A new group within the TUI is calling for the teachers' union to take a tougher stance with the government over pay.
The newly formed "Grassroots TUI" group wants the union to pull out of the Lansdowne Road Agreement.
It is also seeking the reform of the TUI.
Spokesperson Eddie Conlon says members are angry about the leadership's approach to the ASTI dispute: "The TUI felt is necessary to make statements for example that is was normal for people to pass pickets and that there was to be no evidence of TUI support on any picket line organised by ASTI during the recent dispute.
"We think that is not good for trade union solidarity, and it is not good in situations where people have to go back into schools and work together."