As an adolescent, Jem matures and demonstrates his coming of age by losing his childlike naivety, acting responsibly, and exercising perspective.
In part 2, Jem reaches puberty, and Scout comments on his increasing appetite, moody personality, and "inconsistent" attitude. As Jem gets older, he begins to act more responsible and exercise sympathy for others. He stops bothering Boo Radley, informs Atticus that Dill ran away, and tries to comfort Scout when she feels upset. Jem also refuses to leave his father's side in front of the Maycomb jailhouse when they are surrounded by a lynch mob. He recognizes the gravity of the situation and displays his maturity by defying his father's request to leave. Following the incident, Atticus appreciates his son's courage and integrity in the face of adversity.
Once Jem observes racial injustice firsthand by witnessing the Tom Robinson verdict, he completely loses his childhood innocence and becomes jaded with his racist neighbors. Jem thus demonstrates his coming of age by recognizing the hypocrisy throughout his community and acknowledging the dangers of racial prejudice.
In addition to Jem's enhanced outlook on his hometown, he also develops sympathy and transforms into a compassionate, understanding older brother. He goes out of his way to prevent Scout from arguing with her aunt, engages in an insightful conversation regarding Maycomb's social hierarchy, and comforts his sister following her embarrassing pageant incident. Scout even praises Jem for acting mature and sympathetic by saying, "Jem was becoming almost as good as Atticus at making you feel right when things went wrong."
Overall, Jem demonstrates his coming of age by reaching puberty, developing perspective, and exercising responsibility and compassion.