I'm not a parent, but I introduced a 10 year old child to roleplaying, very gently. I told him a bit about how it worked, which rules we were keeping and which we were ditching. Essentially, everything was free, except for some things on which I would roll a d20 (althoug the success threshold was quite arbitrary.) Actually, we both had a lot of fun, making up rules as we went.
An example scene went like this:
"There's a ditch in front of you."
"I look for a bridge."
"No bridge. You can jump over it with some difficulty."
"I try to go around it."
"You have to walk for two hours, and remember that you're supposed to be getting away quickly."
"Oh, right. OK, I jump over it."
"OK... roll, er, a 15 or higher."
"It's such a high number because I'm a hobbit, right?"
"Right."
"OK." (he rolls a 14)
"You reach the other end, but slip. Now you're hanging from the edge of the ditch."
"I try to pull myself up". (rolls a 20)
"You're over the ditch, then. Congrats."
I think this really helped him to learn how to think outside the box. While I was the one who created the world for him, he shaped it through his actions, and pretty much did anything he wanted. It was a lot like freeplay, actually.
We even had a bit of a second session a few days after that where I introduced him to actual roleplaying (before that we had only had actions. He understood quite quickly when I told him "It's like one of your school plays, except you're writing the script as you go along")