Two city principals fired in connection with a state-test cheating scandal have won arbitration rulings and may be rehired by the Philadelphia School District.

According to the arbitrator, the district conclusively proved in both cases that cheating happened at Tilden Middle School and Lamberton Elementary School. But it did not prove that Michelle Burns and Marla Travis-Curtis participated directly in the improprieties.

Burns, who led Tilden in 2009-10 but moved on to run Kensington Urban Education Academy, won reinstatement as a principal and is due back pay minus wages from a 60-day suspension, plus reimbursement of any expenses paid because of lost benefits.

Travis-Curtis, Lamberton's principal, was ordered returned to the district, but demoted to assistant principal. She would get back pay minus wages from a 30-day suspension, and also be owed expenses she incurred on benefits.

The arbitration decisions were handed down last week and first reported by NewsWorks.

Spokesman Fernando Gallard said it was the School District's practice "not to comment on ongoing legal issues, but we are reviewing all our options."

It seems likely that the district will appeal the ruling. Even if it does not, Burns and Travis-Curtis will probably not begin the fall term working in district schools, as administrative vacancies are rare this late in the summer. If the decisions are not appealed, or if they are appealed and upheld, both women would be paid even if there were no jobs for them.

Robert McGrogan, head of the Commonwealth Association of School Administrators, the union that represents principals, said he was pleased by the decisions.

"I am excited on their behalf for them being restored to their positions in the School District, essentially vindicating them of any direct involvement," McGrogan said Wednesday.

Along with Burns and Travis-Curtis, the district fired a third principal, Deidre Bennett, in January 2014. Bennett's termination was upheld by the arbitrator this summer.

Bennett was a teacher leader at Huey Elementary when cheating allegedly occurred there. When she was fired, she was principal of Cassidy Elementary.

McGrogan said the union had decided before the cases were final that it would live with whatever decision the arbitrator handed down, so CASA will not appeal the Bennett decision.

None of the three could be reached for comment.

Fifty-three Philadelphia schools were or are being investigated for possible tampering with state tests in a statewide probe. Seven city charter schools were also under investigation.

The Inquirer first reported Philadelphia test-score cheating in 2011, when some educators told the newspaper about rapidly rising test scores they said were achieved partly by adults tampering with the tests.

Separately, Public School Notebook reported that year on a long-buried forensic analysis of 2009 state exams that showed likely cheating at many city schools and others around the state.

Seven principals and teachers have been criminally charged in connection with cheating. None of the cases has been tried.

The state took charge of investigations in the 12 most serious cases of alleged cheating in Philadelphia; the School District, aided by lawyers volunteering their time, has closed investigations at 19 more city schools.

Cheating was found at 13 of those schools. Altogether, 69 educators were implicated.

As a result of those investigations, eight principals, including Burns, Travis-Curtis, and Bennett, had disciplinary action taken against them.

Seven teachers were disciplined, including three who were fired, the district said. Officials said they could not reveal the names of those implicated.

A number of those found to have been involved in the cheating had left the school system.

The district has yet to begin formal investigations at another group of 22 schools where alleged cheating happened as far back as 2009, Gallard said.

"They're much more difficult cases," Gallard said. "The information we have is not as clear-cut."

Gallard said the district had been hampered by the amount of time it spent on the first group of investigations - the law firm Morgan, Lewis & Bockius L.L.P. spent 5,000 hours on the probes - and its own lack of staff.

State officials have said more criminal charges are possible in connection with Philadelphia test cheating.

Pedro Rivera, the Philadelphia-born state secretary of education, said this month that cheating remains on his radar screen.

Philadelphia as a district remains on "open watch" status, with the most stringent test protocols in place. That's likely to continue, Rivera said.