For Shirley and her family, America represents all sorts of new things they wouldn't have had at home in China. Her dad gets a new job; her mother takes on a new role as a housewife; and Shirley, in particular, gets the chance to reinvent herself and make friends outside of her family.
Importantly, though, America also represents the unknown for Shirley since she doesn't understand a lot of the things here. What are skyscrapers? What's a washing machine? Why do kids play stickball? In other words, America is exciting and scary all at once.
With new social opportunities (think: playing stickball) come new fun things, and as she stops being lonely and starts having fun, Shirley begins to identify America with advancement and opportunity. When Shirley gets a new bed, for instance, she wonders where her dad found it:
When she opened them again, there stood a giant bed fit for an emperor. Shirley threw herself on the mattress and lolled about like a fish tossed back to the sea. "How did you do it, Father? How?"
But before he could say a word, she shouted, "I know. It's just another wonderful engine made in America." (8.21-22)
Now that she's fitting in at school, America is the land where dreams come true to Shirley. And not just in the form of beds—she learns at school in the U.S. that she can grow up to be anything she wants, that she can make a real difference. Like Mrs. Rappaport says about baseball:
"In our national pastime, each player is a member of a team, but when he comes to bat, he stands alone. One man. Many opportunities. For no matter how far behind, how late in the game, he, by himself, can make a difference. He can change what has been. He can make it a new ball game." (6.70)
It's not just Jackie Robinson who can break barriers—Shirley can, too. She has already moved to America after years of anti-Chinese laws didn't allow Chinese people to settle in the U.S., and she is a smart, strong girl who can grow up to break barriers for women and Asian-American people, just like Jackie Robinson did for African-Americans. Whereas in China she was identified as part of her family unit (hey there, Sixth Cousin), in America Shirley can be whoever she wants.