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WASHINGTON – When I look at my phone, I see my daughter leaving for camp on my home screen. She stands at the bottom of an airport escalator, an orange backpack over her shoulder. She’d cut her long, strawberry blond hair the day before, so the person smiling from under the carrot top doesn’t look familiar. But the image of a kid who just needs a backpack and a ticket is one I recognize.

Some parents may have to nudge their children to camp. For the last two summers, our daughter has run out the door.

I hadn’t been at the departure gate for her first trip as an Unaccompanied Minor. I was in the stands at my son’s baseball tournament. For pickup, my wife and I flipped the load-sharing. She did baseball duty, and I flew to Minnesota, driving almost four hours to a packed-dirt road lined with birch trees that ended at the shores of Lake Pokegama: Camp Mishawaka. Thirty-six years earlier, I had been the 9-year-old flying alone from Washington to this place with a new haircut.

When I was at camp, my parents didn’t know what was happening to me. We weren’t allowed to use the telephone, so even on my birthday I just received word that they’d called to wish me a happy one. All they got on their end was a handful of sentences written in loopy script with scattershot spelling. Technology makes hovering easier now. For the last few weeks, my wife and I ended our days poking around on the camp website, scanning photographs for the flash of red hair among the campers playing capture the flag and canoeing. Now, as I stood on the soft grass at the edge of the compound, I was doing the same scan, watching my daughter fling herself around along with the other campers, passing time before the organizing ring of the dinner bell.

Some of my best encounters with our children are the ones they don’t know about. At school pickup, I watch them conspiring with friends. When I drive carpool, I stay quiet so I can hear them making claims and testing theories. I notice that the voicemail messages from my son are different if he’s calling in the presence of his friends. Instead of speaking in his usual soft meander, he delivers crisp, informative sentences. One time I expected him to ask if we had ever really considered the benefits of a term life insurance policy.

These hidden glimpses of children in their natural habitat show us their essential version of themselves. What you see is both new and familiar – like the picture of my daughter on the escalator at the airport. The moments don’t last long. When the kids sense that you’re watching they change, even if it’s to run to give you a hug. As I watched my daughter on the open field, I put my camera under my jacket. They can sense those at 60 paces.

This disturbance in the Force is what walls us off from watching the truly great moments. But this is an evolutionary necessity. The best moments of childhood – the memories that stay with you into adulthood – are ones where your parents aren’t there. They are moments you experienced truly for yourself. In “Homesick and Happy,” Michael Thompson writes about a study where people were asked about their happiest childhood memory; more than 80 percent name a parent-free moment. Thompson explains that kids are better off when they accomplish something without having to think about how their parents would view it. Those memories are also more indelible. The self-confidence that comes from that accomplishment sticks better because it is completely earned.

So, as a parent you should want to push your kids out of your space to where they can rack up these 80 percent experiences – to explore, take risks and try new identities. We are not invited, which is a paper-cut echo of the truth at the heart of parenting: You’re doing it best when you’re teaching them to leave you. Camp is an intensive course in how your children can do this successfully. “You step away from the care of your mom and dad into the world of independence. And that’s your job in life. Every one of you accomplished steps in that direction,” said the Girls Camp director at the final-night campfire.

My kids are at that sweet age before the teenage years, before they are encased in those headphones that look like hamburger buns. Nursing resentments about the parents is not yet their full-time occupation. So when we picked up our son from a week of surfing camp, he went on a talking spree, explaining where he got his necklace made of shells, describing each room of the World War II defense bunker at the state park, and showing the campground layout with objects on the dinner table.

We had five hours inside his world, until after dinner, as he was scrubbing his utensils thoroughly the way he had each night at the campground, he stopped and looked at us: “What am I doing? Shouldn’t you be doing this?”

Good one, Necklace Boy. We all laughed and then started the slow descent to the old relationship.

John Dickerson is Slate’s chief political correspondent and author of “On Her Trail.”