Stewart, 63, reported to the federal prison in Alderson, W.Va., on Oct. 8 to begin serving a five-month sentence for lying about a stock sale. She was convicted last March of lying to investigators about why she sold stock in biotech drug aker ImClone in December 2001, just before its price plunged.
Reporters for People magazine have heard that Martha entered prison with "a really good attitude," Gleick told The Early Show co-anchor Julie Chen. "(Martha) said, 'I just want to be one of the girls.' So far, apparently, that's what she's been doing.
"She has been very friendly. She has been talking to the other prisoners and to their visitors over the weekend and they, too, have been sort of excited to have a celebrity in their midst, I think."
Gleick noted that the facility where Stewart is doing her time is minimum security and all-female. Most of its inmates are drug offenders.
She says Martha's not with the general population yet: "For two weeks, she'll be in a sort of orientation area that they call a cottage. But it sounds a lot more like a barracks. It has 60 women. She was assigned a lower bunk. She'll be there for two weeks undergoing psychological and physical tests.
"She's being treated, supposedly, like all of the other inmates and part of (the testing) is to determine what kind of work detail she'll be assigned to.
"At the end of the two-week orientation, she'll be moved in with the general population. She will then do 90 days, like all other new inmates, of kitchen duty, which I'm thinking she'll be pretty good at!"
Martha's daughter, Alexis, "has been (there) quite a lot already," Gleick continued. "There seems to be a lot of visiting hours at Alderson. All day Saturday, all day Sunday and part of the day Monday, every week, are visiting days.
"And Alexis was there with a good friend of theirs, a staffer, Kevin Sharky, Saturday and Sunday for much of the day. There's an open visiting area and they spent the time playing Yahtzee and Scrabble and getting food from the vending machine."
Gleick told Chen that Alexis had a bit of a problem her first day visiting her mother: "She didn't realize she needed (so much) change for the vending machine. She was planning to be there, I think, all day and she ran out of quarters. So there was nothing for her to eat so she had to cut her visit short."