Unlike many high schools in Chicago, Steinmetz High School has no trouble filling its seats — including, on Thursday evening, with mayoral candidates debating some of the toughest questions facing the city.

Thirteen of the city’s 15 mayoral candidates took the stage at Steinmetz for a forum that addressed school finance, the city’s school sex abuse scandal, and who should control the city’s schools.

All but three of the candidates present said they would support returning authority over Chicago Public Schools to an elected school board — a promise that would undercut their power as mayor. Two candidates, state comptroller Susana Mendoza and former city police chief Garry McCarthy, committed to supporting an elected school board after previously saying they wanted the mayor to retain partial power to choose board members.

The forum was not exclusively about education, and candidates spent much of the time explaining how they would lead the city out of the shadows of several recent and ongoing scandals, including a federal probe of Alderman Ed Burke.

While the unfolding Burke scandal and corruption in city politics commanded much of the energy of the event, several candidates said the Chicago Public Schools district was also suffering amid similar conditions. Amara Enyia, a policy analyst and activist from the Austin neighborhood, said she would bring an end to what she called “a culture of corruption that has been allowed to thrive at CPS.”

And multiple candidates said they could improve on the school district’s response to recent revelations that it had mishandled student sexual abuse investigations over the past decade. Six months after the scandal broke, the district hadn’t hired anyone to head the office formed to protect students.

Lori Lightfoot, who oversaw recent Chicago police reform efforts, said she would handle the response differently.

“I would have gotten trained investigators who know how to interview child victims, and would bring parents into the process, and arm teachers with the information they need to be able to educate, protect and support the kids,” Lightfoot said.

And Dorothy Brown, who manages the city’s courts, said she would open an office reporting directly to the mayor to oversee sexual abuse allegations in the district. “I will have zero tolerance for sexual abuse in CPS, as I do in my office,” said Brown, who is facing a federal corruption investigation and a ballot challenge that could remove her from the mayoral race.

Brown and Lightfoot joined most of the other candidates in saying that they would cede power over the city’s schools more generally. Only Paul Vallas, a former city schools chief; former mayor Richard M. Daley’s chief of staff Gery Chico; and Daley’s brother Bill Daley said they wanted to see the city’s mayor retain full or partial control over its school board.

Toni Preckwinkle, whom a teachers union poll recently cast as the frontrunner, did not attend.