The General Secretary of the Association of Secondary Teachers in Ireland has said they would like the ongoing industrial dispute to be resolved speedily.
Almost 60% of secondary schools were closed today as members of the ASTI withdrew from the supervision of students during break times.
However, the ASTI said its members were available for normal teaching duties.
Speaking on RTÉ's Six One News, ASTI General Secretary Kieran Christie said the union is open to proposals for an invitation to the Workplace Relations Commission in an effort to resolve the dispute.
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Mr Christie also said Minister for Education Richard Bruton's construction of the dispute is entirely erroneous, saying his members would have worked today if the Minister had not reneged on commitments made in the Haddington Road agreement.
He said the Minister is clouding issues that are not related, adding that ASTI members would have been in school today supervising and undertaking substitution duties if they were paid money due to them on 1 September.
School management bodies have urged both sides to come to a resolution for the sake of the thousands of students and families who are affected.
Despite the ASTI claims, school management bodies say schools are being forced to close as a result, on health and safety grounds.
Some schools with ASTI staff have managed to open - paying Special Needs Assistants and others to fill in.
A very small number were opened partially for exam students only.
But schools say the union's decision not to allow ASTI school principals work to set up alternative plans has hampered such efforts.
ASTI teachers whose schools remain closed will not be paid and when these schools will be able to open again is unknown.
Mr Christie said both the ASTI and the Department of Education are maintaining contact and talks "will continue that process and our interest here is to bring a speedy resolution."
ASTI teachers locked out of Clonkeen College, Deansgrange #asti pic.twitter.com/g4xP4EWMRt
— Petula Martyn (@petulamartyn) November 7, 2016
Mr Bruton has said the ASTI must comply with working one extra hour per week, if they want to be paid for supervision and substitution.
Mr Bruton said that hour is something every public servant works, and many work more than one hour.
Speaking on RTÉ’s Morning Ireland, he said the ASTI are trying to re-write the entire approach to public pay in this dispute.
However, he said, if teachers agree to work that one hour a week, it would trigger immediate positive gains for ASTI members.
Speaking on the same programme, ASTI President Ed Byrne said that there is no sign of the dispute being resolved.
Mr Byrne said that one size fits all is not always the best way and this was highlighted by the deal reached with gardaí.
He said that if there was a successor to the Lansdowne Road Agreement, then it would be seriously considered.
Members of the Right2Change group, which includes AAA-PBP, Sinn Féin and independent TDs, have described the dispute as a "lock-out".
Spokesman Brendan Ogle said if teachers turn up to school and the gates are locked, it is a lock-out.
Meanwhile, a professor of industrial relations at UCD has said that Lansdowne Road Agreement on public sector pay is now effectively "a dead letter".
Bill Roche said one union after another is claiming that they are under pressure from members to try to win concessions that have been won by gardaí.
He added that the current situation needs to be seriously addressed or there could be "chaos throughout the public service."
