Eight into four doesn't go - as every primary pupil knows. So when North Lanarkshire Council merged eight departments into four this week, there were four directors left over.
The most high-profile of these is Michael O'Neill, one of the influential directors of education in the last decade, who decided not to apply for the new post of head of learning and leisure. He will leave the council in March.
The moves at North Lanarkshire mirror activity in other authorities.
Glasgow City Council is aiming to cut pound;1.2 million from its budget by reducing senior management layers, and it is increasingly hard to find an education director who does not have responsibility for other services, such as the wider social work aspects of children's services, culture or leisure.
This week's annual conference of the Association of Directors of Education in Scotland has public service reform as its theme. The catalysts behind the reform agenda are the Scottish Executive's efficient government strategy and the cost of implementing the regulations on equal pay for jobs of equal status.
It is being predicted that Mr O'Neill will appear in some other guise on the education scene when he leaves. In the 11 years he has run the council's education department, he has established a reputation as a groundbreaker, delivering vocational education in schools and pioneering "enhanced comprehensives" in sport, music and enterprise.
Mr O'Neill was also the forerunner in using the relaxation of age and stage regulations to enter pupils for Standard grade and Intermediate exams in S3. The adoption of co-operative learning, in which 2,500 teachers have now been trained, was another focus.
Mr O'Neill is proud of the fact that he has insisted on maintaining direct contact with teaching staff. He still does evaluation visits to schools, works with heads on their personal review plans and is involved in target-setting for secondary schools and key appointments.
There is now a growing likelihood of education coming under the control of directors who have never been teachers (the current advert for the Pounds 120,000 a year post as director of children and families in Edinburgh does not stipulate any requirement for an education background, only that applicants should have "significant general management experience at a senior level in a large, complex organisation").
Mr O'Neill believes this would be a retrograde step. "Someone with no education background has no understanding of what is going on on a day-to-day basis," he believes. "They can't make appropriate decisions. You need to have someone in charge of education who has credibility with headteachers.
"If the person in charge is defining a vision, they need to understand it themselves, otherwise they are not in a position to tell whether the advice being given to them is good, bad or indifferent."