It is obvious to me that Jem is an oldest child and Scout is a youngest. The way they interact with their father shows the difference in their ages, gender, and birth order. It also might have something to do with the way they communicate and learn.
Jem learns best by watching things modeled. He is calculated and independent. He does not necessarily want to be told what to do, though he obeys directions. (Consider the incident with Mrs. Dubose.) Jem is observant and a listener. One of the best examples of his learning style comes at the end of Chapter 10 when he says, "Atticus is a gentleman, just like me!" Jem learns by watching and copying those whom he respects most.
Scout, on the other hand, learns in a variety of ways, not the least of these being through making mistakes and talking about them. As the narrator of the book, the first clue into Scout's learning style is in her way with words. She processes things by talking or writing. She doesn't usually think before she talks and acts (hence, provokes several fights at school), but when she tells the story later, she has it all figured out. Scout obviously learns by experience. Whenever Atticus sits her down to teach her a lesson, he always provides a "for-instance" story. He gets her to think about how others feel by telling her to imagine being them. Scout is less observant, but naturally intuitive. She reacts most quickly to feelings and learns best by emotionally investing in the lesson.