Other states are recruiting in Europe to fill critical gaps in subjects like maths and science, while some have responded to the shortage by issuing “emergency” credentials to unlicensed teachers. One state, Kentucky, is accepting those with only high-school diplomas.

Education Secretary Richard Riley has warned school districts not to sacrifice quantity for quality as rising pupil numbers have created a huge demand for teachers.

This year, enrolment at public and state schools reached a record 52.7 million, 500,000 more children than last autumn. But as the corresponding demand for teachers increases, many of those hired in the 1960s and 1970s are facing retirement and the still strong economy is luring qualified people, particularly in the sciences, to other fields.

The government estimates that American schools will have to hire 2.2 million teachers in the next 10 years to cater for the children of baby-boomers and an influx of young immigrant families.

At the beginning of the school year, Mr Riley called on states to stop giving emergency credentials. “You cannot set standards and then immediately discard them,” he said.

“Too many school districts, I am afraid, are sacrificing quality for quantity in order to meet the immediate demand of putting a warm body in front of a class.”

He urged Congress to authorise new funding for teacher training, and the creation of a national job bank to streamline recruitment.

School districts across the country say increasingly that good teachers are hard to find - with the exception of Florida, it is reported, where the sunny climes still draw plenty of willing candidates. At the same time,school boards face mounting public pressure to raise teaching standards.

In Massachusetts, where a political furor broke out after 60 per cent of teaching applicants failed a basic entrance examin, the state is offering bonuses of $20,000, spread over four years, to the 175 most promising new recruits. Up to 300 veteran teachers with proven records would qualify for $50,000 bonuses spread over 10 years.

Similar stories are to be found from Baltimore, Maryland, which offered an incentive package of $5,000 towards a new house and $1,200 in relocation costs, to Las Vegas, Nevada, where exponential growth in the gambling capital has forced the city to hire 2,000 new teachers a year. Many districts are reaching outside their home states for recruits.

New York City this summer went even further afield, hiring 24 Austrian maths and science teachers and seven from Spain. At least one Texas school district has followed suit, hiring from Germany.

New York City’s deputy director of human resources said if the Austrian teachers performed well the city would also seek to recruit from Scotland and Switzerland.