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LOWER MANHATTAN — For four years, she made her mark on New York City’s public schools and the more than one million families connected to it. Now, days before her boss, Mayor Bill de Blasio, begins a second term, Carmen Fariña has formally announced her retirement.

She’s garnered widespread praise for doing a thorough job in a high-pressure position, but those kudos did not come without criticism, or without calls for her successor — whoever that may be — to do better.

The announcement of Fariña’s retirement came in a City Hall news conference hosted by the mayor and First Lady Chirlane McCray, along with three other key city officials flanking them. Fire Commissioner Daniel Nigro, Police Commissioner James O’Neill and Corporation Counsel Zachary Carter, the city’s chief lawyer, were all seated at a head table with Fariña.

The mayor used the occasion to share that Nigro, O’Neill and Carter were all remaining in their jobs. Fariña, however, the mayor said nearly 20 minutes into the event, will be leaving in the “next few months.”

It was an occasion for Fariña, 74, to look back on her tenure.

“If I have to think about what I’m really proud of [it was that] we put in a system that worked on collaboration, not competition, from day one,” he said.

Her record was praised by the mayor.

“[We’ve seen] the highest graduation rate in the history of New York City,” said de Blasio, adding that under Fariña, the schools have their “highest college enrollment rate for our young people, highest college readiness rate,” and other accolades.

Despite those statistics, however, a variety of educators, including education professor David Bloomfield of the City University of New York Graduate Center and Brooklyn College, point out that a lot of the improvements in the DOE system began with Fariña’s predecessors. He singled out Michael Bloomberg’s first chancellor.

“Joel Klein was the transformative chancellor,” said Bloomfield. “This was the restorative chancellor. [She is] someone who could really restore the superintendencies that we had before, and restore good relationships with the union.”

Fariña reinstated area superintendents — DOE administrators below the chancellor level — in 34 districts across the city. The superintendent positions had been part of the city’s educational structure, formerly known as the Board of Education, for many decades, but former mayor Bloomberg did away with them, choosing instead to re-center and re-name the system.

His Department of Education, as it’s still called 15 years later, had its leadership concentrated at Tweed Courthouse, its headquarters, as well as in individual principals at the city’s schools.

The number of schools increased, from about 1,600 to 1,700, after Bloomberg split up the city’s largest schools into smaller entities co-located in buildings where the larger schools had once been.

The change resulted in lower absentee rates, as school administrators came to know students better, with lower overall school sizes. Graduation rates also went up. Fariña increased those improving figures, according to Bloomfield.

The retirement announcement came just three days after the chancellor announced the closure of 14 schools, including the Urban Assembly for Wildlife Conservation, near the Bronx Zoo. It’s where, two months ago, the city had its first fatal crime in more than a generation.

In early October, Abel Cedeño, 17, fatally stabbed fellow Urban Assembly student Matthew McCree, 15, in a case of possible self defense, that may have involved bullying. Fariña’s announcement ended up being an unfortunate coincidence in relation to the tragedy.

“This is Matthew McCree’s birthday, and his mother is at the cemetery as we speak,” said Sanford Rubinstein, the attorney for McCree’s family. “Yet it happened in her schools, under her watch.”

Rubinstein said that the family is calling for Fariña’s successor to be more willing to install metal detectors in schools, and to take a more active stance against bullying.

Fariña has long maintained that she’s been highly proactive with the Urban Assembly school, including making five visits to its campus in the West Farms section since the stabbing happened.

Fariña gave a recommendation for her successor and to others, including critics,possibly, as she officially stepped aside.

“My advice is to listen more, talk less,” she said. “Get really good advice from people you’re going to work with.”

Mayor de Blasio did not share much about a possible replacement. He said that he and a team of close advisors had been doing a wide search “for some time,” but he would not elaborate further.`

Bloomfield pointed out, though, that de Blasio, who’d given a speech in the key presidential primary state of Iowa earlier this week, is seeking to have a national profile.

De Blasio may be seeking a candidate who is “an anti-Trump, and anti-[Education Secretary Betsy] DeVos,” Bloomfield said.