At about pound;4 billion a year, education is the largest budget managed by Scottish councils, accounting for roughly 30 per cent of expenditure.
But in East Lothian Council, the education service is run by an official with no schools experience and a background in banking and marketing. And according to education directors' body ADES, there is a similar shortage of expertise in at least three other councils. TESS understands that these are Scottish Borders, Renfrewshire and Highland.
ADES has warned that this is part of a trend by some local authorities to phase out the director of education role. In Renfrewshire and Highland, the directors with responsibility for education come from social work backgrounds, and in the Scottish Borders the depute chief executive with responsibility for education is a former police officer.
However, the councils have defended their leadership structures, arguing that education has a strong voice.
ADES made its claim that some councils lacked educational expertise to the Scottish Parliament's Education Committee, which was scrutinising the government's plans to force councils to appoint a chief education officer. Education secretary Angela Constance has said that she wants to "guard against" education being run by people without teaching backgrounds.
"There should be someone who has experience of teaching and working with children - who knows what it is like at the chalkface - within the senior management team of any education service," Ms Constance told the committee.
But according to ADES' general secretary, John Stodter, over the past three years four councils have "begun not to have the [chief education officer] post".
"Councils act as education authorities," he said. "The fact that they do not have a person who is appropriately qualified and experienced to advise them in that capacity seems strange."
ADES president John Fyffe told TESS that Scottish councils were close to the tipping point where quality education advice was concerned.
"If you want legal advice you go to a lawyer; the same logic applies here, but local authorities are employing fewer and fewer directors and heads of service because of financial austerity," he said. "Local authorities need flexibility to be able to respond to financial challenges but they also need high-quality advice, guidance and leadership."
Larry Flanagan, general secretary of the EIS teaching union, agreed, warning that directors of education were being "marginalised". He said: "We are sympathetic to the idea that there should be someone in a senior position in local authorities who is a qualified teacher and understands how schools operate and the legislation around schools."
Eileen Prior, executive director of the Scottish Parent Teacher Council, told the committee: "We have seen, on several occasions, that those at a very senior level can lack an understanding of, for instance, parental involvement legislation."
ADES added that introducing a chief education officer role would ensure that councils met legal requirements around additional support needs, Gaelic provision and school closures.
A new panel set up to review councils' plans for school closures has already overturned one decision, explaining that Highland Council had not fulfilled its legal obligations when it sought to shut four primaries on Skye.
However, the council rejected claims that its senior management team lacked educational expertise. A spokeswoman said that the council had integrated education, health and social care services to promote improved outcomes for children, families and communities. She added that the director of care and learning was not from an education background but he was supported by the head of education, a former headteacher.
Scottish Borders Council, meanwhile, argued that it had actually increased the number of senior education officers in its restructure last year.
The education convener for Renfrewshire Council, Jacqueline Henry, said that the senior management team had several heads of service with teaching and school management experience.
She added: "The evidence shows that Renfrewshire's integrated approach on education and broader children's services is delivering for children, parents and communities."
According to local authorities umbrella body Cosla, which opposes the introduction of chief education officers, "practically every local authority in the land" employs someone senior with an education qualification and experience.
However, the body's Robert Nicol admitted to MSPs that one council "would need to make an appointment" if chief education officers were introduced. Further investigation by TESS revealed that authority to be East Lothian.
East Lothian Council said it had decided more than six years ago to introduce a management structure based on generic heads of service. Post-holders were expected to have "key leadership skills and experience" rather than "specific technical skills".
The current head of education has been with the council since 2012; before that he was product and marketing director at investment and savings business Alliance Trust.
The requirement for local authorities to employ a director of education was removed in 1996. Today it is relatively uncommon for Scottish councils to have a service consisting solely of education led by a director with an educational background. More frequently, education forms the largest part of a service with wider responsibilities.
However, in its submission to the education committee, the Royal Society of Edinburgh argued that the Scottish government had "not produced evidence of a widespread problem that called for the legislative establishment of the post of chief education officer".
Mr Flanagan, meanwhile, warned that the move could "hasten the demise" of educationalists in roles more senior than that of chief education officer.
"This could make it easier for councils not to have a director of education and instead simply to have a cheaper and ultimately inferior chief education officer," he said.