“You sort of know what he must have felt the first time he saw me,” Kross said of the birth of his oldest son, Miles, now 5.

The New York City stay-at-home dad sees his kids more than his father saw him, and he said that it makes a difference.

“My middle child knows 200 words and I’m the only one that knows 160 of them,” said Kross of Stella, 22 months old.

Kross also is the father of a 4-month-old, Violet.

“The best part of being a dad is seeing how you can make someone infinitely happy just by smiling at them,” Kross said.

In the Evolution of Dad, a documentary, filmmaker Dana Glazer explores what it means to be a dad today. The modern dad has evolved from the sometimes-absent breadwinner to the increasingly common stay-at-home dad.

As Father’s Day approaches, children, no matter how old, remember riding on their father’s shoulders and dancing on his toes. Dads remember those things too, but what really stands out are the unexpected rewards of parenthood.

“He gives me a hug when I’m not expecting it,” said Colby Trane, father of 18-month-old Theo. “When I pick him up and he puts his arms around me and pats my back, there’s something so incredibly rewarding about that.”

Trane, another New Yorker, loves it most when he gets little Theo laughing to the point where he’s gasping for air.

Father-Child Bond Seen in Nature

Trane’s bond with Theo is comparable to the bond between fathers and children seen in nature. Scientific research has shown that lab mice grow extra brain cells when they become dads. The extra brain cells are for dads to be able to create lasting memories with their babies.

Human dads grow new neurons, too, when they become fathers.

“We’re very instinctive creatures and there’s a lot of programming in there that you really just can’t deny,” said Jake Ward, editor of Popular Science. “I think any new dad will tell you that there’s just something inside that gets triggered when he sees his child for the first time.”

Scientists said that fathers develop a sort of affection in response to the smell of their infants, but you don’t have to tell any new dad that.

“When you have kids, you realize a love that you never thought possible,” said New Yorker Matt Schneider, father of 21-month-old Sam.

Easygoing Dad, Unstructured Fun

Part of that love means giving kids enough freedom to learn life’s lessons. Remember your dad letting you fall off your bike so you can learn how to make sure it doesn’t happen again?

Kross and Trane, along with their children, belong to NYC Dads Group, a New York City play group designed and led by fathers.

Lance Somerfeld founded NYC Dads as way for involved fathers to navigate fatherhood together. Somerfeld said that stay-at-home dads and involved fathers sometimes feel invisible. Groups like NYC Dads allow fathers to bond with one another and their children.

Kross and Trane said a play group organized by dads has a different perspective, calling it a “dad-ternity.”

“How you run after them, how you let them take a fall, let them get into a situation they have to work themselves out,” Trane said, “dads are more relaxed and let their kids explore. The moms are prone to saying no, no, no.”

Sociologists agree that the dads typically let kids be more adventurous.

“Something only dad does best is play and have unstructured fun,” said Christine Carter, a sociologist and author of “Raising Happiness.” “That’s how kids learn to interact and follow direction, and kids know dads can make mom happy.”

A happy mom means a happy marriage, and sociologists say that it’s important for kids to live in a stable home.

“Good old dad represents the downtime we long for,” Carter said. “He’s the easygoing, playful, teasing love in our lives.”

He can be the love in our lives that holds our hand as we take our first steps, and when we’re older, that holds our nervous arm as we walk down the aisle. He’s the humble man of the house with few words but infinite love.

New Dad

At Roosevelt Hospital in New York, new fathers held their newborns for the very first time.

“When the doctor raised her up, it was just breathless,” said one new dad of his daughter.

Another dad said, “I think the best part about being a dad is this — being able to see someone who you helped create.”

It makes one wonder why they call it a maternity ward when dads beam so proud too, filing memories away in the heart.