In a major new departure, the Minister for Education, Mr Dempsey, is set to involve parents' groups in discussions on such issues as parent/teacher meetings at night and the timing of school holidays.
Talks on parent/teacher meetings at times "more convenient for parents" and on a common school year will begin next Wednesday.
All three teaching unions have committed themselves to discussions on this "modernisation" agenda - in return for the 13.5 per cent pay increase due from the benchmarking deal.
Sources say the department wants to widen discussions beyond what one called "the usual debate" between teacher unions and the department. "These issues are of direct concern to parents - particularly those who are juggling two jobs - they have a right to be fully consulted".
Mr Dempsey is said to be anxious to "widen dialogue" on all education issues. The move comes after a significant recent speech by the IDA chief executive, Mr Seán Dorgan, in which he suggested that the "introspective" education debate needed to be more "connected" with the wider society.
The Dempsey plan is that groups like the National Parents' Council (primary), the National Parents' Council (post-primary), the Congress of Catholic Secondary Schools Parents' Association (CSPA) and other interested parties will be centrally involved in the "modernisation" talks.
One teacher union source insisted that his union would not tolerate parent groups becoming involved in employer/employee discussions. He said provision for some input from parents was already provided in the Education Act.
But Mr Dempsey appeared to suggest this weekend that some schools are paying no more than lip service to the notion of parental involvement. "Parents as stakeholders are hugely under-utilised and in many cases under-valued. That issue needs to be addressed," he told a weekend conference.
For its part, the ASTI could withdraw from discussion on new curricula if the Minister presses ahead with the modernisation agenda. Next week's ASTI conference will consider a motion demanding this kind of action - even though a huge majority of members voted for the benchmarking deal.
Both the INTO and the TUI are open to discussions on parent/teacher meetings and a common school year - provided there is due regard for "local flexibility".
This weekend, Mr Dempsey signalled his unease with the very modest role given to parents. "We must deal with the general conservatism of schools on the role of parents and the obstacles to their involvement," he told Catholic primary school managers.
The department is determined to change current arrangements where normal classes are suspended to allow parent/teacher meeting take place, usually at lunchtimes. The department would like to see the meetings take place at night.
It also wants to end the current practice where schools take different mid-term breaks and school holidays, as this it maintains is very inconvenient for parents.
The department is also concerned about the erosion of class times for students because of unregulated school breaks.