What are some big moments for Jem that define him as either brave or a child with the loss of innocence in Harper Lee's To Kill a Mockingbird?

All throughout Harper Lee's To Kill a Mockingbird, Jem learns what bravery is. Through his experience with Mrs. Dubose, he learns his most valuable lesson about what bravery truly is. Yet, Jem does not display his bravery in any profound way until the end of the book when he tries to defend himself and his sister against Bob Ewell's attack.

In Chapter 11, through his experience with Mrs. Dubose and growing to understand her better, Jem learned that being brave is pursuing what you feel is right despite the chances of failure. Atticus explains to Jem what Atticus believes to be the true definition of bravery in the following speech:

[Courage is] when you know you're licked before you begin but you begin anyway and you see it through no matter what. You rarely win, but sometimes you do. (Ch. 11)

In Chapter 28, Jem does what he can to try and get himself and his sister safely home, despite chances of success looking bleak.

At the moment of attack, since Jem is a quick thinker, he is able to speedily identify the warning signs of danger. He is also quick to think of a way to verify warning signs such as by asking Scout to be quiet at intervals, which allows him to hear for certain the sounds of someone following them. After assessing the danger, he knows he must act bravely and keep his head in order try and keep himself and his sister safe. He suggests she change out of her costume since the white paint resembling fat streaks in a ham can be seen in the dark. When she says she is unable to change, he tells her to just keep very quiet. He also thinks they are almost out of danger since they are nearly to the tree in front of the Radleys' place from which they can see the street light. When Jem recognizes that they are now being charged by their pursuer, Jem responds to the danger in multiple ways to try and keep them safe. First, Jem screams for Scout to run.  After escaping their attacker the first time, Jem next tries to pull Scout along towards home, but they are attacked a second time. During the second attack, Jem's arm is broken, and he goes unconscious, showing us that he has ultimately failed in succeeding to accomplish the task of reaching safety he had set out to do. Regardless of his failure, his ability to keep his head in a time of turmoil and to attempt to act upon his desire to get safely home shows that Jem was able to act bravely in this moment since it shows he was able to begin a task he knew was right despite minimal chances of success.