“‘Is there a ball somewhere? Throw the ball,’” she said. “‘Kick the ball.’”

Among affluent parents, fear of phones is rampant, and it’s easy to see why. The wild look their kids have when they try to pry them off Fortnite is alarming. Most parents suspect dinnertime probably shouldn’t be spent on Instagram. The YouTube recommendation engine seems like it could make a young radical out of anyone. Now, major media outlets are telling them their children might grow smartphone-related skull horns. (That, at least, you don’t have to worry about: no such horns have yet been attributed to phones.)

No one knows what screens will make of society, good or bad. This worldwide experiment of giving everyone an exciting piece of hand-held technology is still new.

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Gloria DeGaetano was a private coach working in Seattle to wean families off screens when she noticed the demand was higher than she could handle on her own. She launched the Parent Coaching Institute, a network of 500 coaches and a training program. Her coaches in small cities and rural areas charge $80 an hour. In larger cities, rates range from $125 to $250. Parents typically sign up for eight to 12 sessions.

“If you mess with Mother Nature, it messes with you,” Ms. DeGaetano said of her philosophy. “You can’t be a machine. We’re thinking like machines because we live in this mechanistic milieu. You can’t grow children optimally from principles in a mechanistic mind-set.”