Sinn Féin says some teachers and principals are being left to make public health decisions.
It comes as a Dublin primary school sent home a class of students after one child tested positive for COVID-19.
The south Dublin school confirmed 30 students were sent home as a precaution, and the decision to close the class was taken on public health advice.
The school re-opened after almost six months on Wednesday.
While Eoin Ó Broin, Sinn Féin's housing spokesperson, told Shane Coleman on Newstalk Breakfast he has been contacted "by a large number of parents" who are concerned with the way in which the school re-opening is happening.
"I've been talking very much off the record to some teachers and some principals who feel that they're being left making public health decisions without adequate guidance from the Department of Health.
"We're seeing a lack of coordination, for example, between the Department of Transport, the National Transport Authority and schools in terms of school transport provision.
"So you've situations, and this is not just in my own constituency, where you could have no social distancing on school buses to and from school, you can have children in school buses for anything up to an hour - and yet then they're attempting to socially distance."
"While we want the schools to re-open, and we want them to re-open in a way that is safe for both pupils and teachers, unfortunately - again a little bit like other things - the last minute nature of this it's a little bit chaotic, it's a little bit haphazard."
He added: "I was contacted for example by one principal who was only getting access to a new school building four days before her teachers were due to arrive in and six days before her pupils arrive in".
"The difficulty is, though, we're hearing lots of these types of cases... there is no question that the Department of Education and the then-minister came very late in the day to engage with the unions and the schools."
As schools reopen, Sinn Féin's @EOBroin says teachers are 'being left to make public health decisions' @BreakfastNT #BKNT pic.twitter.com/6Ta4EWLIE2
— NewstalkFM (@NewstalkFM) September 2, 2020
On plans for the Leaving Certificate, he said: "The greater the level of transparency, the better for everybody.
"So for example the methodology they've used for the standardisation should be published so everybody can see that.
"I think part of the problem is all of this stuff is being announced or left so late in the day, it's just part of that general trend where everything is right up to the wire, people are stressed, people are confused and then people aren't being given the full information.
"So while we welcome the move yesterday, we still think there's a need for greater transparency."
The Education Minister Norma Foley confirmed on Tuesday that ‘school profiling’ would not be used to calculate grades.
It means students will not be downgraded based on their school previous academic performance.
As a result, some 17% of the grades handed out next week will be downgraded, 4% will be upgraded and just over 79% will remain the same.
