In the first few chapters, Scout is shown to be a child who means well, but lacks the tact to not make her statements and explanations rude. This is shown when she is trying to explain the financial predicament of the Cunninghams. She tries to explain why he has no lunch by saying "He's a Cunningham" (p 26) and saying nothing else. She is rude when she later has to explain to the teacher, and she is punished for her rudeness. Later on in the story, when Walter Cunningham is eating lunch at the Finch's house, she openly criticizes him about his eating habits (p 32). This rudeness earns her another punishment, this time from Calpurnia.
However, as she gets older, Scout does learn some tact. She learns to hold her tongue (somewhat) and learns to explain things without being as rude. This is shown when she explains to her Uncle Jack in Chapter Nine about why she beat Francis up. As she says, "I don't mean to sass you, I'm just tryin' to tell you" (p113). She uses her words instead of her fists, which shows how much she's grown.
Scout was shown to be a quick-tempered and hotheaded child. She would much rather duke it out on the battlefield with fists then participate in an intellectual discussion. This is most prominent when she decides to beat on Walter Cunningham when he inadvertently gets her in trouble with the teacher on her first day of school (p 30). He really had done nothing to get her in trouble; Scout had defended him rudely and gotten reprimanded for her sassing of the teacher.
After Atticus talks to her about her fighting, though, especially where he is concerned, she learns to calm down, lest she faces a beating. She shows admirable strength against Cecil Jacobs when he puts her father down and taunts her about being a coward for not fighting "because her daddy told her not to" (Chapter 9). She also manages to keep her wits about her when Mrs. Dubose insults Atticus and her family (although Jem doesn't keep his cool that time around). However, she is shown that she is still a fighter and is willing to fight family when she beats up her cousin, Francis Hancock, after he badmouths her father. She will hold back her fists in public, but if your family and you say something she disagrees with, you'll be paying for it.
One of the things that sets Scout off is the topic about her father being a "nigger-lover" for defending a black man in a trial. (p 112) In the beginning of part one, there is no real racism or bias shown, or at least none that is noticeable. This all changes as the children get older and start to notice the world around them. The older the kids get, the more is revealed. When Atticus takes the case of Tom Robinson, a black man accused of raping a white woman, he opens himself to a barrage of hateful remarks. These remarks are not only directed at him, but also his children, Jem and Scout.
While most of the remarks directed at the children are from fellow kids, sometimes the adults make the remarks to the children as well. A prime example of this is Mrs. Dubose. A racist old woman who has issues with drugs, she viciously insults Atticus in front of his children (p 135). The kids soon learn that almost every white person in the town is against Atticus and Tom Robinson, and isn't afraid to show it. Scout has to learn that the world is not fair and it is a biased and racist place.
In conclusion, Scout shows considerable growth as a character throughout the first part of the book. She learns to keep her temper and not fly off the handle at people who aren't her family. Scout also learns to keep her tongue in check along with her attitude. She acquires tact and uses it sparingly. Even when Scout learns that the world is not fair, she still does her best to keep her temper and use words instead of fists. This is an exponential growth from the little girl who would try and kill anything or anyone that looked at her funny, and never curbed her words or tongue. That is why I believe Scout Finch grows substantially as a character in the first part of the novel, "To Kill a Mockingbird.