How does Jem mature throughout To Kill A Mockingbird?

Early in the story, we find Jem to be a typical child of Maycomb. He is impetuous and given to mischief, and believes all the rumors and superstition that surround the enigmatic figure of Boo Radley.
One of the early events that forces Jem to mature is his interaction with Mrs. Dubose. He thinks that he is being punished just because he destroyed a flower bush. However, after Mrs. Dubose's death, he learns that he had been helping her with her crippling morphine addiction. Events like these mature Jem and make him realize that things are not always as they appear. By the time of the Robinson trial, Jem has matured greatly, though he retains some childish idealism. When the evidence is stacked in Tom's favor, he seems very excited and certain of his father's victory. This is a turbulent time to see the justice system fail, but regardless, Jem keeps his father's sense of justice close to his heart.

Jem Finch is Scout’s older brother who has a better understanding of the prejudice that exists in Maycomb than Scout. Nevertheless, Jem is only nine years old when the novel begins and so is still able to fill the role of Scout’s playmate. As the novel progresses, however, Jem begins to retreat from the childish games that he used to enjoy with Scout. His character becomes moodier and more withdrawn as his awareness and experiences of the world deepen. Jem has a strong admiration for justice and in turn, finds himself in utter disappointment over the outcome of Tom Robinson’s trial. At the end of the novel, however, Atticus tells us of his certainty that Jem will eventually be able to move on from his devastation over the trial.

In part 1 of the novel, Jem is portrayed as a relatively immature, naive child who fears Boo Radley, believes the rumors surrounding his enigmatic neighbor, continually argues with Scout, and expresses his childlike innocence regarding serious matters like the community's overt prejudice. As the novel progresses, Jem begins to mature and follows in his father's footsteps.
In part 2 of the novel, Jem demonstrates his maturity by no longer fearing Boo Radley, informing Atticus that Dill ran away from home, defending his father in front of the Maycomb jailhouse, and attempting to comfort Scout following her arguments with Aunt Alexandra. Jem ends up losing his childhood innocence after he witnesses racial injustice firsthand during the Tom Robinson trial, and he becomes jaded with his prejudiced community members.
Following Tom's wrongful conviction, Jem begins to sympathize with defenseless individuals and truly understands the importance of protecting innocent beings. Jem becomes more patient and understanding of Scout and demonstrates his maturity by walking her to the Maycomb Halloween festival and attempting to lift her spirits after her unfortunate performance during the pageant. By the end of the novel, Jem has matured into a morally upright, protective older brother who has a genuine understanding of the nature and makeup of his community.