How are the ways people view gender roles in Maycomb different from the way we view gender roles today? How are they similar?

Gender roles in Maycomb are, for the most part, radically different from how they are today. To Kill a Mockingbird is set in the Deep South during the 1930s, when the respective roles of men and women were clearly fixed, and almost immovable. Generally speaking, women were expected to stay at home and raise the children, while the men went out to work. To be even more specific, African-American women were expected to help raise white women's children, or at least those who could afford to hire help. Respectable white ladies were put on a pedestal in Southern society. They were expected to be gracious, demure, and dignified at all times. This is the ideal of womanhood that Aunt Alexandra tries so hard to instill in Scout.
The elevated notion of Southern womanhood also extends to those from less privileged backgrounds. Even though Mayella Ewell is widely despised throughout the town as a member of a notorious "white trash" family, she still has the privilege of being a white woman, and as such her honor must be protected against the depredations of an alleged black sexual predator. Mayella gives her evidence on the witness stand in court, but women are excluded from serving on the jury, as their delicate sensibilities are thought too fragile to withstand the sordid details of a rape case.
There aren't too many similarities between gender roles then and now. But Scout very much points towards a more modern, more enlightened approach to women's roles. Scout is an unashamed tomboy, and her rough and tough behavior is far removed from prevailing standards of female conduct. She mixes with Jem and the other boys on a more or less equal basis and always gives as good as she gets. Aunt Alexandra wants to turn her into a fine, upstanding Southern lady, but it's pretty much a losing battle. Although gender roles remain largely fixed throughout the book, in the character of Scout we see the possibility of their transcendence. Scout represents a link between gender roles as they operated in the 1930s and how they operate today.