A separate Times analysis shows that since 2002, opening hundreds of new schools and raising salaries have swelled the principals’ payroll 43 percent after adjusting for inflation. The average salary among the current 1,500 school leaders tops $133,000, 10 percent higher than their 1,200 counterparts in 2002 in inflation-adjusted dollars, even as the median household income nationally has risen only marginally.  An average of 649 students are under each principal’s purview, compared with 879 six years ago; pay per pupil, then, has jumped to $205 from $138 in 2008 dollars.  Nearly 80 percent of the city’s principals were not on the job in 2001; Chad A. Altman, the 28-year-old head of a Bronx elementary school, was still studying public policy at Carnegie Mellon University when the mayor was petitioning Albany for school control. Indeed, 22 percent of today’s principals are under 40, compared with 6 percent in 2002; about 20 percent of them have less than five years of teaching experience, double the percentage in 2002.  Mr. Klein’s cultivation of a new breed of school leadership is being watched around the country, where many cities are grappling with waves of principal retirements even as more is being asked of public schools.  As New York State lawmakers consider whether to renew the 2002 mayoral control law, which expires June 30, one proposal on the table would revive the district superintendents, now largely powerless, to more closely supervise and support principals.  For all of New York’s recent focus and investment in school leadership, more than a quarter of teachers said in city surveys last spring that they did not trust their principals or consider them effective managers, and more than a third of those leaving the system cited the quality of school leadership as among the main reasons. “Perceptions of principal leadership skills are drivers of attrition,” an internal report concluded.  Teacher turnover has been higher at schools run by Leadership Academy principals — over the summer of 2007, nearly a quarter of these principals lost at least a third of their teachers, compared with 9 percent of other principals — though some see that as evidence the new leaders are shaking things up. Iris Blige, a graduate of the first class of the Leadership Academy, has seen at least eight assistant principals and dozens of teachers leave the Fordham High School of the Arts since she took over in 2004; she was the subject of an angry protest in March.  In interviews with three dozen principals, former principals and education experts, many said the newfound ability to select faculty was invaluable, but painted a portrait of a job that has grown complex and unwieldy.  “You’re a teacher, you’re Judge Judy, you’re a mother, you’re a father, you’re a pastor, you’re a therapist, you’re a nurse, you’re a social worker,” said Maxine Nodel, principal since 2003 of the 481-student Millennium Art Academy in the Bronx. “You’re a curriculum planner, you’re a data gatherer, you’re a budget scheduler, you’re a vision spreader.”  Ms. Nodel, who has taught math, English, science, art and chess over 18 years, earned two A’s in a row under the city’s new school report card system. But, she said, “This is the most exhausted I’ve ever been.”  Allison Gaines Pell could be the personification of the new principalship. A graduate of Brown University with a master’s degree in education from Harvard, she taught for three years at St. Ann’s, a Brooklyn private school, and two in Syracuse, and worked for educational nonprofit agencies before being fast-tracked to the principal’s office through the Leadership Academy in 2005.  At 34, she is one of 132 current school leaders under age 35, up from 26 in 2002, and one of 237 who have worked in the district less than a decade, up from 54 in 2002. She earns $127,000 a year running a middle school of 278.  Over a few days at her Urban Assembly Academy of Arts and Letters in Fort Greene, Brooklyn, this spring, Ms. Gaines Pell gave out high school acceptance letters, videotaped two lessons, revised the laptop security policy, joined a meeting between the school nurse and a student with a hurt hip, and experienced the joys and headaches of being in charge of her own budget.  Headache: a rumor that when students did not pay for lunch, she would have to make up the shortfall (she has yet to determine whether this is true). Joy: a new computer program — which she could buy without approval from on high — designed to help teachers collaborate online.  “That’s hot!” Ms. Gaines Pell exclaimed to her assistant principal, John O’Reilly. “That’s really hot,” he seconded.  But while Ms. Gaines Pell’s school earned an A from the city this fall, The Times’s analysis shows that Leadership Academy graduates were less than half as likely to get A’s as other principals, and almost twice as likely to earn C’s or worse. Among elementary and middle-school principals on the job less than three years, Academy graduates were about a third as likely to get A’s as those who did not attend the program.  While Academy graduates do tend to be placed in some of the city’s lowest-achieving schools, the report-card system has built-in controls to account for that, emphasizing progress over performance and comparing schools with similar demographics. Still, Sandra J. Stein, chief executive of the Leadership Academy, said the cards — the city’s primary accountability measure — are not a fair gauge of her graduates because, as she put it, “it takes time to reverse a downward trend.”  After five years running primarily on private donations, the Leadership Academy won a city contract last June for up to $10 million a year. Its centerpiece is the Aspiring Principals Program, a 14-month paid boot camp that has graduated 336 people since 2003, 227 of whom are now principals — 15 percent of the total.  One Leadership Academy alumnus was removed from his post this month, pending Education Department investigations, after a public screaming match with the school’s parent coordinator; more than 250 parents had signed a letter citing a “litany of problems” including “increased staff turnover, parent dissatisfaction and general turmoil.” Another was removed upon his arrest in February for driving while intoxicated and fleeing the scene of an accident.  The first independent analysis of the academy’s effectiveness, done at New York University, is due in June. “I think our batting average is quite good,” Mr. Klein said. “Could it improve? I’m sure it could improve.”  