A-level maths and science students will be given up to £15,000 if they agree to become teachers after graduating from university, prime minister David Cameron has announced.

Under new government plans, high-performing teenagers will be given grants towards their university costs if they agree to spend at least three years as a teacher once they have graduated.

The move is part of a £67 million package of measures designed to bring an extra 17,500 maths and physics teachers into the classroom. It comes after Ofsted warned in December that a shortage of new teachers was a “pressing” problem, and that the shortfall in maths and physics was particularly acute.

Other measures include new “fast-track” programmes to enable “skilled professionals” in engineering and medicine to switch careers to teaching, and “tailored support” for former maths and science teachers to re-enter the profession.

A statement from Downing Street says the government wants to bring an extra 17,500 maths and physics teachers into classrooms. Of these, 15,000 will be existing teachers not currently specialising in maths and physics, who will be retrained to teach the subjects.

The remaining 2,500 will be a combination of new graduates, career-changers and former teachers returning to the classroom. 

In addition, the government will make £20,000 available to school partnerships to set up pilot training programmes for career-switchers, the statement adds. The first trainees under these programmes will enter classrooms in September 2016.

Universities will pilot new physics degrees giving students a teaching qualification alongside their three-year degree course.

The government will also offer salaries of up to £40,000 to more than 100 university fellows to teach in schools and train teachers, the statement says.

“I want to make Britain the best place in the world to learn maths and science - and because of our growing economy, we have a clear plan to deliver the best teachers to make this happen,” Mr Cameron said.

Education secretary Nicky Morgan said: “We want to attract more high-quality candidates to teach maths and physics and further raise the status of teaching as a rewarding career. By offering more flexible routes, we will open up the teaching profession to talented career-changers who can bring a wealth of experience and transferable skills to the classroom.”

Brian Lightman, general secretary of the Association of School and College Leaders, said the announcement was “welcome” but did not go far enough.

“Far more fundamental reforms are needed to address a crisis in teacher recruitment,” he added. “There is a need for a robust strategy plan to make sure there are enough teachers coming through in every subject.”

Christine Blower, general secretary of the NUT teaching union, said the government should fund all trainee teachers rather than “just those in selected subjects and phases”.

“Teacher recruitment and teacher retention have become areas of crisis,” she said. “There is growing evidence of shortages in secondary subjects like music, geography and design and technology.

“[The government] needs to develop a comprehensive strategy to address the problems - not a piecemeal approach.” 

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