Teachers have been 'guaranteed' that improvements will be made around the approach to COVID-19 in schools, according to the TUI.
It comes as thousands of school children are restricting movements after being deemed close contacts of confirmed coronavirus cases.
Michael Gillespie is general-secretary of the TUI. He told Newstalk Breakfast the last week put everyone under pressure.
"Last week what we saw was unacceptable and hugely stressful delays for principals seeking information, especially early in the week.
"We made strong representations that this should cease, and we've been guaranteed that improvements would be made."
And he says that the next week or so will show how the Delta variant is spreading.
"Anybody could have saw that surge coming... but what we're waiting for now over the next two weeks is the results of those tests.
"They're going to come after five and 10 days, and we'll see how the Delta variant is spreading.
"And we're waiting to see how that testing now turns into numbers.
"If there's going to be any change in close contact testing, it must be based on sound public health advice - and not because of any deficits in contact tracing - but we need to wait for a while longer.
"We closed schools last May, June when there was a different variant predominant, we had smaller numbers.
"Now we're going back with larger numbers and the Delta variant is the dominant variant.
"We hope that low numbers will be turned into positive cases, but we need the figures to support that."
He says while principals stuck to the health advice regarding testing and tracing, "they didn't get the follow up support - or they felt they didn't get the support - from the public health".
'Not all schools are the same'
On ventilation in schools, he says this is still a concern - especially as we come into the winter.
"Not all schools are the same, that's the problem.
"We have... modern schools that have been built very recently, we have schools that were built at a certain time when there's cross-ventilation.
"But then we've other schools that have not great ventilation - the CO2 monitors are a tool to be used to see can we predict when we need air changes.
"That becomes very more [sic] important when we we get into the cold weather as well.
"We all know what schools were like last year, everybody was wearing two layers of coats and whatever.
"So not all schools are the same, and some schools are able to create ventilation far easier than others".
Speaking last week, Education Minister Norma Foley rejected claims adequate resources were not provided to ensure testing and tracing could cope with the pressures of schools re-opening.
She told Newstalk: "I don't accept that, I think we have resourced our schools incredibly - 650m of resource has gone into our schools, providing a variety of prevention infection [sic] control measures.
"And that's everything from enhanced cleaning, PPE, substitution - all of the things that were needed and directed by public health.
"And in relation to the carbon dioxide monitors they are also being rolled out in our schools.
"We ordered them more than four months ago now; there is an international demand on them.
"More than half of our schools have received them, will be receiving them in tranches, all of our schools will have them."