how does jem mature in chapter 11 and in chapter 21?

I think that in chapter 11 Jem matures through his experience with Mrs. Dubose. Through his reading to her and his flower at the end, he may not have liked her but he comes to understand her. This is exactly what Atticus wanted his son to see. In Chapter 21 Jem realizes that despite his father's best efforts, the world can be an unfair dark place. Tom Robinson is deemed guilty despite his obvious innocence. Jem too looses his innocence that day. He sees the ugly side of his friends and neighbours, he sees that the right verdict didn't come after doing the right thing.