“Guess who we have a play date with this Saturday?” I asked Leo as we walked to school one morning.

“Zelda?” he answered. My husband, Karl, had recently introduced our 7-year-old to the video-game land of Hyrule, home to Link, Calamity Ganon and the perennial damsel in distress, Zelda, an elfin beauty with golden-blond hair and, as is customary, a magical bow of pure light.

“No,” I answered, “a real play date.” I waited a beat before adding, “With a friend.”

"Zelda is my friend,” he said, sounding irritated.

Our walk continued like a courtroom drama. I argued against the legitimacy of having a cartoon elf as a BFF; Leo countered with an airtight defense: “She is real because she just is.” Zelda was so alive to him that she invaded his dreams, and most of our conversations walking to and from school.

After a few rounds of heated debate, I decided enough was enough. “Oh really?” I said. “If Zelda is such a good friend, how about you invite her over for dinner tonight, because I'd like to meet her."

As soon as I threw down the gauntlet, I realized how ridiculous I sounded. I didn’t really want to dash Leo’s fantasy world; I just wanted it to be accompanied by some real-life experiences (with some upright and breathing kinderfolk).

Ever since his early days in pre-K, I have been waiting for Leo to find a buddy. Preferably, one who shares his interests, including ant colonies, infectious diseases and gardening. Most kids Leo's age want to talk about Minions, which makes me worry. As much as I admire Leo for being an outlier, for greeting every day in a stellar mood and for navigating the world in ceaseless wonder, I still want for him what I most wanted for myself as a kid: the security and the acceptance that comes with having a true friend.

For his part, Leo remains oblivious enough to think that everyone is his friend and doesn’t seem fazed when the evidence — usually in the form of not being invited to a classmate’s birthday party — proves otherwise. An only child, he’s content to spend weekends hanging around with us. He prefers the company of adults, who might be persuaded to indulge his interests in, say, the physics of boiling water, in a way that kids his own age would not.

“It will happen,” says Karl, when I fret about Leo’s lack of friends. An only child until he was 7, Karl said he hung out with local kids who were “just convenient” for years. He was 14 before he finally met a kindred spirit, Rob, who remains his best friend to this day.

Still, I wondered if I should be doing more. On the recommendation of a friend who just happens to be a licensed therapist, I phoned Maria Zimmitti, president and clinical director of Georgetown Psychology, for some thoughts on children and friendship.

“Friendships can look differently for certain kids,” she began. Some children, she explained, are highly sociable and have many friends — at school, in the neighborhood, on their sports team. Other children may have a smaller group of friends or prefer one friend. In general, she says, “if the child seems happy and content, then he or she probably is.” But, she continued, “as parents, we have very good intuition about our kids, so it makes sense to want to check things out if you have a nagging concern.”

Zimmitti offered some practical steps parents might take to figure out what is going on in their child’s social life. You could approach her teacher and say something like “Can we talk about what you see with my daughter in class and on the playground?” Or you could show up on the playground yourself.

Zimmitti's third suggestion felt the most right to me, because it involved the child directly in the process. She suggested asking your child, “If you could have a friend at school, who would it be?"

So later that night, I asked Leo that very question. And instead of the “I don’t know” I was expecting, he came up with a name, a little girl I’ll call Gretchen. He went on to describe a game they played, which seemed to involve throwing sticks up and over the top of the swing sets. “It was mischievous,” he said, smiling as he relived the memory. “It was so good.”

“Well,” I began, trying not to ruin things by sounding overeager, “what do you think she likes to do?

Leo put down the book he was reading. “I don't know. I never asked her about her hobby,” he said. “But I will,” he assured me.

For the rest of the week, a Hollywood movie montage played out in my head: Leo and Gretchen skipping rope, sharing a sundae, chasing fireflies. I even allowed them a game or two of Zelda. At school pickup, I gave Gretchen's teacher my contact information and asked her to pass it along to Gretchen's parents.

A few days later, while we were walking home from school, Leo said that he had spent the day's recess walking the perimeter of the playground, alone. “No one wanted to play with me,” he said. “So, I did what I wanted to do."

"What about Gretchen?” I asked hopefully. “Did you ask her?"

He stopped and let his backpack fall to the sidewalk, “She said she didn't want to be my friend.” Before I could think of an appropriate response (one that didn't involve calling upon Zelda and her magical bow), Leo looked up at me. “Mama?” he asked quietly. “Will you help me make a friend?"

Up until then, it never occurred to me that Leo might be internalizing these schoolyard snubs and putting on a brave face. I tried not to cry; Leo was sad and hurting and looking to me to make it all better. I was startled by my feeling of helplessness, but also resolved. Now that I knew what was going on, and how Leo felt about it, I needed to figure out what to do.

When we got home, Leo sat down to do his homework while I Googled various combinations of “kids” and “friends” and “how to make.” Eventually, I found a column on Psychology Today’s website headlined, “Is Your Child Inviting Rejection? Behaviors That Push Away Peers.” Judging from the list of “off-putting” behaviors — from trying (unsuccessfully) to be funny to ignoring “stop” signals (like “Go away”) — it appeared as if the author, Princeton, N.J., psychologist Eileen Kennedy-Moore, had used Leo as her case study. I emailed her immediately.

When we spoke on the phone the next day, I told Kennedy-Moore, author of “Growing Friendships: A Kids' Guide to Making and Keeping Friends,” about the image I had of Leo wandering forlornly on the outskirts of the playground. “When kids struggle socially, they might avoid social situations,” she explained gently. “It’s like a neon sign saying, 'I don’t belong here.’ ”

But what if the child wants to be social but perhaps doesn’t know how? I recalled how I once witnessed Leo trying to barrel his way into a trio of girls he knew by kicking over a city of stick buildings.

"It can be hard to break into a group of two or three,” Kennedy-Moore said, explaining that groups of four or more are looser and easier to slip into more gracefully. “We know from research that kids who successfully join a group do not draw attention to themselves."

When a child can’t “read the room,” Kennedy-Moore suggests parents employ something she calls “soft criticism” to help him or her understand that no one likes a buttinsky. A script for Leo would sound something like I know you are so excited about subwoofers, but when you interrupt a conversation about Minions, you can accidentally make kids feel like you don’t care about their interests.

I asked her if 7 is too late to start learning these social skills. “Absolutely not! It’s not like we master relationships at age 9,” she said with a laugh. “There are a lot of things you can do."

So, I’ve been working on my soft criticisms and helping Leo understand something Kennedy-Moore called the “theory of mind,” which is the ability to comprehend another person’s perspective. He is, as are we all, a true work in progress.

Yet just the other morning, on our way to school, we happened to see one of his classmates along the way.

"Hi, Leo,” she said, waiting for us to catch up.

"Hi,” he said, giving her a big smile.

It's something I had never seen him do while playing with Zelda.

Cathy Alter is a writer based in Washington. Find her at cathyalter.com.

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