For a brief period that began in December, students in Northampton, Mass., arriving at elementary schools were greeted once a week by police officers lining the sidewalks to deliver high-fives and encouragement.

It was part of a trust-building program called High Five Fridays, intended to show children that police officers were not the scary men and women they might have heard about or seen on television. Parents overwhelmingly supported the program.

But in January, Jody Kasper, the city’s police chief, started hearing from a small number of parents who said that their children — especially minorities and those who have had difficult experiences with the police — were uncomfortable with the officers’ presence. Concerned that the education of those students might be harmed, Chief Kasper and the school district’s superintendent, John Provost, decided last week to scrap the program.

“Certainly we do not want to have our officers at a school and have kids, even if it’s a handful of kids, be traumatized and have a negative experience with our officers,” Chief Kasper said in an interview on Tuesday. “That’s the opposite of the goal we’re trying to accomplish.”