The plans for a radical shake-up of education would also see councils having much less of a role to play in the day-to-day running of schools.
Such a shift would give headteachers greater control over a range of areas, including the recruitment of talented teachers to work in deprived areas by offering financial incentives.
The proposals are contained in the final report of the independent Commission on School Reform, which was set up in 2011 by the think-tanks Reform Scotland and the Centre for Scottish Public Policy.
The commission, chaired by educationalist Keir Bloomer, has produced 37 recommendations covering improvements to the Curriculum for Excellence reforms, targeted support for pupils and schools in disadvantaged areas and greater support for families from birth.
It also calls for a centre dedicated to improving education outcomes in deprived areas and argues previous reforms have failed to close the attainment gap and are not delivering sufficient improvements in either basic literacy and numeracy or more advanced skills vital to the future of the economy.
Mr Bloomer said the changes were needed to address deep-seated problems with the schooling system that have developed over decades.
"There is an assumption in Scotland that our education system has always been and is now among the world's best," he said. "There may have been a time when that was true, but unfortunately it is not true now.
"Scotland's schools do an excellent job. The standard of education they provide is high and it is remarkably consistent across the country.
"But they are no longer world-leading. If we want to be back again in the position of being the world's best then there is no alternative but to make some quite significant changes."
Mr Bloomer said the commission had ruled out a move towards academy schools introduced in England, where funding comes from central rather than local government. While local authorities would still be responsible for allocating money to education in their areas, the commission is advocating a significant shift in their role.
"At the present moment, in many cases councils have a tendency to be too much involved in the day-to-day management of schools," he said.
"We do think that once money has been determined for allocation to education then that should be delegated to schools and it should be as far as possible be delegated to schools without strings attached.
"We are suggesting that schools must be more empowered than they are at the present time, freer to take decisions that they believe to be in the interests of the young people in the circumstances in which they are found. Scottish education, at least at the macro level, is astonishingly uniform, and the problem with a uniform system is that it does not have the capacity to learn from its own varied experience."
Douglas Chapman, education spokesman for council body Cosla, said the suggestion could damage the work councils did with other services such as social work and the NHS.
"We would argue that more autonomy does not necessarily lead to better outcomes for children and could potentially make the inter-agency working that is happening right now more difficult," he said.
"While we would encourage staff to work within schools, across clusters and with other professionals, we do not accept there is enough evidence for wholesale change within school structures, nor would we accept a dilution of democratic oversight of school performance and pupil outcomes."
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