In "To Kill a Mockingbird" by Harper Lee, how do Jem and Scout develop throughout the novel?

Both Scout and Jem develop and change throughout the novel as they grow older.   At the beginning of the novel Jem is quite content to play with Scout and is entranced by the story of Boo Radley.  As he grows and gets to know Boo a little throughout the exchange of gifts in the tree hole, and in the incident in which Boo fixed his pants, Jem begins to have empathy for Boo and his interest in Boo becomes less sensational and more sincere.  As Jem grows he becomes less friendly with Scout and wants to be by himself more.  Aware of the injustice of the Tom Robinson case and the prejudice against black men, he is nevertheless, astounded at the verdict.  I think this is when he realizes that although his father is a good and admirable man, he cannot fix everything the way he took care of the rabid dog.  Bigotry was a sick animal that was too big for Atticus to defeat himself.

As Scout develops she becomes more able to control her emotions, particularly her anger, as she learns to "walk in another's shoes."  By the time of the trial, Scout has learned to live with Aunt Alexandra and how to empathize with poor Mayella Ewell, thinking she must be the loneliest person in the world.  Her remarks at the end of the book when she analyzes the character of the story that Atticus read to her also shows that she had developed that ability of walking in another's shoes to enabling her to empathize as Atticus did.