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PHOTO: Provided by Matt Whooley
Mayoral candidates gather in the auditorium of Eagle Academy for Young Men.

Mayoral candidates had to dig deep into history to unearth an unpleasant memory about the United Federation of Teachers at a schools forum in the Bronx on Tuesday night.

Asked to recall a time when they disagreed with the UFT, Bill Thompson and City Council Speaker Christine Quinn cited the union’s initial opposition to district centralization nearly 20 years ago.

Thompson at first praised the UFT’s role in the re-centralization, which shifted some hiring responsibilities to the chancellor and required changes to state law. Pressed to name a time that he disagreed with the UFT, Thompson said it was when the union obstructed the same shift.

“The resistance, before that, of the UFT to change the system that existed, to changing from decentralization, was a mistake,” he said.

Thompson’s delicate answer reflected how carefully the Democratic candidates are handling issues dealing with the union, which is hosting its own forum before thousands of members this weekend. On June 19, the union’s Delegate Assembly will vote to endorse a candidate, a decision that could tip the scales in the Democratic primary.

The union was barely mentioned during the first 45 minutes of the education forum, which was organized by the Eagle Academy Foundation, a nonprofit that supports the Eagle Academy network of public schools. Instead, the candidates polished their education talking points. Quinn went after testing and de Blasio, renewing his attack strategy, went after Quinn.

“Speaker Quinn, you had 12 years to challenge the mayor on his obsession on high-stakes testing and you didn’t do it,” de Blasio said. “It’s kind of hard to say it now and have people believe it.”

Former Bronx Borough President Adolfo Carrión, Jr. also appeared on the panel. He was the first to bring up the teachers union, offering what might have been the night’s — or the race’s — most notable flip-flop.

Carrión, who left the Democratic party to run as an Independent and who is also seeking the Republican nomination, had previously blamed the UFT for the city’s failure to reach a teacher evaluation deal before a state deadline in January.

“The city and the teachers union were at the table, and as far as I know, the teachers union removed themselves from the negotiations,” Carrión told Capital New York at the time. He also credited Bloomberg for standing up against the UFT on negotiations.

On Tuesday, Carrión basically said the exact opposite when asked to name one thing he would change about the Bloomberg administration.

“I would change the posture that the mayor has taken as it relates to the relationship with the teachers union,” he said. “I don’t believe the mayor should ever, ever walk away from a negotiation of teacher evaluation.”

Former teacher Sal Albanese, a long-shot candidate, also said he had been at odds with the union over its resistance to city changes to governance structure (Blasio and Carrión had left by that point).

Comptroller John Liu, the only candidate to point to a different issue when discussing the union, criticized the UFT for its silence when the Department of Education “chastised” Khalil Gibran International Academy, the city’s first dual language Arabic program, “to the point that it is now a mere semblance of what it used to be.

“The United Federation of Teachers should have taken a strong stance in helping that school stay around and succeed,” he said.

Carmel Macklin, a special education history teacher at Eagle Academy, said Liu’s candid response impressed her the most.

“I liked when he went out on a limb about the Arab school,” she said after the forum ended. “I appreciate those organic responses over those canned responses.”

Quinn made an impression on a small group of students who gathered outside in the school’s lobby after the event.

“Besides what she was saying, she was very sure of what she was saying and she had evidence and proof of what was going to do, so that’s what I really liked about her,” said ninth-grader Habeeb Lewis.

It was the second candidate panel at a school in five days but the first time that all of the front-running Democratic candidates were together talking about education policy in months. The event was moderated by Elinor Tatum, publisher of the New York Amsterdam News, and Gerson Borrero, a columnist for El Diario and regular guest on NY1’s Inside City Hall. It drew more than 100 people, many from Eagle Academy.