What are three ways Scout and Jem grow up in To Kill a Mockingbird?Examples of how Jem and Scout matured and where are they found in the book?

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.