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Russell Hobby, general secretary of the Haywards Heath-based National Association of Head Teachers (NAHT), says schools which had taken in students when the Discovery New School, Crawley, was shut had reported that some youngsters were a term behind where they should have been in their education.
In his speech to the NAHT's annual conference in Birmingham, Mr Hobby will express concerns about the pace of education reforms, arguing they have been rushed through in order to show results before the next election.
"The dangers of poorly thought through policy, rushed in to be able to claim a result, are also exemplified in the shaky results delivered by the earliest free schools.
"Some free schools are performing highly and, to be fair, few schools could have lived up to the hype attached to them, but some people were given schools to run who should not have been allowed near them.
"I have spoken to schools who have taken in children after the collapse of one free school. They reported for one group that after one term of education they were precisely one term behind where they should have been. They had been taught nothing.''
Free schools - state schools that are free from local council control with power over areas such as the curriculum - are one of the Government's key education policies.
Three-quarters of the first 24 free schools that opened in autumn 2011 have been declared good or better by Ofsted.