How does Jem change his perspective of Mrs. Dubose by reading to her and how does this all tie into discrimination in To Kill a Mockingbird?

Jem learns that Mrs. Dubose has been hurting, and was courageous in her own way. 

Mrs. Dubose is the meanest old lady in the neighborhood.  Jem has been afraid of her or disliked her for most of his childhood.  Most of the neighborhood kids feel the same way. 

Mrs. Dubose lived two doors up the street from us; neighborhood opinion was unanimous that Mrs. Dubose was the meanest old woman who ever lived. Jem wouldn’t go by her place without Atticus beside him. (Ch. 4) 

When Atticus is defending Tom Robinson, Mrs. Dubose changes her mocking to be specific to him and to the case.  He gets so frustrated by her racist diatribe one day that he attacks her flowers, destroying all of them with Scout’s baton.  She thinks he has lost his mind, but he is just fed up.  She is one more racist in Maycomb and he is tired of hearing taunts about his father. 

Atticus has told Jem that Mrs. Dubose is old and sick.  When he finds out about the flowers, he sends Jem over to apologize.  He comes back saying that she wants him to read to her every day for a month.  Atticus agrees.  The children go, and they realize that after a while Mrs. Dubose is not listening to them.  Atticus tells them it is because she is sick. 

As time goes on, Jem develops more of an understanding of or acceptance of Mrs. Dubose. 

Jem’s chin would come up, and he would gaze at Mrs. Dubose with a face devoid of resentment. Through the weeks he had cultivated an expression of polite and detached interest, which he would present to her in answer to her most bloodcurdling inventions. (Ch. 11)

After Mrs. Dubose dies, Atticus explains to them that she was addicted to morphine.  She wanted to die not beholden to anyone, and that was why she set to alarm clock and had Jem read.  Atticus wants Jem and Scout to understand that courage comes in many forms.  

Despite everything, Jem is a little upset when Mrs. Dubose dies. He buries his face in Atticus’s shirt front.  Atticus says that she was a great lady, and Jem asks how she could be a lady when she said such horrible things.  Atticus reminds Jem that although she had different views than he did, he still respected what she accomplished.

From this incident, Jem learns that bigotry and discrimination are more complex than he thought.  Mrs. Dubose was a racist, and a horrible woman.  She said racist things because she knew that they would get a rise out of Jem.  Although that does not excuse what she said, it creates a more nuanced picture of her behavior and gives Jem something to think about.