A senior figure in Scottish education has backed the idea of allowing charitable trusts and not-for-profit companies to run schools.
Keir Bloomer is a former leader of the Association of Directors of Education, who has also been an adviser to the Scottish government.
He thinks councils should no longer run all publicly-funded schools.
But Scottish teaching union, the EIS, warned against sweeping changes to the way schools were run.
Drew Morrice, the union's assistant secretary, said the current system was working well.
Education expert Mr Bloomer will be among a number of speakers at a conference in Edinburgh on managing Scotland's schools.
He suggested that if schools were run by non-profit making companies or charitable trusts they would be more effective, as they would have more control over what they do and how they spend their money.
He argued that clusters of schools could become directly funded and take control of all their functions - including payroll, catering and cleaning as well as matters such as development of their curriculum.
Mr Bloomer said that after next year's election the new Scottish government should set up a commission to examine how schools are run.
He said: "Frankly education systems all round the world are falling behind the needs of children in the contemporary world and the reason for that is the way in which systems are run is unduly centralised, top-down and bureaucratic.
"What we need to do is give much more power directly to individual schools to ensure that decisions are made near to the point where they have impact."
He said he believed that when teachers were able to make direct decisions it would benefit children in the long run.
Mr Bloomer added: "I think progress is made in the modern world by releasing the creative energies of people, in this case the teacher, and the system that we have at the present moment constrains them far too much by direction from the top."
The architect of the new Curriculum for Excellence approach in Scottish schools also argued that decisions on support services, such as maintenance and catering, should be made at a more local level.
He went on to say that his suggestions were not based on a political agenda but rather a bid to empower schools to do a better job.
However, Mr Morrice said that the people who knew where the problems were in education were at both the council level and school level.
He added: "They are directors of education who have a fountain of knowledge and can deliver across the services.
"If you divide schools, how do schools deal with such things as falling school rolls and the pressures which arise from school closure situations?
"You need that level above the school to organise and structure education - you remove that at your peril."