By RANDI WEINGARTEN

MOST of us who backed the 2002 law that gives the mayor control of the city’s schools believed that it would bring stability, accountability and cohesion to the system. We still believe there is promise in that model, and we want to see the law, which expires next month, renewed. That is why we are offering the following suggestions to preserve it. As many New Yorkers know, we think the model can be improved, based upon what we have learned in the last seven years, by creating more checks and balances.

Think of it as Mayoral Control 2.0.

We have thought that a good way to do this would be to reduce the number of mayoral appointees on the 13-member Panel for Education Policy, which must approve policy changes, from eight to five. The mayor would no longer control a majority of members, but others with a stake in the system would be empowered. We have backed such a change in the law. But because Mayor Bloomberg, Assembly Speaker Sheldon Silver, Senate Majority Leader Malcolm Smith and others (including The Post) have disagreed, why not consider other possibilities that maintain the mayoral majority on the PEP but similarly provide for greater public input, broader discussion and more checks and balances on the mayor’s prerogatives?

What sort of alternative measures might work?

Ultimately, it’s up to the Legislature to decide, but here are some suggestions:

* Give PEP members fixed terms. Under the current law, the mayor can remove his appointees at any time. Giving them fixed terms instead would make them more independent and allow them to weigh in on issues without fear of being removed.

* Require the panel to hold hearings on the school system’s expense and capital budgets. Although decisions may ultimately rest with the mayor and the Department of Education, public exposure and debate of these issues might also serve as a useful check.

* Have policy proposals made in public in advance of panel meetings, complete with a list of pros and cons about the issues being voted on. Again, the additional debate and exposure could help inform — and improve — ideas pushed by the mayor and could act as a brake on ill-conceived plans.

* Structure meetings to allow for more public discussion and have them broadcast and archived online. The point here is not that any one of these measures is a prerequisite for renewing the law, but rather to note that there are many different possible ways to make improvements, bolster public input and provide greater balance. Indeed, other ideas may yet surface that would accomplish these goals.

In the end, all of us want a governance structure that creates and nurtures high-quality, safe learning environments that prepare children for college and life. The best such structure would ensure real discussion and debate before major policy shifts occur by creating an institutional voice for parents, students and teachers. That would lead to policies that best serve the interests of all parties. We know, for example, that schools that are collaborative, where teachers’ voices are heard and respected, are better for learning. Likewise, schools with parental input are inherently stronger. Thus, the Legislature could bolster the law to strengthen school-leadership teams, district-leadership teams and community-education councils as the 2002 law originally envisioned. Rather than being marginalized, these entities should be able to carry out their responsibilities so that parents have a role in decisions affecting their children and have their issues addressed.

Superintendents, who for a long time served as an important link between their communities and the central Department of Education, should also be re-empowered to provide schools with more local support, strengthen instruction and improve parental access. To improve confidence in student-achievement data and increase transparency over spending, the Legislature could require broader access to the numbers — and perhaps even an independent analysis.

The public’s trust in the data is crucial to its confidence in the system as a whole.

Finally, lawmakers should strengthen oversight and enforcement mechanisms. One shouldn’t have to go to court or hold a protest to get the school system to do the right thing. There are many different ways to run our schools. As the debate over governance moves forward, we should be looking for ways to ensure that every child has a quality public school to attend that actually improves outcomes for its students. Every company can improve its products. Teachers consistently work to improve their methods. So, too, can the Legislature produce a Mayoral Control 2.0 that improves the current system without totally reversing course. Doing so would put the city on the right track. Randi Weingarten is president of the United Federation of Teachers.