It wants all schools to establish boards which would have equal representation of parents, teachers, school owners and the wider community. The boards would also have to be gender-balanced.
The majority of schools already have boards of varying composition but some smaller and some family-owned private schools are holding out, and have taken legal advice which suggests that the government's threat to freeze their funding is unconstitutional.
The threat is contained in the government's long-awaited Education Bill which, if carried, would be the single most important piece of Irish educational legislation this century.
It proposes to devolve power from the over-centralised Department of Education to 10 regional education boards and to individual school boards of management.
Parents would be the main winners as they would have statutory representation, for the first time, on boards of management as well as legal access to school records on their children. A new procedure would be introduced to process appeals against school decisions that materially affect the education of their children.
Education minister Niamh Bhreathnach is hoping that the Bill will be passed by the Oireachtas (parliament) before the general election which is due in a few months time. But some constitutional experts predict that there will be legal wrangles arising out of many of the provisions in the Bill.
The two main opposition parties, Fianna Fail and the Progressive Democrats, who may form the next government, say that they will disband any education board established by the present minister, as they regard the boards as bureaucratic and costly.
Education in Ireland has largely avoided becoming a party-political issue in the past, but that may be about to change.