The ASTI is to hold a special convention in October on the issues of supervision and pay, which continue to divide the union's leaders.
The union's position going forward will be decided by the 500 delegates expected to attend the event.
In the meantime, the union has initiated a "consultative process" to get the views of branches on supervision and benchmarking.
This process will involve a series of information meetings around the country.
Yesterday the union's standing committee met in Dublin to discuss strategy. While several members wanted to maintain the union's ban on supervision/substitution, others said it was important for a wider group to make that ultimate decision.
According to the Joint Managerial Body, which represents school managers, all second level schools should open as normal on Monday.
VEC schools will be able to operate because TUI members are providing supervision and substitution.
Because of the ASTI ban on this work, voluntary secondary schools will use non-teachers to do the work. They will be paid €37 per hour. Many of them undertook similar work earlier this year for the same pay.
While most people at primary and second level are relieved that schools will open as normal, there is concern that the use of non-teachers as supervisors is causing increased indiscipline in some schools.