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In the aftermath of the massacre at Marjory Stoneman Douglas High School in Parkland, Fla., President Trump embraced a proposal to arm teachers as a way to prevent further mass shootings in schools.

His support for the idea, which had been proposed by the National Rifle Association, invigorated a nationwide debate over whether the people educating children should also bear the responsibility of wielding firearms to protect them.

In New York, the answer from state lawmakers was a firm no.

Gov. Andrew M. Cuomo on Wednesday signed a bill that prevents local school districts from allowing teachers and administrators to carry guns on school grounds.

“The answer to the gun violence epidemic plaguing this country has never been and never will be more guns,” Mr. Cuomo said in a statement.