The move is part of what David Cameron labelled a “full spectrum” response to extremism in schools, universities and prisons.
A Whitehall source likened radicalisation of young people to child exploitation and said that the guidance sent to teachers will tell them that it must be treated as a “safeguarding issue”.
They said: “This is grooming and should be dealt with in the same way as child exploitation.
“The extremists use the internet to recruit young people and schools should be teaching about the dangers of that.”
It comes as the Prime Minister announced a national minute’s silence on Friday of the victims of the tunisian terrorist attack – in which 18 British people have been killed.
It is also feared that up to 30 Britons could have died in the attack, carried out by 24-year-old Seifeddine Rezgui.