Young pupils from European backgrounds fear they may be forced to leave Britain, heads are warning in an open letter to the Prime Minister.
National Association of Head Teachers general secretary Russell Hobby says many are fearful of a potential rise in racism and community conflict.
He called for a government statement to reassure European Union pupils.
David Cameron has told MPs that EU nationals’ rights are guaranteed while Britain remains in the EU.
And he stressed that those in the Leave campaign also wanted to guarantee the rights of those working and studying in Britain.
“But,” he added, “we can’t say that now, we have to say that as part of the negotiation that will shortly take place.”
‘Address their fears’
Mr Hobby said in his letter: “Pupils are worried about being forced to leave Britain.
“They are fearful of a potential rise in racism and community conflict. They are concerned about their prospects in an uncertain and isolated Britain.
“It is not just the economic markets that need calming. Our young people need a statement from the government to address their fears.
“NAHT strongly urges the government to give pupils from the EU better assurance that they will be able to complete their school education without interruption; that they and their families remain welcome and valued members of the communities they call home.
“Our schools are the places in which we shape our future as a nation. Our teachers and school leaders can help young people make sense of dramatic changes and build their own plans.
“To do this, we need clarity, swiftly. Please do not ignore the impact of the EU referendum result on the next generation.”
The letter comes after a reported upsurge in racist incidents, in the wake of the vote to leave the EU.
In Parliament on Monday, Mr Cameron said: “In the past few days we have seen despicable graffiti daubed on a Polish community centre, we’ve seen verbal abuse hurled against individuals because they are members of ethnic minorities,” Cameron said.
“Let’s remember these people have come here and made a wonderful contribution to our country. We will not stand for hate crime or these kinds of attacks, they must be stamped out.”
In a statement a Department for Education spokesman said no child “should live in fear or racism or bullying”.
“The Prime Minister has been clear there will be no immediate changes for European citizens living in the UK.
“We will not stand for intolerance and hate crimes of any kind must be stamped out,” said the spokesman.
The National Union of Teachers is now working on materials to teachers to use in schools at a time of increasing racial tension.
