Some schools have still not put the necessary social distancing safety measures in place, according to the Teacher's Union of Ireland (TUI).
Teaching unions are before the COVID-19 Response Committee to discuss how the reopening of schools is going.
They are collectively calling for rapid testing to be made available to teachers and students to minimise any disruption to schools.
General Secretary of the ASTI Kieran Christie said there has been a number of teething problems.
He said: "The number that was involved was 84, two or three more of them were in a premises in Clifden.
"It was bizarre in the context of all the controversy that that attracted that teachers were being invited to go into sports halls in those kind of numbers.
"We intervened and schools have been told that the likes of that is unacceptable and that school staff meetings need to be remote, so we have had teething problems.
In its opening statement to the Committee, Mr Christie said that "planning for the return to school in a context of an evolving public health situation was a fraught and complex process".
Discussing the new Leaving Cert grading system, the Teaching Unions said they were shocked to learn that students will have access to the order in which their teachers ranked them.
As part of the calculated grades process, teachers had to submit a class rank list.
Both the TUI and ASTI said they understood that this information would only be available to students who issued a formal appeal.
TUI President Michael Marjoram told the Committee they have been discussing the issue with the Department of Education.
He said: "Our members cooperated with something that was almost anathema to them to put such rankings down on paper and to put down on paper the position of children that they had supported and kept in school and boosted the morale of and the confidence of.
"So we are really concerned about the correct treatment of that data."
Schools 'refusing to purchase PPE'
Meanwhile, non-teaching staff are reporting that a number of schools have either refused to purchase PPE or are requiring them to re-use face masks, according to Fórsa Trade Union.
In its opening statement to the Committee it said that while the Department of Education has advised schools that a range of PPE is available and can be purchased, including face visors and medical-grade face masks, this is not being adhered to in certain schools.
Fórsa represents almost 20,000 non-teaching staff in schools which includes secretaries, caretakers, special needs assistants (SNAs), Bus Escorts and others.
The trade union said that "it is too early to be definitive as to the extent of this problem", they intend to survey members next week on the issue.
"We can state to the Committee that there are a significant number of staff today providing
personal care to students without adequate PPE."
Other issues raised before the Committee were the position of staff returning to school with underlying health conditions, testing in schools and the use of isolation rooms for students exhibiting symptoms.
Additional reporting by Kacey O'Riordan