A new HSE study shows just 4 per cent of children tested positive for the virus during the last school year.
On Saturday the country saw infections hit a 7-month high, but the Taoiseach has warned case numbers may not peak until the end of September.
ASTI President Eamon Dennehy says teachers are very worried about this:
"If we ignore the warning signs that we might be getting now, schools will inevitably not be able to continue if Coronavirus becomes a serious issue inside them. Every measure that we can take, has to be taken to keep them safe, the worrying thing, of course, is as we move into September and October, the weather will disimprove, I assume. It will make ventilation etc. in schools somewhat more difficult."