The shortage of science and maths teachers is being made worse by a lack of reliable statistics, scientists say.
Science and maths expertise is key for economic growth
Analysis for scientists body the Royal Society concludes there are not enough physics, chemistry, biology and maths specialists in the UK's schools.
The government's own data showed science and maths recruitment targets were missed in 2005-6, it said.
But the patchy nature of the figures hampered the government's ability to tackle the issue effectively, it added.
The report said the quality of data available on teachers was "patchy".
But the government's own information suggested recruitment to teacher training courses in 2005-6 fell short of targets by 10% in science and by 18% in maths.
The targets themselves were based on unreliable information, with the teacher shortage likely to be much higher.
The report added: "No accurate estimate of the population of science and mathematics teachers in the UK exists, nor can this be obtained from the available data."
This was partly because there was no consensus about how a "specialist" science or maths teacher should be defined.
It was also because there was no up-to-date detailed knowledge of the number of UK primary teachers with a maths or science background.
And the two main sources of data on secondary school science and maths teachers were not reliable enough to represent the national picture.
Director of education at the Royal Society, Michael Reiss, said the government often talked about the importance of science and mathematics to the economy.
He said: "The vision of an economy driven by innovation will never become a reality unless there are enough high quality teachers in science and mathematics.
"The government's own workforce modelling is simply not fit for purpose.
"It is time that people woke up to the true scale of the problem and did something about it."
The Royal Society called for the teachers' regulatory bodies - the General Teaching Council in each part of the UK - to monitor the specialisms of the teachers they registered.
It also said the demand for maths and science specialists should be monitored more rigorously.
England's Department for Children, Schools and Families rejected the claims, saying it had done a great deal to recruit science and maths graduates into teaching.
"Thanks to bursaries and 'golden hellos' for maths teachers we have seen a large rise in recruitment of maths teachers – over 2,300 last year compared to 1,400 in 2001," it said in a statement.
"We have set targets for improving the proportion of physics and chemistry specialist teachers and our strategy of recruitment, retraining and retention is working.
"By 2014 25% of science teachers will have a physics specialism (compared to 19% currently), and 31% of science teachers will have a chemistry specialism (compared to 25% currently)."
But assistant director of the Campaign for Science and Engineering in the UK, Dr Hilary Leevers, said: "We appreciate many of the government's efforts to increase teacher training in shortage subjects, it must recognise that its own targets are not being met and were conservative to say the least.
"These targets could be lower if the appalling retention of teachers, could be improved.
"Currently only 50% are still in the profession five years after graduating."