"I do this and then I go (home), and I'm with my son, who goes to a parents' co-op," she said.
"I work in his school, and I have a very different existence at home (in New York City) that keeps me kind of out of the loop of how the politics in this industry works. So this is all kind of new to me," explained the 31-year-old actress.
Right now, Connelly, like many other parents, finds herself facing the difficult task of explaining the tragic events of Sept. 11 to her child.
"We live in downtown Manhattan, so a lot of kids have lost people, family members, and a lot of kids saw it happen, including my son. So they're still drawing pictures of the towers. They're building block towers and knocking them down. They're going into cubbies and saying that they're stuck and calling rescue workers on pretend cell phones. It's still going on. It's diminished a little bit, but it's still going on," Connelly said.
The beautiful, dark-haired star of "Inventing the Abbotts," "Requiem for a Dream" and "Pollock" said she tries to reassure her son that President Bush and the police are doing everything they can to protect the city from further attacks, but the little boy still worries about the safety of the Big Apple.
"That's part of their awareness now," she stated, adding that her son, who is showing some early signs of wanting to be a film director, has come up with some ideas of how a new World Trade Center might fend off attackers. For example, he thinks the new buildings should be made of rubber instead of steel and concrete. Guess it's better he become a film director than an architect.
So, how would Connelly feel if her son ultimately chose a career in the entertainment industry?
"I would never push him into anything that was not his own choice and I would try to protect him as much as I can as long as he'll let me," she said.
Connelly started her career as a model when she was just a child herself. She made her film debut at age 14 in Sergio Leone's epic, "Once Upon A Time in America" and acted opposite David Bowie in the Jim Henson fantasy "Labyrinth" when she was 16. Although she has worked steadily since then, many critics have observed that it is just recently that she is coming into her own as an actress.
"A Beautiful Mind" director Ron Howard agreed with that appraisal, saying this of his leading lady: "Jennifer has really emerged in the last few years. She's very intelligent, a great beauty and has a lot of integrity. And she's developing this extraordinary screen presence."
But Connelly emphasized that she is continuing to hone her acting techniques and still has much to learn. She said that as of now she uses "trial and error" until she finds a method that feels comfortable.
"You have to do it. You can't keep thinking about it, you just sort of surrender to it, especially when you get the opportunity to work with great actors," she said. "I still don't know if I have the hang of it ... It's kind of a work in progress ... (But) I've felt more invested than ever and committed and passionate since the birth of my son."
A huge fan of Oscar-winning actress Meryl Streep, Connelly confessed that when she hits a rough patch in her work, she wonders, "What would Meryl do?"
Asked what she thinks about the Oscar buzz her portrayal of Alicia Nash has generated in the last few weeks, Connelly admitted that she feels extremely flattered, but says she doesn't want to speculate about the possibility. She did say, however, that she has imagined what a thrill it would be to say something special to her little boy in a public arena like an awards show acceptance speech.
Connelly called the decision to accept the role that has brought her so much acclaim a "no-brainer," recalling how she fell in love with the fictionalized account of the inspiring couple's life the moment she read the script.
"I thought, 'This is such a beautiful script. I love Ron. Russell Crowe's a great actor. This part ... this woman is beautiful, what I wouldn't do to do this movie! They'll never cast me ...'" she remembered. Crowe plays her mathematician husband, John Forbes Nash Jr.
Connelly described being hired for the job as "a great experience."
"It was such a blessing," she said.
Although the movie is only loosely based on the Nashes' extraordinary life together, Connelly met with the real-life Alicia Nash to discuss what the woman might want or not want conveyed about the character that bears her name in the film.
"She's a lovely woman, but it became more about having a nice lunch, and she gave me her blessings," Connelly recalled.
Alicia Nash did have one serious question for Connelly, however.
"She wanted to know what Russell Crowe was like," Connelly said.
"A Beautiful Mind" is in theaters now. Connelly can next be seen in the big-screen version of "The Hulk," directed by Ang Lee ("Crouching Tiger, Hidden Dragon," "Sense and Sensability") and due out next year.
Celebrity Families of 2014 [PHOTOS]