The motion represents a further straining of relationships between the NAHT and Ofsted, coming just days after the association raised concerns about the quality and impartiality of school inspections.
It would also pave the way for more schools to become academies, for reduced school inspections and for greater intervention in failing schools.
Perhaps school league-tables and regular inspections are improving the quality of teaching.
Under the plans, there will be changes to school performance tables, Ofsted inspections and governance, and a "pupil premium" system will channel more money to the most deprived children.
The general secretary of the NASUWT teachers' union, Chris Keates, said the national curriculum had been undermined for far too long by the "punitive" school accountability regime based on performance tables and Ofsted inspections.
"I think inspections have improved standards and if there are problems or difficulties in a school then there are mechanisms to help that school, " he said.
Previous changes to school inspections had "raised the bar" because the country had higher expectations and standards appeared to drop when a new framework was introduced.
The Association of Directors of Children's Services says the decision to bring in new inspections of council school improvement services "without notice" is "regrettable and unsound".
Mr Kershaw said the council welcomed the latest inspections and that it was on "a secure journey of improvement to ensure that every school in Coventry is good or outstanding".
West Dunbartonshire said food safety officers were carrying out inspections on four meat production plants in the area but that meals supplied to school canteens and council care homes were not affected.
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