All week long in Brady Shutt’s classroom at Liberty High School, north of Iowa City, his students have been talking about school shootings.

So on Thursday, when President Trump proposed arming teachers to curb violence, Mr. Shutt posed a question to his students: What do you think of the idea of training teachers to have guns in schools?

Eyes bugged out. Heads vigorously shook no.

“They said, ‘You mean arming teachers? Teachers like you? Why would a teacher ever have a gun in school?’” Mr. Shutt recalled. “It just didn’t fit into their worldview. And there were concerns about what that would do to the relationship between teacher and student.”

Mr. Shutt said he was deeply opposed to Mr. Trump’s proposal — in particular the idea that federal funds should be used to train teachers in how to use a gun, when educators, Mr. Shutt said, had so many other needs.