They’d gathered for supper one night in July, at the summer camp at the Kfar Silver school, in Ashkelon, Israel. For the last couple of weeks this group of kids — some from Israel, some from Palestine — had been trying to learn something about conflict resolution, by playing Ultimate Frisbee. Some of them had become friends.

That was when the air raid siren went off.

The rockets came from Gaza, part of the ongoing clash between Hamas and the Israel Defense Forces. The missiles didn’t land in Ashkelon. But they did score a direct hit on the hopes of some of the people who had looked to the camp as an oasis of peace.

“Well, we’re not trying to bring peace to the Middle East,” said David Barkan, who volunteers as the chief executive of Ultimate Peace, which sponsored the camp. “That’s not the goal. It’s about changing a mind-set through the values of the sport that we know leads to peace between people.”

As I interviewed Mr. Barkan by phone last week, I felt the temptation to roll my eyes. As he described his hope of changing hearts and minds through Ultimate Frisbee, all I could think about were those incoming rockets, and the long tragic history of that endlessly conflicted region. I struggled to imagine how Frisbee — seriously, Frisbee? — might succeed where a half-century of diplomacy had failed.