Three years ago, Mayor Bloomberg said his 20-point margin of victory in his reelection campaign showed that New Yorkers were happy with his schools leadership. Next year, voters could have a chance to reaffirm that choice — or reverse it.

Tomorrow, Bloomberg will announce plans to run for a third term, despite the two-term limit imposed by voters 15 years ago. Although polls indicate that the public isn’t happy about the mayor’s bid to use the City Council to overturn democratically imposed term limits, they also show that he is popular enough to coast into office for a third term.

What would a third Bloomberg term mean for the city’s schools? Judging from Bloomberg’s attitude when he was reelected in 2005, he will interpret a win at the polls as voter approval of his education initiatives, regardless of what issues New Yorkers actually consider when casting their ballots. His reelection would be a disappointment to his critics, some of whom have already started counting down the days until the end of his term. But it would provide stability for principals and students in schools that have only recently found their feet after the most recent round of disruptive reorganizations. Consistency in the DOE could also generate data that’s desperately needed to evaluate the city’s recent school reforms.

Four more years of Bloomberg would mean four more years of Children First initiatives and four more years of Chancellor Klein, who has long said that he will continue to lead the city’s schools as long as the mayor asks him to. A third Bloomberg term would likely herald four more years of business-style, accountability-driven reforms and ambitious experiments, such as the pay-for-performance incentives program organized by Harvard professor Roland Fryer. And, unless the State Assembly mandates parent involvement or checks and balances on the mayor’s power in June when it must consider the 2002 law that gave control over the city’s schools to the mayor, we’re likely to see four more years of top-down education reform that doesn’t include parents, teachers, or students in the decision-making process.

Solidifying assembly support for mayoral control is one of Bloomberg’s major goals for his third term, the Post reports today. In some ways, knowing that the mayor is not likely to change immediately simplifies the assembly’s task, because lawmakers will be dealing with a known quantity. Regent Merryl Tisch, who backs mayoral control, told the Post that Bloomberg’s potential run is “very encouraging” because he has used his control over schools in a “reasonable and responsible way” that has “yielded real benefits to the school system.” On the other hand, the assembly is supposed to approach the question of mayoral control without considering who the mayor is. The complication of a prospective third Bloomberg term could prompt the assembly to defer its decision about mayoral control.

Consistency provides stability for schools, although with multiple system-wide reorganizations stability has been sporadic even during Bloomberg’s two terms. Still, any iteration of existing initiatives would be less disruptive than changes to the system based on a new mayor’s vastly different principles. Consistency could provide deeper information about the DOE’s pioneering experiments in education. But it also means that any mistakes currently being made will affect more children, and given the difficulty researchers and reporters have had getting reliable information from the current DOE administration, the public could have to wait even longer for independent analysis of whether current initiatives are working.

One thing is for sure: We can safely say that the chancellor is unlikely to pursue the mayoral bid that consultants have been planning for him if it means running against his boss.