Five Democratic mayoral hopefuls agree on one thing: City schools badly need fixing.

On Tuesday night, they offered up ideas - and occasional sharp words - at a forum focused on education issues, the dominant issue in the campaign.

State Sen. Anthony H. Williams, viewed as the strongest supporter of charter schools, said he was "exhausted" by the debate of charter vs. traditional public schools.

"We need to stop beating up on one type," said Williams, who has the backing and the financing of three wealthy charter-school proponents, the founders of the trading firm Susquehanna International Group. "We need to fix them all and fund them all."

Williams was joined by Nelson A. Diaz, Jim Kenney, Doug Oliver, and T. Milton Street. Lynne Abraham had a scheduling conflict and did not join the panel.

Kenney, who has been endorsed by the Philadelphia Federation of Teachers and so has the financial muscle of the local union and its national arm, said that he would have "less of a problem" with charter schools if the state fixed reimbursement for those schools, and if some charters didn't cherry-pick the best students.

"I am not an enemy of charter schools," Kenney said. "I am a fan of public schools."

Diaz, who suggested he supported a school-funding lawsuit now being pursued by some Philadelphia parents, statewide nonprofit organizations, and the William Penn School District in Delaware County, took a jab at Kenney and Williams, saying he disliked when longtime politicians talked about fixing schools but did nothing about it.

Williams bristled, saying that the "only person up here who's delivered a quarter of a billion dollars since 2010 is me."

Pushed on the issue, Williams said: "It's mine. I'm going to take credit for it."

Each of the five said he was against the property-tax increase proposed by Mayor Nutter to raise $105 million in new money for city schools, but said the district ought to have more money through other sources.

Diaz said that he wanted the School Reform Commission ended immediately and that he, as mayor, should be given responsibility for reforming the schools.

Oliver said he wanted a forensic audit of the Philadelphia School District, and called for underperforming city schools to undergo management changes. He also said he would scrutinize the city budget to find ways to help schools.

"How do we have a health department and no nurses?" Oliver asked.

Kenney, who touted his plan for universal prekindergarten, said that the city's biggest problem was its poverty rate and that teachers were not to blame for the school system's problems.

He said Philadelphia schools had been hurt by the lack of a unified message in Harrisburg. The mayor and council president, in recent years, had lobbied lawmakers separately.

"I can tell you I'll be in the car with Darrell L. Clarke going up the turnpike to Harrisburg," Kenney said.

Street said that was not the job of the mayor, who should "stay in Philadelphia and do your job!"

Kenney shot back: "I'm glad you're not going to go, because it wouldn't be helpful."

Street drew perhaps the biggest reaction of the evening when he said that asking white lawmakers in Harrisburg for more money for a district composed of mostly African American and Latino children wasn't going to work.

"Come on, people! Wake up and smell the veggie burgers!" he said to guffaws.

The next mayor must address violence in city schools, Street said, if Philadelphia wants to be taken seriously in Harrisburg.