By Sean Coughlan
BBC News education correspondent
Michael Gove called on the union to show how it could run a school
A teachers' union has been challenged to open its own school - in a debate with the Conservatives about their "free school" policy.
The Tories want parents and other organisations to have state funds to set up their own schools.
Shadow schools secretary Michael Gove issued the call in a speech to the NASUWT teachers' union conference.
The union's leader, Chris Keates, rejected the idea, saying the policy was for the "pushy and the privileged".
Eve of election
Mr Gove's speech to the NASUWT conference - and the response from the union's general secretary - was made against the backdrop of the approaching general election.
The Tories want to "dismantle state education", says Chris Keates
It was literally against an election backdrop - as Mr Gove was made to watch a giant screen showing teachers talking about how poorly funded schools had been under the last Conservative government.
In a sharply-delivered exchange of ideas, Mr Gove promised his commitment to promoting the professional integrity of teachers, and Ms Keates pushed him for promises on the future of state education under a Tory government.
Against some heckling - unusual for a NASUWT conference - Mr Gove defended his proposals for free schools - which would give state school funding to other providers to run their own schools.
Challenged on whether he would guarantee that there would be no profit-making companies taking part in this project, he said that he could not give such an assurance, as there were already profit-making companies involved in state education.
But Mr Gove also lay down his own challenge - calling upon the union to put its own principles into practice by setting up its own school, under the free school policy.
'Pushy and privileged'
He gave the example of charter schools in the United States working in the most deprived areas and giving an extra option for the poorest communities.
The Conservatives want to follow the example of US charter schools
And he called on the NASUWT to create a school which would demonstrate the skills and beliefs of the teachers' union.
This would not be the first time a union has run a school - in Boston in the United States a teachers' union is running its own "pilot school", which is a form of autonomous school within the state system.
The proposal was given a terse response by Ms Keates.
The union did not want to run a school, she said. Schools should be "democratically accountable" and not operated for and by "the pushy and the privileged".
Speaking ahead of the speech, Ms Keates had told journalists that she thought that the free schools policy was "dismantling state education".
The Conservatives have also praised the free schools in Sweden, but Ms Keates took issue with this system where she said such schools could be bought and sold for profit.
"There is something abhorrent about selling schools and their pupils and staff," she said.
But speaking after the conference exchange, Mr Gove challenged the idea that state education always had to be provided by the state - saying that historically it had had many different and diverse providers, such as faith schools.
And he argued that if there was evidence from other countries that a wider range of providers raised standards then it would be "perverse not to pursue diversity".
Mr Gove's speech to delegates sought to find common ground with the teachers' union.
He recalled his own time as a striking journalist on a picket line - "warming my feet on a brazier" - and then set out some of the areas of common agreement.
The Conservatives want a cutting down to size of Ofsted, a less prescriptive curriculum and the scrapping of plans to make teachers have a renewable "licence to teach".
Mr Gove also promised to do more to protect teachers who might have their careers ruined by malicious allegations from pupils.
He also argued that teachers should not be expected to act as "social workers or surrogate parents", solving all of society's problems.
But the prospect of divisions over the forthcoming election overshadowed common ground and Mr Gove admitted at the outset that the next few weeks of the election campaign would be one long "extended job application".