What does the narrator's mother believe about America in "Two Kinds"?
Jing Mei's mother believed
"...you could be anything you wanted to be in America. You could open a restaurant. You could work for the government and get good retirement. You could buy a house with almost no money down. You could become rich. You could become instantly famous".
In other words, Jing-Mei's mother believed that in America, you could make all your dreams come true. For a woman who had lost everything in her old homeland, China - "her family home, her first husband, and two daughters", - America was "where all (her) hopes lay". Unfortunately, Jing-Mei's mother decided to fulfill her own hopes and dreams through her daughter.
In trying to compete with her friend, whose daughter was a champion in chess, Jing-Mei's mother determined that, since in America you could achieve anything you wanted, her own daughter would be a prodigy. At first she wanted Jing-Mei to be "a Chinese Shirley Temple", but when that endeavor ended in disaster, she then tried to make her daughter into an academic wonder. Needless to say, that experiment did not turn out well either. Finally, Jing-Mei's mother decided that Jing-Mei should be a piano-playing prodigy. Even though the child had no talent and little interest in the piano, she tried to force the issue, resulting in heartbreak and embarrassment on her part and resentment and feelings of worthlessness on the part of her daughter.