ASTI members have voted to withdraw from working additional so called 'Croke Park' hours which form part of the Haddington Road Agreement.
They are expected to stop working the 33 hours annually from September.
The vote was 68.5% in favour of withdrawal, 31.5% against. The turnout was 76%.
This puts the union on a collision course with the Government.
The Government has warned that a failure to work the 33 'Croke Park' hours would represent a repudiation of the Lansdowne Road Agreement and teachers, as a result, would lose payments that were due to be restored to them as well as increments due.
The union has said that if the Government takes this course then it will ballot its members on strike action.
It says such an action by Government would be out-of-proportion.
The 'Croke Park' hours are used for school meetings and their loss would not directly impact students, the union says.
The union's Standing Committee will meet tomorrow morning to consider the implications of today's result.
A spokesperson for the Minister for Education said they are concerned at the implications for individual teachers as well as the disruption facing students and schools from September if the ASTI proceed with the proposed action.
In a statement, the spokesperson added that the union has not yet accepted an invitation to meet with the Department of Education to discuss their issues of concern.
They added that the invitation remains open.
Separately, Minister for Education and Skills Richard Bruton has said he will meet with the ASTI to discuss junior cycle reform.
Mr Bruton told the Dáil he received a letter from the Union on 9 May which said the ASTI looked forward to engaging with the minister on a number of issues, including junior cycle reform.
