Do headteachers have to have been teachers themselves? Does each school need its own head, or could a "chief executive" oversee several schools?
These are two of the questions being considered by the House of Commons education select committee in its review of the headteacher's role.
Chairwoman Margaret Hodge MP said the committee was not merely aiming to alter the current head's responsibilites, but was looking for ideas on how a new school staffing structure could meet the challenges of the new millennium.
But three headteachers' organisations told the committee it was crucial that heads had classroom experience if they were to command the respect of staff.
David Hart, general secretary of the National Association of Head Teachers, said: "The respect of the staff comes partly through an acknowledgement by them that the head understands the dynamics of teaching in the classroom. It would be difficult for someone without such experience to motivate a staff who felt the head did not understand what it means to be a teacher."
But Don Foster MP, the Liberal Democrats' education spokesman, said such a system already operated in hospitals.
"The reality of the health service is that someone with no medical training effectively manages a hospital full of highly skilled doctors and nurses," he said. "You cannot say that the doctors have no respect for their chief executive because he's not a doctor."
Mr Hart countered: "Look what happened to the health service when managers with no clinical knowledge were brought in to manage clinical staff and budgets - massive demotivation and tension between the two camps."
The National Primary Headteachers' Association, the Secondary Heads Association and the NAHT were unanimous that running one school was a full-time job and that the introduction of "super heads" would simply add another management layer and accountability would be diminished.
Education officers and governors' groups who gave evidence last week agreed that the role of the head must change. Pat Petch, chairwoman of the National Governors' Council, said schools would become learning centres that needed new-style leaders. "I envisage a centre manager would be needed to oversee the school day and another manager would be in charge of community work," she said.
"The two would work together at the interface where you could have children teaching adults because that is how you bring people back into learning."
The committee is due to publish its report before Parliament's summer recess.