In chapter one, Jem is a strange mixture—in some ways a child, in other ways mature and sensitive. Referring to specific examples from the first chapter of To Kill a Mockingbird, show the truth of the statement.
This novel, although narrated by Scout, is really about how Jem comes to question his immature view of the world. It's Jem who is hit hardest by his understanding of Boo and the treatment of Tom Robinson. Scout is just too young to really mull over and analyze the events while she's going through them. It's only in her adult voice that she comes to an understanding.
In chapter one we see that although Jem is about four years older than Scout, he still plays with her and their new neighbor, Dill. They play act—a childish activity. Another sign of his sensitivity in chapter one is the fact that he really seems to be missing his dead mother. Scout is too young to really remember her, but Jem feels her absence.
On the other hand, Jem starts to show a resistance to this sensitivity and childish games as the novel progresses. He is awakened to evil in the world and the fact that people are more complex than they seem (Boo, Mrs. Dubose, Walter Cunningham, etc.). In chapter one he shows some strength by going along with Dill and attempting to lure Boo out of the house, but even here he is easily "spooked" and runs away like a small child.
If you follow the maturation of Jem through the chapters, you will see him let go of his young ways more and more.