Councils must come up with imaginative ideas to improve education in exchange for the freedom to cut teacher numbers, the Education Secretary has said.

Increasing the school starting age to six, more shared services between local authorities and sending pupils to "hub" schools for certain lessons were among the ideas floated by council representatives at Holyrood's Education Committee today.

Education Secretary Mike Russell has suspended sanctions for councils that want to cut teacher numbers while discussions on the 2015/16 budget are under way in a move designed to broaden ideas on improving education.

Mr Russell said he does not believe cutting teacher numbers will improve education, speaking at Holyrood's Education Committee today.

But council umbrella group Cosla said "the jury is still out" on the link between teacher numbers and attainment, and said it wants to move away from "crude input measures" towards improving the educational output.

No agreement has been reached on maintaining teacher numbers in 2015/16, Cosla confirmed.

But council officials have warned that any alternatives must demonstrate a clear educational benefit, be cheaper and more efficient, and must not disadvantage pupils and parents.

Mr Russell said: "Let me make it absolutely clear: I don't believe you can drive up attainment and improve outcomes with fewer teachers.

"We are, of course, committed to working with local government, with the engagement of parents and trade unions, in seeking to reach an agreement on better educational outcomes and what those might be."

He added: "There is strong argument for imagining and putting in place better ways of delivering, for example, shared services and issues of that nature."

Mr Russell said it is "perfectly possible" to increase teacher numbers "provided the resources are provided", but said people must recognise "the realities of finance, austerity and the roles of Scottish local authorities - in particular Labour authorities".

"If there is no agreement on outcomes, then the sanctions will continue," he said.

"They haven't been lifted, but they are not going to be operated while we have this discussion."

Local government minister Derek MacKay told the committee: "We want public authorities and local authorities to be free to work across boundaries.

"The boundaries are arbitrary and if you were to design local government nobody would design it the way it is right now - it's a construct of previous Tory gerrymandering.

"But the energy and years of court battles it would take to redraw local authorities I don't think would be worth the effort when all our focus and energy should be on productivity and the outcomes that really matter, rather than boundary disputes."

Cosla education spokesman Douglas Chapman said: "In years gone past a lot of local authorities have tried to protect education because they valued that as a key service.

"We are now at a stage where it is difficult to offer that level of protection as much as we would want to do because there are other demographic pressures of people growing older and needing more care."

He added: "We're trying to move away from crude input measures to looking more at what the outcomes might be.

"In terms of teacher numbers if there was a reduction, the impact might be you have larger classes in some subjects.

"Whether there is a direct link between a fall in teacher numbers and maintaining the level of attainment you want to see or improvement in attainment - I think the jury is out on that one but nevertheless it would have an impact in terms of teachers I'm sure."

John Stodter, general secretary of the Association of Directors of Education in Scotland, said: "There's two things that need to happen before we get into the detail of what the ideas might be.

"One is an agreement from politicians - the government, MSPs and Cosla - that we can look at the whole system of the learner journey from the very early years to 18 and beyond.

"We would then need discussions about specific ideas and what these might mean.

"These should work in a way that shows that, one, there is clearly an educational advantage and benefit that improves it and, two, that it is more efficient and that there may be a financial saving it.

"The third element would be that we have to ensure that no-one is disadvantaged by it.

"I'm not suggesting this, but people have talked about the age at which children start school.

"Some schools and authorities say that six-years-old could be a better time to start school education.

"If that were to be educationally proven then you would have to ensure that families weren't disadvantaged by that process, and that you had a system that could support children starting at six and you were confident that it was going to lead to improved outcomes."