Schools can build pupils' "resilience to radicalisation" by promoting British values, according to official advice on new counter-extremism measures.
From last month councils, public bodies were placed under statutory duty to take action to stop people being drawn into terrorism.
The Department for Education (DfE) has issued advice for schools and childcare providers on how to meet the new requirement - known as the Prevent duty.
It said: "Schools and childcare providers can also build pupils' resilience to radicalisation by promoting fundamental British values and enabling them to challenge extremist views.
"It is important to emphasise that the Prevent duty is not intended to stop pupils debating controversial issues.
"On the contrary, schools should provide a safe space in which children, young people and staff can understand the risks associated with terrorism and develop the knowledge and skills to be able to challenge extremist arguments."
The obligation to protect children from the risk of radicalisation should be seen as part of schools' wider safeguarding duties and is similar to the requirement to guard against other harms such as drugs, gangs and sexual exploitation, the advice said.
Schools are expected to assess the risk of children being drawn into terrorism, which can include support for extremist ideas that are "part of terrorist ideology".
Extremism is defined by the Government as "vocal or active opposition to fundamental British values, including democracy, the rule of law, individual liberty and mutual respect and tolerance of different faiths and beliefs".
The definition also includes calls for the death of members of the UK armed forces.
Schools should also be aware of the increased risk of online radicalisation, the guidance said, citing terrorist organisations such as Islamic State - also known as Isil - who "seek to radicalise young people through the use of social media and the internet".
Measures to meet this requirement include making sure adequate online filtering is in place in school IT departments.
The DfE advice says: "As with other online risks of harm, every teacher needs to be aware of the risks posed by the online activity of extremist and terrorist groups."
Teachers are also told that even "very young" children may be vulnerable to radicalisation.
The advice says: "The Prevent duty does not require teachers or childcare providers to carry out unnecessary intrusion into family life but as with any other safeguarding risk, they must take action when they observe behaviour of concern."
Councils, prisons, NHS trusts and schools are required under the Counter Terrorism and Security Act to have "due regard to the need to prevent people from being drawn into terrorism".
The measure is a strand of the Government's efforts to tackle extremism.
Last month figures showed that children and teenagers are being referred to the Channel counter-radicalisation programme at a rate of one a day.