Michael Jackson’s three children, Prince Michael I, 12; Paris, 11; and Prince Michael II (“Blanket”), 7, have been trying to gain a sense of normalcy since their father’s death in June. With the support of their grandmother and guardian Katherine Jackson, the children are “slowly coping.”

One source tells PEOPLE that Prince and Paris have become more confident over the past several months. “It would have been hard to imagine them going out in public or showing up at someone’s house hanging out and playing video games before [their father died],” says the source. “That had a lot to do with Michael, because every time he showed up there were bodyguards and [chaos]. And now, not so much. It feels much more normal and they’ve adjusted really well to that.”
“They’re doing great, thanks to the love and support they’ve gotten,” Adam Streisand, an attorney for Katherine Jackson said.

Katherine is raising the kids with their former nanny, Grace Rwaramba, who had stopped working for Michael before his death but returned afterward upon Katherine’s request. Sources reveal “nothing over-the-top happens” at home and she is trying to have the children live as normal a life as possible. And now when the children go out in public to karate lessons or to the library and church, their faces are no longer concealed. “They like not wearing the masks,” the family source says of the trio. “It’s a different experience for them.”

“Katherine really listens to the kids,” says Streisand. “She wants to give them a sense of freedom when she can. She wants to encourage them.”

Their father’s influence lives on though. “Talking to Prince is like talking to Michael,” says the family source. “He’s so smart and mature – way beyond his age.” Paris, meanwhile, “wants to be a singer.”