Ofsted's report on maths teaching, published at the end of last year, said too much of it was "taught to the test" and that this did not equip pupils for their futures.

BBC: Maths teachers 'taught to teach'

One analyst told the BBC the military might ultimately wish to equip soldiers with a range of these pencils to provide a portable test kit for a range of harmful gases.

BBC: MIT pencil 'draws' gas sensors onto paper

"Strategies to improve test and examination performance, coupled with teaching that focuses heavily on preparation for the qualifications, does not equip pupils for their futures, " says the booklet destined for secondary schools.

BBC: Maths teachers 'taught to teach'