Thousands of schools will either shut down completely or be sending some pupils home when teachers stage a one-day strike next Wednesday, heads warned today.
Members of the Association of School and College Leaders warned that there would be widespread disruption throughout England and Wales as a result of the 24-hour stoppage.
They also rejected suggestions previously made by Education Secretary Michael Gove that they should consider enlisting an army of volunteers to help keep the school going.
Ian Bauckham, president of ASCL, speaking at its annual conference in Birmingham, said: "I would have far more sleepless nights over an army of mums and dads coming in to keep the school open than I would over anything else."
Members of the National Union of Teachers are staging the one-day strike in protest over their pay, pensions and working conditions. In particular, they are incensed over government plans to introduce performance-related pay by giving headteachers the power to set their own staff's salaries.
The second union involved in the dispute, the National Association of Schoolmasters Union of Women Teachers, is resisting strike action at this time - but its members have said they will not take the classes of colleagues who are on strike.
Headteachers said that that more than half of the 3,500 secondary schools could be severely disrupted by the strike - as the union represents secondary school heads and deputies. However, the NUT's strength is in the primary sector, so many of the 16,000 primary schools are likely to close as well.
The unions are involved in talks with Mr Gove's department over the dispute but so far these have not shown any sign of a settlement being reached.
The dispute is likely to escalate in the coming months, with both unions holding their annual conferences over Easter. At the NUT conference there are likely to be demands for more militant action from delegates.
The Department for Education has condemned the strikes - saying all they will do is disrupt children's education.
Meanwhile, in his address to the ASCL conference, Mr Bauckham warned that the "culture of celebrity" was stopping young pupils from striving to improve themselves at school.
"We inhabit a culture which idolises celebrity," he said. "Look at TV shows such as X Factor or Britain's Got Talent. The problem with them, to my mind, goes further still than encouraging a reliance on chance to make your fortune.
"The subliminal message is one which says: you either have or you haven't got 'talent' or the 'X Factor'. There is little you can do, we are encouraged to think, if you are one of the unlucky ones."