Pupils across the country have continued attending classes, even when 11 local council areas were placed under the toughest level four Covid-19 restrictions.
The EIS teaching union has reiterated its calls for the Scottish Government to consider blended learning - where youngsters learn remotely from home for part of the school week.
General secretary Larry Flanagan said: "Our members want to be in schools working with pupils, but they also want pupils and staff to be safe.
"The Scottish Government's rejection of remote or blended learning for schools in areas with high rates of infection has increased the level of risk for pupils, teachers and their families.
"It is time for the Scottish Government to rethink this damaging policy, with the danger of increasing rates of community infection throughout the winter months."
The EIS has published new papers highlighting teachers' concerns.
These include difficulties with social distancing in classrooms, face coverings "not being worn consistently" in secondary schools where senior pupils and teachers are required to wear them, and fears from some that case numbers in schools are not being recorded accurately.
One teacher said: "It is a pretence to say that Covid protections are fully in place."
But Ms Sturgeon cited new reports from Public Health Scotland as backing up the Scottish Government's stance that schools should remain open.
The First Minister, speaking at her regular coronavirus briefing on Wednesday, said the figures showed "almost two-thirds of schools have not had any pupil cases of Covid".
Around 620 children aged between two and 17 are diagnosed with coronavirus every week in Scotland - a rate of 70 per 100,000 children, Public Health Scotland found.
Speaking about the impact of the virus on school staff, Ms Sturgeon said the experts had found "no evidence of any difference in the risk of hospitalisation for teachers when compared to the general population".
She said the risk of severe Covid-19 "actually seems to be lower in teachers than in the population as a whole".