Independent children

In The joy Luck Club by Amy Tan, she writes an introductory paragrah or paragraphs before each section of her book, which is more than one chapter each. The paragraphs do not necessarily have anything in especific to do with the stories in the section, but there are connections that can be made and there is a purpose to all of that.
I think that the introductory piece's purpose is to give the reader the idea that children like to be independent when they benefit from the independence.
As I read the chapter, Rules of the Game I realized that the girl, Waverly Jong gets to the point in her life where she starts doing something that gives her life progress which makes her be more independent from others.
Waverly Jong discovers that she has a talent; she is an amazing chess player. She became well known and was one of the best. I think that she likes to be independent after her successes.
One way that she becomes independent is by not being a part of the family. She is a part of the family, but it does not seem like she is a part of the family since she is always busy.
When se wants to practice or think about chess in her room, she can't concentrate when her siblings are making noises so she tells them to be quiet. Being good at chess and actually playing outside of home with other, professional I guess I could say, players makes her change. She does not seem like a little girl anymore. She likes to be alone and independent.
One day, Waverly and her mother went out, not because Waverly wanted to but because her mother made her. They kept seeing people and her mother would proudly tell everyone that she was her daughter. Then Waverly said,

"I wish you wouldn't do that, telling everyone I'm your daughter." My mother stopped walking. ..."Aiii-ya. So shame to be with mother?" She grasped my hand even tighter as she glared at me.

This does not necessarily shows "independence", but I think that the fact that she is embarrased of her mother and she does not want to accept it makes me think that she would like to be independent from her mother. I think that almost all kids go through that point in their lives when they don't like their parents being with them. In this case, chess has changed the life of Waverly and now she doesn't like being with the family. She prefers being alone and independent. But when she realizes that she really depends on herself at the end, she does not want to be independent anymore. What happened at the end was that her mother told the family to leave her alone because Waverly didn't care about them. When she knows she is alone, then she wants it all back.