What are some American rules that Jingmei's family adopts?and the chines rules that Jingmei's family retains

Jingmei's mother tells her daughter at the beginning of the story that

"Of course, you can be a prodigy, too," my mother told me when I was nine. "You can be best anything. . . ."

She tells Jingmei that she can own her own home or even train herself to be a prodigy.  Thus, her mother has definitely bought into the typical American Dream--if one works hard enough, he or she can be whatever he/she chooses in America.  Her mother has eternal optimism for Jingmei's future, which again is a very American philosophy of looking at life.  Interestingly, Jingmei's mom does not have the same optimism for herself.  This is part of her clinging to Chinese traditions.  She thinks that her opportunity has passed her by; so she continues as a cleaning woman, never once seeing herself rise higher in society.  In Chinese culture of her time, people were born into set social classes, practiced arranged marriage, and did not seek to move out of the social classes.  Her mother has been unable to banish this way of thinking about her own lot in life.

Jingmei's mother is also very American in her quest to make her child a star at a young age.  After all, during Jingmei's childhood, her mother saw Shirley Temple and other other children perform on the Ed Sullivan show.  Child performers became huge during this part of American culture, and Jingmei's mother sees the potential for her daughter to profit from Americans' interest in talented youngsters.

Finally, Jingmei's parents, though they have been through many hardships still maintain their sense of dignity and honor, a remnant of their Chinese heritage.  When Jingmei's performs so badly at her recital, she recounts that she

"felt the shame of [her] mother and father as they sat stiffly through the rest of the show.
We could have escaped during intermission. Pride and some strange sense of honor must have anchored [her] parents to their chairs."

While Jingmei's mom was obviously disappointed in her, she did not truly show it or take it out on Jingmei.  It did take her years, though, to tell Jingmei once again (as an adult) that she is a genius and could do whatever she tried to do.