How do Scout and Jem change their behaviors in the middle of the novel To Kill A Mockingbird?

Jem grows apart from Scout, and Scout develops empathy.

At the beginning of the book, Scout and Jem are both young and behave like children.  By the trial, which is roughly the middle of the book, they are both behaving more maturely.  The trial demonstrates that Scout has learned how to empathize.  Jem also behaves in a more grown-up way, paying less attention to Scout.  Both of them have moved on from the kids’ games...

Jem grows apart from Scout, and Scout develops empathy.

At the beginning of the book, Scout and Jem are both young and behave like children.  By the trial, which is roughly the middle of the book, they are both behaving more maturely.  The trial demonstrates that Scout has learned how to empathize.  Jem also behaves in a more grown-up way, paying less attention to Scout.  Both of them have moved on from the kids’ games they used to play, acting out books and neighborhood gossip.

The relationship between Jem and Scout changes around the middle of the book.  Jem enters adolescence, and Scout can no longer understand him like she used to.  An example is the fact that the two begin to drift apart.

Jem was twelve. He was difficult to live with, inconsistent, moody. His appetite was appalling, and he told me so many times to stop pestering him I consulted Atticus: “Reckon he’s got a tapeworm?” Atticus said no, Jem was growing. (Ch. 12)

Jem wants to behave in more adult ways, and is less interested in playing with his little sister.  He wants to be grown up.  Scout is hurt by his actions, because she is still young enough to want to hang out with her big brother.

The fact that Scout and Jem are growing up is evident during the trial.  Both of them have to face hard truths about life.  Scout realizes that people are more complex than she thought, and Jem learns that the world is not fair.  However, throughout the trial Jem understands the process (or thinks he does) better than Scout.

Jem turned back to Dill, explaining, I suppose, the finer points of the trial to him, but I wondered what they were. (Ch. 18)

Scout and Jem are both affected by the trial on a person level, because their father is the defense attorney.  The trial is the talk of the town, and they are trying to understand their father’s part in it.  Scout's behavior also changes because she is capable of appreciating Mayella Ewell's situation, and Dolphus Raymond's, as well as her father's.

Scout and Jem both undergo a kind of coming of age throughout the novel.  However, while Scout is younger and has to mature a great deal throughout the course of the book, Jem also grows up.  By the end of the book, Jem is twelve and practically a teenager.  The events described in the book had a meaningful impact on both of their lives.