We can divide growth of a person in a majority of ways. I think for the purposes of your question we can consider moral growth, social growth, and pyschological growth.
Moral growth refers to how a person develops a set of behaviors that are in line with his own spiritual beliefs and understanding of right and wrong. The children learn that racism is destructive while witnessing Tom Robinson's trial and that people who are different are not necessarily bad people through their interactions with Boo Radley.
Social growth refers to how a person relates and interacts within his social environment. Clearly, the family lives in the south during a time when black people were several discriminated against. Children during this era where raised to believe that nothing was wrong with this behavior. However as the children mature throughout the novel, they realize that society can be wrong. They come to understand the their father has to work within a society that does not agree with him, but that he can do it in a way that does not anger most people. I would refer you to the evening he sits outside Tom Robinson's jail cell for an example of this.
Finally, I would point out that as the children physically mature, they psychologically mature as well. They come to accept the imperfections of their father, of themselves and of people in general. When Jem is injured by Mr. Ewell, the whole family must accept that anger and rage exist. They are able to transcend their own childish selves and see the more far-reaching affects that actions have on others.