What evidence showed that Jemwas starting to grow up and was beginning identify with the adult world?

Jem's evolving maturity and widening outlook were highlighted by a number of clues in Harper Lee's ``To Kill a Mockingbird," which indicated his gradual shift from a whimsical child to a young man with a growing awareness of the adult world.

Growing sense of responsibility: Jem has a new awareness of his duties as a big brother and starts taking care of Scout. He becomes a mentor to Scout and starts educating her about the moral standards of Maycomb.

Increased knowledge of social injustices: Jem's knowledge of Maycomb's social imbalances grows, and he comes to grasp racial bigotry and unfairness. When Tom Robinson is found guilty despite overwhelming evidence in his favor, he is deeply disappointed.

Atticus Finch, Jem's father, is looked up to with more reverence: Jem has a higher opinion of Atticus as he becomes older, showing his increased maturity and respect for his father's moral and ethical principles.

Growing up and maturing mentally: As he goes through puberty, Jem's emotional experiences and physical development both deepen. He begins to question his previous beliefs and behaviors and displays traits of introspection.

Understanding racial disparities: Jem's understanding of the complex racial dynamics in the South broadens, and he comes to see the suffering of African Americans in their community and the obstacles they confront. He becomes more compassionate towards others.

Participation in legal processes: Jem participates more actively in the trial of Tom Robinson, paying close attention to the legal proceedings and making an effort to understand the intricacies of the case. He starts to form opinions and viewpoints that are unique to him.

These indicators demonstrate Jem's maturation, deepening perceptions, and developing adult mentality as he develops from a young child into someone with a deeper understanding of the complexities of the world surrounding him.