The ASTI has withdrawn from talks with the Department of Education aimed at coming up with a solution for this year's Leaving Certificate exams.
The union is meeting with Education Minister Norma Foley on Friday, but has stressed it is "not back in talks".
In a statement on Thursday, the group said the current plans are "unacceptable" and accused the Government of asking students to prepare for "two versions of a Leaving Cert, with calculated grades being the dominant option."
Ann Piggott, President of the ASTI, told Newstalk Breakfast this is down to their unhappiness with the calculated grades system.
"As a union, we're committed to getting a solution to this as soon as possible whereby we can move forward to have an exam result that will have standards".
She said the talks were meant to include discussions on a non-examination process, but the group had an issue with his.
"Throughout the talks it has come to our attention very clearly that this non-examination process is a system of calculated grades without any great focus on what other alternatives were available.
"We have a problem with calculated grades because of the issues it threw up last year.
"Last year we entered into this on a once-off commitment, we were happy to do it at the time just to allow students to move forward.
"We have serious reservation about so many aspects of it".
She also suggested the lack of data is an issue, as "students have not done their mock exams, some schools have not a 5th year summer exam.
"We don't have as much data as we had las year".
'Lack of standardisation'
She said at this point, there are too many choices on the table.
"If they wanted a choice we would be happy - not completely happy - but whatever the alternative process is, one choice or the other.
"The discussions we have had... have led us to believe that they can take 'a bit of this and a bit of that' - they may then choose to do calculated grades in some subjects and an exam in other subjects."
"The issue with that is that teachers will be in a classroom having, perhaps, given a calculated grade earlier - so we'll have some students in class with no motivation who will have a calculated grade.
"We'll have other students in the same classroom preparing for [the] Leaving Cert".
"It would be ideal if the grades were given out at the same time".
On remarks that students want a choice in the process, Ms Piggott suggested: "A choice is not doing both and deciding, coming up to the very end, what they're going to do.
"A choice is a choice where you make your decision and you move forward in that way".
And she added that standardisation could also be a problem.
"We've a problem with the standards that might be applied throughout the country - one teacher at one end marking in one way, another teacher marking in a different way".
Acknowledging that this issue was dealt with last year, she said: "A standardisation process was applied where people's marks were pulled down to create a bell curve.
"Some people were pulled down - consequently missed a place in college, they repeated their Leaving Cert and got the grades that they were given originally.
"So that remains to be a problem".