One theme of To Kill a Mocking Bird is how children are educated "how they are taught to move from innocence to adulthood "recurs throughout the novel (at the end of the book, Scout even says that she has learned practically everything except algebra).
I recall a quote made by Atticus early on in the Novel that governs the two children while they mature. The quote was: "You never really understand a person until you consider things from his point of view . until you climb into his skin and walk around in it."" I believe this quote has a lot of significance to the whole maturation process but mainly my first example of how Scout and Jem matured in the story. The children were playing the "Boo Radley Game- and spreading more gossip about him. Though this just shows juvenile behavior it was their actions after they were told that it was wrong to play the game mocking Boo Radley. They began to feel remorse and recognized it was inappropriate to mimic somebody they didn't know anything about except the rumors that they had a part of spreading.
The biggest maturing stage in the novel and my final example is after the verdict was given at the trial of Tom Rob Robinson. Jem didn't agree with the Justice system at all after Tom was found guilty. An example of this is when scout wanted to crush the bug. Jems words were, "Leave it alone, it didn't do anything."" Also he wanted a lot more alone time. .