SCHOOLS SUPERINTENDENT Arlene Ackerman has often been accused of being tone-deaf, and lacking in communication and political skills. On Friday, she confirmed the worst of these accusations when she announced that she had struck a deal with the state to save all-day kindergarten.

What should have been a moment of triumph for the city's youngest students was instead a rather stunning diss to Mayor Nutter, who, for the last week has been pushing the highly unpopular idea of raising taxes to, among other things, save all-day kindergarten.

Ackerman let the mayor know a little more than an hour before her public announcement that she had gotten the state to grant an allowance to use Title I federal funds for the kindergarten restoration. (That will mean a shift of those funds from something else, and won't impact the overall deficit.) The whole incident is a head-scratcher: It's unclear how long she had been working on the deal with the state, but surely it couldn't have come completely out of the blue.

We imagine that if the mayor had been informed there were even a remote chance the state could make such a deal, he might not have taken such a strong stand on all-day kindergarten. Or did Ackerman miss the news that the mayor had made saving kindergarten (as well as transportation) one of his priorities?

If so, she also missed how far Nutter had gone out on a political limb for the schools, by proposing another property-tax hike and/or a reboot of the dreaded sugary-drink tax. What Ackerman's breach of courtesy and political protocol does for the district's attempt to fill its $610 million deficit, caused in part by major cuts from the state, remains to be seen, but it can't be good.

Then again, all of this might have a silver lining if it results in the city and the Nutter administration thinking twice about handing over a big blank check to the district with no strings attached, especially since state law prohibits the city from reducing its school funding once it raises the amount.

Even before Friday's developments, there were plenty of questions about what accountability measures the city might impose for whatever funds it gave. Laws are likely to limit the strings that the city can place on its contributions - or even whether it can stagger its payments, as suggested last week by Councilman Darrell Clarke - but both Council and the mayor should demand that the district and the School Reform Commission give frequent and public answers to questions about how they are maximizing whatever money the city is investing - which is already considerable, considering that the property-tax share that goes from the city to the schools is $800 million.

The fact is the school district, while legally under control of the state, is not an island. Further financial support from the city is not a gift - it should be earned. The district can begin earning our support with a willingness to be more transparent, and to start acting like an equal partner.

Otherwise, the district will have to answer the ultimate question: why taxpayers should bother helping out at all.