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DURHAM, N.C. — Hillary Clinton made a pitch for public schools at a get-out-the-vote rally on Thursday, proposing to create a teaching task force that would recruit more young people and midcareer professionals to the country’s struggling public schools.

“I think public education needs some T.L.C.: Teaching, Learning and Community,” she told a rowdy crowd at Hillside High School, a predominantly black public school. “Thousands of teachers cannot make ends meet, are leaving the profession.”

Mrs. Clinton mentioned seeing crumbling schools in rural South Carolina and urban classrooms in Detroit infested with rodents and mold. She said that when she traveled across the country as first lady she would apply what she called “the Chelsea test” to public schools she would visit.

“I would say to myself ‘Would I send my daughter there?’” she said. “A lot of places, the answer was yes, and proud to do it, but too many times the answer was no.”

The plan came days after Mrs. Clinton defended teachers’ unions at a Democratic debate in Flint, Mich., on Sunday. Asked by CNN’s Anderson Cooper if unions — the largest of which have endorsed Mrs. Clinton — protect bad teachers, she pushed back on the assumption.

“It really pains me,” she said, “a lot of people have been blaming and scapegoating teachers because they don’t want to put the money into the schools system that deserve the support that comes from the government.”

North Carolina, which holds its primary on Tuesday, has seen its public schools stripped of funding in recent years. Mrs. Clinton has come under criticism for expressing skepticism of charter schools and teachers’ evaluations, two topics she hardly broached in Thursday’s upbeat address.

Instead, Mrs. Clinton tried to make her remarks personal. She talked about studying North Carolina’s public schools as first lady of Arkansas when she was given the task of improving that state’s schools. But since then, she said, Republicans in the state had “slowly eroded” public education.

“I am a product of really good public schools,” she said. “I had great teachers from kindergarten through high school. They challenged me. They helped me understand the world that I l lived in and what I could do to make a difference.”

The speech on improving public education came on a busy day of campaigning for Mrs. Clinton as she shuttled to campaign events from Florida to Illinois (with a stop in North Carolina on the way) leading up to Tuesday’s voting contests. At a stop in Tampa, she discussed investing in infrastructure.

At a late-night rally outside Chicago, Mrs. Clinton discussed manufacturing and job training — topics that have become central to the race in the Midwestern states where her opponent, Senator Bernie Sanders, has criticized her record on trade deals.