Atticus is a moral example and straight-shooter with his children. Being a lawyer and state legislator, Atticus has likely seen the ugliest of people's treatment of each other while living in a position to help develop the most ideal circumstances for the people he serves.
He speaks to his children and deals with them almost as if they were adults. For example, pg. 6 refers to his 'courteous detachment' of them.
He also gives Scout a straight answer when she asks about rape as if he were talking to an adult. This relationship is exemplified in Chapter 9 as Atticus tells Uncle Jack:
When a child asks you something, answer him, for goodness' sake. But don't make a production of it. Children are children, but they can spot an evasion quicker than adults, and evasion simply muddles 'em.
He gives his children credit for the intelligence they have instead of treating them like most people do with children, that they are lesser. This philosophy leads him to take Tom Robinson's case because it is the right thing to do and he admits to his children he knows they are watching him. Maudie comments on Atticus' moral character regularly in an effort to teach the children about this rare phenomenon found in their father.
I agree with the previous two posters in their assessment of the parenting practices of Atticus in Harper Lee's novel To Kill a Mockingbird, particularly in their discussion of how he treats his children as young adults.
At the same time, however, I get the sense that the children have a strong respect for Atticus that borders on fear. My view probably has something to do with how I was raised, without even the threat of a whipping, but I am struck every time I read the novel by the frequent references to corporal punishment that is actually delivered by Calpurnia (one of the first details we learn about her is that her hand "was wide as a bed slat and twice as hard") and frequently threatened by Atticus. Atticus, I believe it's fair to say, often approaches his children as young adults but isn't above resorting to physical punishment to keep his children in line. He may just threaten this sort of punishment, of course, but he must know that Calpurnia delivers it.
In the book "To Kill a Mockingbird" Atticus became a father when he was older. Atticus has patience and treats his children like small adults. He does not shelter Scout and Jem from learning experiences but rather serves as a guide through them. Atticus does not teach his children through lecture or preaching. Instead, Atticus practices his beliefs. By taking on the the role as Tom Robinson's lawyer, he demonstrates to his children that one should do the right thing even when it is not the popular thing to do. He sets an example for his children.
Atticus also listens to his children. Scout becomes upset after Calpurnia scolds her for making comments about Walter pouring syrup over his food. Scout goes to her father wanting Calpurnia. He does not stop Scout from talking but allows her to ventilate. In the same manner he teaches his children to look at different sides to people. When Miss Caroline corrects Scout for being able to read, he could become angry or mock the woman. Instead he tries to get Scout to understand that Miss Caroline has a lot to learn as a new teacher and for Scout to see things through her eyes.
One of the best lesson's he teaches the children is about human nature. They do not understand why Atticus who identifies Mr. Cunningham as his friend doe not become angered when Mr. Cunnungham acts against Atticus with the mob of people.
Philosophically, I will have to say that Atticus is the children's moral and ethical guide through life.