Why does Waverly's mother allow her to compete in tournaments?

Waverly's mother is proud of her Chinese heritage and tries to impart Chinese wisdom to her children. One of her "rules" is that, to win an argument, one should be silent: "Strongest win cannot be seen." When a man suggests to her mother that she should allow Waverly to play in chess tournaments, her mother smiles but says nothing. Waverly fears her mother will not allow such a thing. So, Waverly remains silent (as her mother has taught her) and then uses reverse psychology: 

I desperately wanted to go, but I bit back my tongue. I knew she would not let me play among strangers. So as we walked home I said in a small voice that I didn't want to play in the local tournament. They would have American rules. If I lost, I would bring shame on my family. "Is shame you fall down nobody push you," said my mother. 

Given her mother's penchant for following rules, she must find something admirable about chess and the rules of that game. She also wants her daughter to master the American rules simply to prove herself. Her mother thinks the Chinese do things better than Americans. Learning the American rules and beating them at their own game would please her mother. She takes great pride in Waverly's wins. When they walk to the market, her mother shows her off. There is the sense that her mother is living vicariously through Waverly. Waverly notes this and eventually says " If you want to show off, then why don't you learn to play chess?"