The claims mean that the Covid tracking app will not report any close contacts.
Jane Peckham, National Officer (Scotland) of the NASUWT union, said: “I am aware that sometimes staff contacted through the Test and Trace app feel pressure from management not to isolate themselves.
“And there is also an issue where staff in some areas are being asked to turn off Bluetooth enabled for their app in case it causes a significant number of employees to self-isolate.
“We are getting reports that members are being asked to exceed class size limits because there is not enough staff. Members believe they should move towards a blended learning model. ”
It comes after two more deaths from the coronavirus were recorded yesterday in Scotland overnight.
The Scottish government announced the figures and also said that 746 new cases of COVID-19 had been reported in the same period.
The total number of coronavirus deaths in Scotland since the start of the pandemic is now 3,722 and the total number of positive cases is 94,689.
Yesterday 1,049 people were hospitalized for Covid-19 and 76 people were in intensive care.