Thursdays, when I’m the day care provider for my toddler granddaughter in Brooklyn, N.Y., usually unfold fairly routinely: books, Legos, songs, meals, naps, walks to the park.

But some Thursdays become more memorable. On a winter afternoon, when the sun was low, we were crossing an empty basketball court at the park when my granddaughter, whom I call Bartola as an affectionate nod to former Mets pitcher Bartolo Colon, noticed our elongated side-by-side shadows. I could almost hear her wondering: What’s that?

“Look, there’s your shadow,” I said. I showed her how the shadows waved back if we waved at them; if we danced, our shadows danced with us. So we boogalooed across the court with Bartola happily calling, “Sadow! Sadow!” She seemed puzzled, the following Thursday, when the sky was overcast and no shadow appeared.

Only later, telling friends about this cherished interlude, did I consider that my daughter Emma, Bartola’s mother, had at some point discovered shadows, too.

But when did that happen? Was she 2 or 4? Was I even there? I was a working parent, like most of us, so maybe our nanny witnessed it but I didn’t. I was never one to record every milestone in one of those keepsake books. Maybe I plain forgot.

I’ve wondered since what makes grandparenting feel so special, in some ways more indelible than parenting itself. We’ve done all this before, from diaper changing to reading and rereading “The Story of Ferdinand.” But this time, it feels different.

Schmoozing with other involved grandparents around the country, I’ve found broad agreement with this observation, and developed some ideas about why.

First, though we do a lot of the same stuff, it’s not the same job. Parenting, sweet as it was, so often also became consuming, exhausting. Long before anyone heard the word “multitasking,” most parents were simultaneously trying to build careers, manage expanding households, maintain marriages or other relationships, all while preparing our kids for this crazy world.

Life could be such a blur that it’s no wonder certain tender memories have evaporated. We often overlook how crushing all that responsibility could feel.

“I remember the visceral fear of making a mistake, of dropping the baby, of doing something wrong,” says May Benatar, a psychotherapist and author in Silver Spring, Md. The worst part, she adds, was her constant anxiety about child care. “That I didn’t have it. That it wasn’t adequate. That the kids would be sick on the wrong day.”

That’s no longer her obligation. She and her husband pick up their two nearest grandkids at school every Friday, spend the afternoon with them, serve dinner and sometimes give baths, then take them home.

“All the joy and none of the worry,” says Myrna Cozen, an epidemiologist in El Cerrito, Calif., who uses the word “magical” a lot when talking about her 7-year-old grandson.

As a young parent, divorced when her son was little, she put herself through college, fretted about money and her son’s minor health problem, functioned on insufficient sleep. Now, “I’m a step removed from the everyday struggles.”

Work once loomed as a constant distraction and stressor. Steve Adamczyk spent 25 years building the software company he founded. As a father, therefore, “part of my mind was always on getting back to that terminal.” Maybe the pressure is worse for men, he muses, whose self-worth is so tied to providing.

Since selling his company, he can spend part of almost every day with his three grandchildren in Bloomfield, N.J., ferrying them to or from school. This time around, “I’m not thinking about anything else except the kid I’m hanging out with,” he says. “I try hard never to take my phone out. I don’t check my email. I don’t worry about what I have to do later. I can just be with them.”

Let’s acknowledge an important exception: those heroic grandparents actually raising their grandchildren. More than a million children live in their grandparents’ households without parents present, says the advocacy group Generations United. Grandparents who are distant, geographically or otherwise, probably also have different experiences.

But many of us, even if we’re still working, have left life’s climbing phase for the maintaining-altitude part of the flight. I carve out a day each week, and feel secure enough to tell my colleagues and students that Thursday is Bubbe Day (it’s Yiddish for “grandmother”) and that almost everything else can wait until Friday.

Vacations aside, how often could I have devoted eight uninterrupted hours to my daughter when she was little?

But grandparenting feels different not only because the task has changed, but because we have.

Other grandparents tell me how much more patient and attentive they’ve become, how much less anxious, how willing to be silly. Freed of the oppressive conviction that everything we do, or fail to do, shapes children’s futures, we can simply revel in being with them.

“I don’t get as uptight as when I was a mother,” says Mary Scott- Boria, 67, a semiretired social worker and teacher in Chicago. She describes herself as a somewhat rigid parent, filled with expectations for her kids. As a grandmother, “I’m looser,” she says. “I’m able to hear what their lives are like. They trust me; they talk to me.”

Micki Berg, who lives outside Detroit, would like you to know that she did “a damned good job” of raising six children before earning a doctorate in human development. Now, with most of her grandkids close by, “I can be more playful,” she says. “I don’t have to get anybody ready for their spelling test.”

This likely will not come as news to Laura Carstensen, the Stanford University psychologist who has long pointed out that research shows older people are happier than younger ones, in part because we adjust our emotional lives.

Recognizing that our time is growing limited, we learn to savor our most important relationships, to turn toward positive experiences.

Our children will have one advantage. They’re not going to forget as many of parenthood’s daily wonders and tortures because they’re compulsively documenting them with the phones we all carry.

Thirty years ago, we had to remember to bring actual cameras along, to buy and develop film, so my albums are filled with pictures of birthdays and vacations but not of everyday life. I can’t recall my daughter’s first haircut — but I have a photo of Bartola’s, as she calmly sat in a car-shaped chair.

Still, I’ll bet that a couple of decades hence these young parents, if they’re lucky enough to become grandparents, will marvel at how unexpectedly swell the experience is. I wish that for them.