The city Department of Education is once again investigating a bad teacher for fixing grades — more than a decade after trying to fire him for falsifying Regents test scores, The Post has learned.

Critics say it’s a case study in what is wrong with a school system where tenured teachers are protected by their powerful union — even when they are failing children miserably.

In June 2011, Osman Abugana, now 63, was accused of “inappropriately changing the scores from failing to passing” on the state Regents physics exam for five students at Medgar Evers College Preparatory, a public middle-high school in Brooklyn.

Osman Abugana refused to answer questions about an allegation that he’s been fixing grades. Helayne Seidman

“The deceit and dishonesty which the department finds to underlie this conduct are, in its view, moral failings which cannot be remediated,” according to a 2013 disciplinary opinion by a state-appointed arbitrator obtained by The Post.

The DOE called for Abugana, then a 19-year veteran of the system, to be fired.

“There is no option for a penalty in this case short of termination,” the DOE argued at the time, after a probe by its own Office of Special Investigations (OSI).

The department said Abugana’s testimony at his administrative trial was “riddled with lies and misstatements” and made him “unfit” to teach.

But Abugana, then 51, fought his firing with the help of New York State United Teachers’ union, which provides defense to NYC teachers in these hearings.

Students at Edward R. Murrow High School in Brooklyn have questioned Abugana’s teaching skills. Helayne Seidman

Instead of firing him, the arbitrator suspended him for one semester and ordered him to take a course on proper testing and grading procedures.

While he was under investigation and his case was being adjudicated, he would have spent close to three years in a DOE “rubber room,” the notorious holding spaces where disgraced teachers get paid to do nothing.

Abugana is back in a classroom and makes $140,000 a year, records show. He is still teaching physics, now at Edward R. Murrow High School in Brooklyn.

Abugana was reported to the principal of Edward R. Murrow High School, who informed the DOE of the complaint. Helayne Seidman

But his teaching skills, and his grading ethics, are still under scrutiny.

After receiving a complaint of recent grade fixing, Abugana’s principal, Allen Barge, reported the allegation to the DOE, The Post has learned.

“These allegations are very concerning and were promptly reported to the appropriate investigative office,” a DOE spokesperson told The Post Thursday, before declining further comment. “NYC Public Schools is committed to upholding the highest professional standards.”

Barge did not return calls, and the DOE would not say when the probe began.

The city Department of Education tried to fire Abugana more than a decade ago. Helayne Seidman

When confronted by The Post outside school this week, Abugana refused to answer questions.

Students at the Midwood school told The Post Abugana is back to his old tricks — quietly boosting grades to keep kids from failing a class he can’t seem to teach to save his life.

“He’s not that good at teaching,” one physics student insisted this week. “It’s really unfocused. He needs guidance on how to actually teach.”

“Everyone in his class cheats on tests,” claimed another.

Critics said the case is emblematic of a broken tenure system.

Abugana was accused of changing test scores at Medgar Evers College Preparatory School, records show. Google Maps

“Once they get tenure there’s no accountability,” said Jean Hahn, vice-president of PLACE, a parent-led education advocacy group. “They’re shortchanging the students.”

Tenure is a form of job security Gotham teachers attain after only four years in the classroom, and which bring a host of guarantees, including the inability to get fired for wrongdoing without due process — even in the case of serious sexual misconduct allegations.

Back in 2011, a teacher was tenured after only three years on the job.

“Tenure is absolutely being exploited and abused for people to be able to keep their job regardless of what harm they do to children,” said state Assemblyman Member Sam Pirozzolo (R-Staten Island), former vice president of the New York City Parents Union, and who was part of a class-action lawsuit against the state over the tenure system.

Abugana has been a teacher employed by the DOE since 1994. Helayne Seidman

He said the union “wants to protect teachers who have done bad things to their students. They don’t care about children, they only care about protecting their teachers.”

Betsy Combier, a paralegal who helps defend teachers in discipline cases, isn’t surprised Abugana quickly found his way back to the classroom.

“The schools don’t want to get rid of somebody that’s willing to change grades. It’s an asset,” she told The Post. “Everybody wants somebody that will do that for them.”

“They want to look good because they need to get funded. They need to get the money, and they don’t want to lose their jobs. They don’t want to go under review by the state. Everything is based on how well they do. So, forging and changing grades is a good thing.”