In what ways do Waverly and her mother differ over their hopes and dreams for Waverly's future in "Rules of the Game" by Amy Tan?

Waverly doesn’t really see chess as her ticket to a bright future as much as her mother.  Her mother is proud of her, in the appropriate Chinese way.  Waverly is enjoying the game for the game’s sake.  She gets tired of her mother holding her up as some kind of prodigy.  She feels like her mother is making too much of a big deal out of her success.

Waverly went from knowing nothing about chess to being amazingly successful.  Magazines had her on their cover and local shopkeepers displayed her success in cakes in their windows.  However, the success came at a cost for Waverly.  She felt that her mother became more and more controlling. 

At first, it was just that her mother didn’t really seem to have the same priorities.  She did not even really seem to understand how chess worked.

"Ma, it's not how many pieces you lose," I said. "Sometimes you need to lose pieces to get ahead."

"Better to lose less, see if you really need."

At the next tournament, I won again, but it was my mother who wore the triumphant grin.

Mother and daughter had bigger issues, though.  Waverly’s mother took pride in her success.  She believed that her daughter could win any tournament and beat anyone.  She enjoyed parading her around the neighborhood.  Yet she also pushed her to win “better” by losing fewer pieces.  Nothing could be good enough.

Waverly did not want to be her mother’s trophy.

But there was one duty I couldn't avoid. I had to accompany my mother on Saturday market days when I had no tournament to play. My mother would proudly walk with me, visiting many shops, buying very little. "This my daughter Wave-ly Jong," she said to whoever looked her way.

She finally got fed up and told her mother that she didn’t like to be paraded around like this.  Her mother was hurt, saying Waverly was ashamed of her.  Waverly and her mother didn’t have open communication.  She didn’t know how to tell her mother that she just wanted to enjoy playing chess, and she didn’t want to be her mother’s prodigy.