Can you discuss how Jem and Scout have changed throughout the course of the novel? How have they remained the same?
Scout and Jem mature in various ways.
Together... they grow a greater respect for their father as they watch him shoot the mad dog, fight for Tom Robinson and hold his head high when spat at in the face by Bob Ewell. They also both learn to change their perspective about Boo Radley. I think Jem knows early in the book that Boo gave them the gifts in the tree, whereas Scout's great confirmation of his goodness came as she escorted him home.
Scout... grew a better understanding of the difference between actions and morality. She used to fight with her fists because that was the way she knew how to achieve success. But it really wasn't success, nor was it as effective at stopping the behaviors she wanted stopped. By the end of the novel, she is learning to do the right thing in tough situations like when she is at the missionary tea. She couldn't beat up the ladies who hurt her feelings by making fun of her dress, but she learned how to bite her lip and hold her tongue before acting.
Jem... learned that all people are equal, but we don't treat each other that way. However, a good goal would be to try. We see this as Atticus honors Jem's feeling about the outcome of the trial. He notes that if there were 11 other boys along with Jem on that jury, things would have turned out justly.