Classes are continuing in full at some schools despite confirmed cases of Covid-19, sparking alarm among parents and teachers' unions.
At least two schools have continued classes as normal following public health advice after there were confirmed cases of the virus.
But unions have raised concerns about entire classes not being sent home in the event of a confirmed student case.
Meanwhile, some parents are calling for more information to be provided on cases due to concerns about at-risk family members.
The Association of Secondary Teachers Ireland (ASTI) said it would "continue to pursue the matter vigorously".
"The ASTI is aware that decisions relating to confirmed cases of Covid-19 in schools are made by the HSE departments of public health," a spokesperson said.
"Experts have argued that if a single child is infected, the entire class at a minimum has to go home and isolate for two weeks - and get tested. Why is this arrangement not being implemented?"
Schools where there are confirmed cases of Covid-19 are not being named by Government or health officials. But a Dublin secondary school alerted staff on Sunday about a positive case in the fifth year, advising teachers classes would resume as normal.
The text said: "After lengthy consultations with the HSE, they have concluded that they don't believe there is a justifiable threat to the school and classes are to resume as normal tomorrow morning."
When contacted, the school said it could not comment. It also declined to confirm whether any pupils excluding the confirmed case had been asked to restrict movements.
Meanwhile, a primary school in Co Cork emailed parents over the weekend notifying them of a positive case.
The principal advised all classes would continue "as normal" this week.
Parents of pupils in the school are calling for more clarity because it has not been confirmed whether the case concerned a student or staff.
One parent, who asked to remain anonymous, called on the school to notify them about which class the case relates. She is concerned about a high-risk relative.
The principal of the school, which has more than 500 pupils, wrote to parents saying: "We have a confirmed case of Covid-19 within our school community. I have been engaging with the local Cork team of national public health.
"I have contacted all the relevant families at this point as advised. If I have not contacted you by phone call, please send your daughter to school as normal. Our school will be open for all classes as normal."
There have been a number of confirmed cases since classrooms reopened in the last two weeks.
Schools in Dublin, Meath, Clare and Kerry all had confirmed cases, with some sending home entire classes.
Yesterday, a primary school in Dublin alerted parents after a pupil in junior infants tested positive for coronavirus.
"Please be assured there is no evidence of transmission in the school to date," the message said.
Close contacts have been asked to restrict their movements for 14 days and arrange a test.
Up to 40 schools have contacted public health officials about cases of Covid-19, the National Public Health Emergency Team (NPHET) confirmed at last night's briefing.
Public health specialist Dr Abigail Collins said many of these cases were community transmission and that no clusters or outbreaks have yet been reported.
The HSE said it could not comment on individual cases.
However, a spokesperson outlined how "responses and recommendations for each facility may well differ".
Under HSE guidelines, schools do not have to alert all parents if there has been a confirmed case.
Only the "close contacts" of the student are told.