The scale of schools' struggle to find supply teachers has been revealed in new figures obtained by TESS.
Schools in parts of Scotland are failing to get the supply cover they are entitled to, meaning that senior management and "babysitting" teachers who have no relevant subject experience are being forced to take lessons.
The figures emerged after TESS asked all 32 local authorities how many supply days that schools were entitled to went unfilled in the summer term. Most said that they did not hold this information but Glasgow recorded 46,679.5 supply days being requested, of which 13,644 were not covered. West Dunbartonshire, a far smaller authority, said that 622 supply days went unfilled in primary, secondary and special schools.
A West Dunbartonshire spokeswoman said the shortage of supply teachers was causing particular problems in Catholic schools, but added: "To date we have managed to deliver all of our classes in our schools through the use of headteachers and deputes to cover when supply staff cannot be found."
Another respondent, Perth and Kinross, had 111 days unfilled, almost all in primary schools. In Renfrewshire 99 days were not covered by a supply teacher and in Midlothian 92 days were unfilled in primary and special schools.
The smallest mainland authority, Clackmannanshire, reported that 90 per cent of supply requests to its human resources department from schools were not met, leaving schools to plug the gaps by arranging their own supply or rely on senior staff.
Greg Dempster, general secretary of the school leaders' body AHDS, said: "I expect the statistics would paint a more bleak picture in many authorities. This pressure on the system compromises the capacity to drive improvement. This needs to be recognised in any assessment of school performance."
Ken Cunningham, general secretary of School Leaders Scotland, said it was hard to assess the significance of the figures without comparable data from previous years. He added that it was easier to cover classes in the last term of the year when exams were taking place and classes were changing.
The picture around the country varied, he said, but the situation did not seem to have worsened in recent months.
Bruce Robertson of education directors' body ADES, formerly a director of education in Highland and Aberdeenshire, said: "The supply situation has been bad all over, as illustrated by Glasgow City Council, but some rural and north-east authorities have been badly hit, with senior staff regularly covering classes and non-subject specialists babysitting lessons."
Pay for supply teachers was one of the most controversial aspects of the 2011 national pay and conditions agreement. They were required to work five days at a lower rate before receiving full pay, although that was later reduced to two days.
A TESS survey in October 2014 showed that most authorities were struggling to recruit supply staff. Earlier this year, in research by the Scottish Secondary Teachers' Association, some schools described the supply situation as the worst they had ever faced. In one case, an 82-year-old teacher agreed to return to the classroom for a few days but ended up staying for months.
Larry Flanagan, general secretary of the EIS teaching union said: "This is placing an intolerable burden on teaching staff. Staff numbers have fallen in recent years and class sizes are rising, so teachers - including management staff - are frequently expected to provide ad hoc cover for colleagues who are ill, with major implications for their own workload."