Andrew M. L. Turay vividly remembers, back when he was principal of the Bronx’s mammoth Evander Childs High School in 2001, the day an assistant principal who had struggled at another school walked into his office and announced she would now be working with him: superintendent’s orders. “You were the figurehead as a principal, but the actual power was in the superintendent’s office,” he said. “They were pulling the strings.”  Now, as principal of Peace and Diversity Academy, a small high school in the Bronx that he founded in 2004, Mr. Turay not only picks his own staff but decides how to train them. Still cringing over the time he returned to Evander from a required daylong monthly session to find that a student had assaulted a staff member in the cafeteria, Mr. Turay can — and does — choose to skip virtually all meetings outside the office.  Where he oversaw more than 3,000 students at Evander, Mr. Turay now has 315, and makes it his business to know who was just absent for five days (the girl with multiple face piercings), and who is struggling with sexual identity (18 students are openly gay). There is no superintendent regularly visiting; it is up to Mr. Turay to call his network leader — his primary support person — on her cellphone when he needs help. Someone sent by the Education Department descends on the school for a few days at least once every three years and then submits a “quality review” on its shortcomings and successes, but Mr. Turay is judged, in large part, by a thick stack of documents.  Compliance checklists, on items including vision-testing and fire drills. School report cards (he got a B). Parent and teacher surveys. A review of how well he has met his own goals.  Mr. Turay, who is 57 and has worked in city schools for 24 years, prefers the new system, or at least the small-school environment. “I didn’t know kids, I didn’t know parents,” he said of his days at Evander Childs. “I couldn’t tell if I helped anyone, really.”  But the independence that has helped Mr. Turay flourish has tripped up others.  Maria Penaherrera — who started as a substitute teacher 20 years ago and worked her way up to the principal’s office — used her financial freedom to hire four assistant principals at the 900-student Public School 114 in Canarsie, and ran up $150,000 in debt. Then she eliminated three of the positions only to have the fourth assistant principal quit. That left a custodian to take charge in February when a carbon monoxide alarm went off while Ms. Penaherrera was out. She has since been reassigned to a central office post while the Education Department investigates, and did not respond to requests for comment.  Peter McNally, executive vice president of the principals’ union — which has generally supported the mayor’s reforms — said the biggest complaint from members was “that they spend more time looking at the data than in classrooms observing and supporting instruction.” Indeed, many had deep reservations about a system in which, as one principal put it, “my report card is my boss.”  “If teaching and learning become about credits and grades, it’s not about learning,” said Jill Herman, who retired last year after three decades as a teacher, principal and network leader.  Philip Weinberg walks the halls of Brooklyn’s 1,250-student High School of Telecommunication Arts and Technology like the beloved mayor of a close-knit town, popping into a young math teacher’s classroom, ushering teenagers off the sidewalk after dismissal in a manner both firm and warm. “He’s cool with all the students,” said Anthony Mesa, a senior who took the liberty of adjusting Mr. Weinberg’s scarf.  Mr. Weinberg, 49, started teaching English at the school, in Bay Ridge, in 1986 and became its principal in 2001; several of his staff members are former students. He is one of 255 principals — 17 percent of the total — in the same post as before mayoral control. (The number of rookie principals soared to 20 percent in 2003 and 25 percent in 2004, but has settled down to 12 percent over the past two years.)  The Times’s analysis shows that experience counts — at least on school report cards. Forty-three percent of principals with at least a decade at their schools received A’s last fall (including Mr. Weinberg), compared with 30 percent of those who had been at their schools up to two years.  “The longer you know a story, the better you know the story,” Mr. Weinberg said. “I would hate to have been judged on my first three years as principal.”  In an interview, Mr. Klein said he would like to see good principals stay 8 to 10 years; 5 out of 6, though, have not been around that long. And the first two principals the chancellor cited as models were Shimon Waronker, 40, a Leadership Academy graduate who is on leave from the school system to attend a graduate program at Harvard, and Marc S. Sternberg, 36, a Princeton and Harvard Business School graduate who plans to leave the high school he founded in 2004, Bronx Lab, this summer.  Elana Karopkin left Brooklyn’s Urban Assembly School for Law and Justice last summer, at 32, for a charter school group, saying she was physically and emotionally “exhausted” from what she described as a “Herculean task.”  And Michelle Harring, 62, retired last year after nearly a decade as principal of the Earth School on the Lower East Side, complaining of too much time spent “belaboring the testing statistics” or on the computer as well as bureaucratic reshufflings that left her scrambling to figure out whom to call for what.  “The job had many more pressures coming from lots of different directions, that I often felt took away from my time as a person who supported both teachers and the children in the classroom,” she explained. “I think of C.E.O.’s as people for whom the bottom lines are numbers and profit lines. I don’t think principals should be C.E.O.’s.”  Amy Ellen Schwartz, director of the Institute for Education and Social Policy at New York University, who is heading the Leadership Academy study, wonders whether the school system has constructed “a job description for which there are very few really good candidates.”  “It may be that it’s an impossible job,” she said. “You’re asking for things that don’t often come in the same person.”  A version of this article appears in print on , on Page A1 of the New York edition with the headline: Principals Younger and Freer, But Raise Doubts in the Schools. Order Reprints| Today's Paper|Subscribe
By some measures, the New York City principals who have come through the city’s celebrated Leadership Academy lag behind veterans who did not.