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“The last thing parents need is more guilt,” Mr. Kleeman says. “If this is something that allows [parents] to cook dinner or take a shower, then what’s the big deal?”

The main thing is to see these apps and other children’s media for what they are: fun and games, he says.

“The key is not to overestimate these things,” Mr. Kleeman says. “Don’t fall for the hype that if you spend half a day on these games it’s a ticket to Harvard,” he says. “It’s not.”

Don’t believe the alarmists either — the people who claim that a few moments of television time will destroy your child, he says.

Dr. Rich agrees but says — if at all possible — unplugged time is preferable to plugged time because of the “displacement effect.”

In other words, what are children missing out on while they’re engaged in screen time? Are they not going outside for physical play? Are they not talking to their parents? Are they not using their imagination?

“We feel we have to entertain and engage our kids every minute,” Dr. Rich says. “That’s why kids are so anxious today. They’re constantly running from one thing to the next.”

Dr. Rich’s advice: “Bring back boredom.”

When kids are “bored,” they let their imaginations run wild and that helps build their neurons and synapses, also know as their brain architecture, he says.

And what will give them an edge in society is not being able to parrot what they see on the screen, but rather building resilient, strong brain architecture, he says.

“Real creativity doesn’t happen when we’re bombarded with external stimuli. It requires a vacuum,” he says.

Mr. Kleeman, though, doesn’t buy the idea of the “displacement effect.”

“Kids’ lives can’t be boiled down to one moment,” Mr. Kleeman says. “These iPhone apps are not going to prevent you from going to the Shenandoah for a hike. Maybe you’re just playing it on the way out there.”

The apps aren’t meant to be played for hours at a time anyway, Mr. Simonian says.

“I don’t think parents are buying it to have their kids on it for hours on end,” he says. “It’s just an added 99-cent benefit of having the phone.”