Before Cathie Black gets a waiver to come in as Mayor Bloomberg’s schools chancellor, there should be a proper hearing in Albany. It would provide a moment not only to explore whether Ms. Black is the right person for the job but to assess how far the city has actually come under mayoral control of the schools.

The mayor, who fashions himself as a great educational reformer, wants New Yorkers to believe that he has found the magic formula that can be executed by any fine manager, even one who, like Ms. Black, is without any educational experience. But where’s the magic?

The fact is that under Mr. Bloomberg’s formula, New Yorkers have increased the education budget to $21 billion a year from $13 billion but have seen only the tiniest increase in student performance, continuing a pattern of similar (and often larger) gains that were being posted by the old, much maligned and allegedly “dysfunctional” Board of Education.

The “historic gains” boasted of last year, when the mayor won reelection, evaporated this year with the admission by the newly installed State Education Commissioner, David Steiner, that New York State tests in grades 3 through 8 had, for the past few years, been wildly inflated. The extreme nature of this situation has, in my opinion, been largely understated.

This deception — and no one should think that it is anything but — was not to help the children, who are, after all, demonstrably worse off by not having been told the truth, but rather to benefit the adults who run the schools. Beneficiaries included Mr. Steiner’s predecessor, Richard Mills, who boasted of the state’s soaring test scores as proof of his success, and Mayor Bloomberg, who used those scores as part of his $100 million campaign for re-election.

The federal No Child Left Behind law has its critics, but it did force policy makers to try to achieve increased scores, with the unrealistic goal of making all children proficient in math and reading by 2014. It was an invitation to game the system by allowing each state to determine proficiency, resulting in the New York state debacle. This compromised the education of hundreds of thousands of students here, denying many of them essential remediation, while facilitating their unearned promotion to the next grade. The concept of “ending” social promotion, central to the Bloomberg educational program, now lies in tatters.

Just as the academic program is emerging as in need of rethinking comes the fiscal bad news. The full effect of the recession, blunted for a while by the infusion of billions in federal stimulus funds, is now upon us. With billions less to spend, we’ve got to achieve the academic gains that we now know weren’t reached when the cash spigot flowed freely. This is a daunting task.

The first step to fixing a problem is admitting that one exists. That is what Mr. Steiner did at the state level with the test scores in July. I suggest that the solution to creating real, not illusive, academic gains will come from better pedagogy, not better management.

Which brings us to Cathie Black. I fear that the mayor still believes his own 2009 press releases and has told Ms. Black that, as far as academics are concerned, all is well with the city’s schools. All she needs to do as chancellor would then be to follow through on the programs the outgoing chancellor, Joel Klein, and his staff have already put in place. But in the harsh light of the revised test scores, what kind of success has Mr. Klein truly accomplished? Achievement has not dramatically increased, while funding has. New educational programs will need to be developed.

There are those who suggest that the mayor, in total control of the schools, have free reign to pick his chancellor. But the mayor, even within the overly-liberal terms of the renewal of his control of the schools in 2009, has control only within state law. That law clearly enumerates certain pedagogical qualifications for district superintendents, and New York City is the largest school district in the state (not to mention the country). Those requirements, not unique to the city, can be waived only for those possessing extraordinary skills.

There have been three waiver requests in my memory. Mr. Klein, in the euphoria of the initial adding of the school system to the mayor’s portfolio, won such a waiver. But he brought extensive government service to the table, at a time when all of the stakeholders, including the teacher’s union, were supportive. His predecessor, Harold Levy, whom the mayor would dismiss as part of the old “dysfunction,” also won a waiver. He had considerable experience as an education advocate in the private sector and had served on the State Board of Regents.

The third application for a waiver, which was denied, was for Robert F. Wagner, Jr., who was — he has since died — the scion of a distinguished New York political family and who was a widely recognized student of public policy. Many at the time were shocked by Wagner’s rejection. Mayor Koch responded by orchestrating Wagner’s election as president of the Board of Education, where he served with distinction.

In Ms. Black’s case, what would be appropriate would be a public hearing at which Ms. Black would be entitled to testify and face questions from a panel of Regents, state and city legislative leaders, and state education department staffers. This would enable Commissioner Steiner, who knows better than anyone the challenges that lie ahead, to make an informed and transparent decision.

It would also enable Ms. Black, a social friend of Mr. Bloomberg, to prove that she is not the education world’s equivalent of Harriet Miers, the ill-fated Bush nominee to the Supreme Court. Or perhaps give her pause, as with Ms. Miers, to withdraw rather than face questions for which she is ill-prepared to answer.