How the split is repaired will reveal how the business of education is to be done in the North, writes DAN KEENAN.
SORTING OUT education will tell us much about the emerging working relations between Peter Robinson and Martin McGuinness.
Certainly the divisions between Sinn Féin and the unionists are cemented in vastly differing views of what shape education reform should take. But the manner in which this split is repaired will tell us much about the how business is to be done when Robinson takes over next month and how McGuinness relates to him.
The minimum that is agreed is that the issue needs to be sorted out quickly, certainly before the Executive takes its summer break at the end of July.
The existing schools transfer mechanism, based on the 11-plus exam, is due for abolition after the final setting of the test next autumn. A replacement or a decision to retain it - or something akin to it - has to be announced to enable primary schools and parents to plan accordingly.
There is further cause to proceed quickly with a sense of purpose. There are 50,000 unfilled school places in Northern Ireland, a figure projected to rise to 80,000 thanks to demographic trends.
Many grammar schools, with their emphasis on academic excellence, are thus motivated to accept children with lower grades in the 11-plus transfer test simply to maintain their numbers.
In the meantime other second-level schools, primarily those more aimed at vocational students, are suffering.
While the schools system produces undoubted excellence at the top end, an alarming proportion of 16-year-olds leave school annually without formal qualifications in core subjects such as English and maths.
Yesterday's Executive meeting ended in impasse and mutual recrimination. Caitriona Ruane, who has received vociferous and frequent personal criticism for taking this long to present her proposals, is branding her opponents "anti-change".
Unionists on the Executive say there is no point in discussing anything she proposes, which they claim to know is neither workable nor acceptable.
At the core of the issue is the DUP assertion that nothing can happen at Executive level without its Ministers' say so. This, they claim, was won at the St Andrews talks which enabled powersharing to commence last year.
And it is this that gives unionists the sense of security they need if they are to put up with a mandatory coalition involving republicans.
It is a position conceived, promoted and put into effect by Peter Robinson. It therefore follows that once elevated to first minister next month, he and Martin McGuinness are the best people to draw up the means (if not the detail) of resolution.
There are just a handful of Executive meetings scheduled to be held before the summer recess - but there is wider scope for other forms of less official engagement.
For all their many and profound differences, Martin McGuinness and first minister-in-waiting Peter Robinson enjoy a pragmatic if straight-faced relationship.
The way out of this damaging impasse about long-overdue education reform therefore lies in the two of them devising a basis for change that allows Sinn Féin to claim it is delivering change while allowing DUP grassroots a sense of protection from a ministerial solo run by an untrusted Minister.
It can be done.