Waverly's family is isolated from people outside her immediate neighborhood. For example, Waverly hears questions at school about whether the Chinese carry out torture, showing that people harbor cultural stereotypes about Chinese people. In addition, the church in her neighborhood brings presents dedicated from a church outside of Chinatown. To get these presents, Waverly must avow that she believes in Jesus Christ, though she is not necessarily a believer in Christianity. Waverly's family is isolated from the cultural mainstream, and people outside Chinatown don't understand her family's culture.
When Waverly begins to win at chess tournaments, she becomes less isolated from the cultural mainstream, but she becomes more isolated from her own family. When she plays chess, she plays against people outside of Chinatown, and she has to play using American rules. For her, it's a way to get to know what life is like outside of Chinatown. At the same time, she becomes more isolated from her family. She is allowed to get out of doing her chores, and she gets to spend more time by herself. She also challenges her mother, a behavior that is more typically American than typically Chinese. Therefore, the price of becoming more connected to mainstream culture and less isolated from mainstream culture is to become more isolated from her own upbringing and culture. Waverly cannot have both connections at the same time.