When is Jem shown to have changed in Harper Lee's To Kill a Mockingbird?

Jem reaches one of his greatest moments of change after Mrs. Dubose's death in chapters 11 and 12 of Harper Lee's To Kill a Mockingbird.

In Chapter 11, Jem is worn down by all the ridicule he faces for Atticus's decision to defend Tom Robinson. He is so worn down that he flies into a violent rage the moment Mrs. Dubose insults the children by saying, "Your father's no better than the niggers and trash he works for!" (Ch. 11). As punishment for his having whacked all the camellias off of the bushes in her garden, Jem is made to read to her daily. The night of her death, Atticus explains he would have asked Jem to read to Mrs. Dubose regardless because Atticus knew she had been working on ridding herself of her morphine addiction, developed due to her illness, before she passed away, and Atticus knew reading to her would distraction her from her withdrawal symptoms. Since Atticus had known she was working on ridding herself of her morphine addiction, regardless of how warranted morphine use was due to the pain she suffered, Atticus explains he saw Mrs. Dubose as a "great lady" because she was such a courageous woman. Atticus further explains he had wanted Jem to see that true courage is more than just being aggressive:

I wanted you to see what real courage is, instead of getting the idea that courage is a man with a gun in his hand. It's when you know you're licked before you begin but you begin anyway and you see it through no matter what. (Ch. 11)

After this lesson of what courage is and that to be a great lady is to be courageous, Jem begins changing a great deal. He especially changes in his treatment of Scout. Whereas before he used to insult her by calling her a girl, now he gets annoyed anytime she does something tomboyish and shouts at her, "It's time you started bein' a girl and acting right!" (Ch. 12). Jem's behavior towards others also becomes gentler, just like his father's behavior. For example, soon after Tom Robinson's trial and death, just as Scout is about to squash a roly-poly bug one night, Jem stops her, saying, "Don't do that, Scout. Set him out on the back steps," which Scout feels is uncharacteristic of Jem (Ch. 25). But, Jem's new behavior reflects all he has learned about courage and showing respect for others.