In To Kill a Mockingbird, how can the reader see Scout change during chapter 9?
For one thing, she doesn't punch Cecil Jacobs when he insults her father because Atticus told her not to. She understood that to do so would have let her dad down, and even though she didn't understand everything going on around her, she at least could grow up enough to handle walking away from a fight.
But she's a little girl and old habits die hard...she did beat up her cousin Francis at Christmas because he called Atticus a "nigger-lover", and although she was punished for it, later she managed to give a very good defense for her actions to her Uncle Jack.
Ultimately, we can see that Scout is beginning to lose her innocence and to understand that things aren't always fair, but her desire to do what Atticus wants and needs her to do is admirable and a sign that she is growing up.