The Guardian (4 September, p7) reported that Mr Woodhead challenged Scottish educationists to consider if their schools should buy services which were not being well provided by local education authorities.
'Is there anything the LEA does now that the market can do better? The question I think should be asked in Scotland as well as in England is how does an LEA's strategic vison mesh with a school's responsibility to manage its own destiny?' said Mr Woodhead.
He said he was concerned that most LEAs retained a fifth of their share of national schools budget for their own use, and that many critics believed that that money would be better spent if it went straight to schools.
But Keir Bloomer, a spokesman for the Convention of Scottish Local Authorities, said most councils spent much less than 20% of their education budgets on central costs and in some cases as little as 10%.
Mr Bloomer added: 'There is a limit to the extent to which headteachers want to be their own accountants, clerks of works and lawyers.
'Local authorities offer a one-stop shop for a wide range of such support services and in that role they provide schools with good value for money.'