FORT LAUDERDALE, Fla. — Faced with mounting evidence that get-tough policies in schools are leading to arrest records, low academic achievement and high dropout rates that especially affect minority students, cities and school districts around the country are rethinking their approach to minor offenses.

Perhaps nowhere has the shift been more pronounced than in Broward County’s public schools. Two years ago, the school district achieved an ignominious Florida record: More students were arrested on school campuses here than in any other state district, the vast majority for misdemeanors like possessing marijuana or spraying graffiti.

The Florida district, the sixth largest in the nation, was far from an outlier. In the past two decades, schools around the country have seen suspensions, expulsions and arrests for minor nonviolent offenses climb together with the number of police officers stationed at schools. The policy, called zero tolerance, first grew out of the war on drugs in the 1990s and became more aggressive in the wake of school shootings like the one at Columbine High School in Colorado.

But in November, Broward veered in a different direction, joining other large school districts, including Los Angeles, Baltimore, Chicago and Denver, in backing away from the get-tough approach.