Adeola Whitney, executive director for Playworks in the Newark area, said that the recess coaches used a playbook with hundreds of games and gave students a say in what they do.

“It’s not rigid in any way, and it certainly allows for their creativity,” Ms. Whitney said. “In some cases, we’re teaching children how to play if they can’t go to the park because it’s drug-infested, or their parents can’t afford to send them to activities.”

Each school pays Playworks $23,500 a year to run a recess program — Broadway Elementary is using a grant from Covanta Energy, which owns a waste-to-energy plant in Newark — and the rest of the expenses for training, equipment, after-school activities and field trips are covered through the nonprofit’s grants and donations.

It is not just about fun and games. At University Heights Charter School in Newark, another of New Jersey’s eight Playworks programs, students have learned to settle petty disputes, like who had the ball first or who pushed whom, not with fists but with the tried and true rock-paper-scissors.

“Recess used to end with bad feelings that would continue to play out in the first 20 minutes of class,” said Misha Simmonds, the charter school’s executive director. “Instead of recess being a refreshing time, it took away from readiness to learn.”

Ms. Parker, 28, the coach at Broadway Elementary, had worked as a counselor for troubled teenagers in a group home in Burlington, N.C. Besides her work at recess, she visits each class once a week to play games that teach lessons about cooperation, sportsmanship and respect.

“These are the things that matter in life: who you are as a human being at the core,” she said.

Broadway Elementary, with 367 students in kindergarten to fourth grade, rises above a rough-hewn industrial neighborhood in the North Ward. Nearly all the students are black or Hispanic, and poor enough to qualify for free or reduced-price lunches.