a top-five performance in science, while Ireland was sixth-equal with Taiwan in reading. In maths, Liechtenstein, Switzerland and the Netherlands were the only European entrants in the top 10.

The UK's performance was virtually unchanged from its 2009 results, when its international rankings suffered with the addition of higher-placed new entrants such as Shanghai. It ranked 20th overall for science, 26th for maths and 23rd for reading – on a par with France and the US, and close to the OECD average for reading and maths.

Andreas Schleicher, the OECD's deputy director for education and skills and co-ordinator of the Pisa programme, said the success of education systems such as Shanghai's was the result of an emphasis on selecting teachers, as well as prioritising investment in teacher training and development.

Shanghai's lead was so clear that the results were the equivalent of its students having had three additional years of schooling, the OECD estimates.

Outside Asia, Brazil, Germany and Mexico have all shown consistent improvement, with Germany, Mexico and Turkey winning praise for improving the performance of their weakest performing students, many of whom were from disadvantaged backgrounds.

David Spieghalter, the Winton professor of the public understanding of risk at the University of Cambridge, said: "Pisa explores many factors associated with country performance but occasionally seem hasty in assigning reasons for change – we can't decide causality from this study, and we should be very cautious in the lessons to be learned."

Spieghalter added: "If Pisa measures anything, it is the ability to do Pisa tests. Aligning policy along a single performance indicator can be damaging. We need to look at the whole picture."

The OECD administered the standardised tests at the end of last year in 34 countries and a total of 64 regions, to 500,000 15-year-olds.

According to the findings, girls performed worse than boys in maths exams in 37 regions and countries, although in the majority of cases the gap was small. In most countries the gender gap favoured girls in reading, while in science there was little difference.

Schleicher said that the OECD found no evidence from its international analysis that competition between private, state or charter-style schools – free schools, in the UK – had any impact on raising standards.

"You would expect that systems with greater choice would come out better because you expect competition to raise performance of the high performers and lower performers, and put out of the market schools and systems that do not succeed. But in fact, you don't see a correlation," Schleicher said.

"Competition alone is not a predictor for better outcomes. And the UK is a good example: a highly competitive school system but still only an average performer."

Instead, Schleicher said parents had higher priorities in choosing schools than simply academic results, according to the OECD's surveys of parental opinion.

"The most important thing for parents is not the performance of the school but what they call a safe school environment. And that is true for privileged and disadvantaged parents," he said.