Final answer:
The mother's offer to give Jing-mei the piano for her thirtieth birthday shows that the mother wants Jing-mei to reconnect with her Chinese heritage and embrace her potential and talents.
Step-by-step explanation:
The mother's offer to give Jing-mei the piano for her thirtieth birthday shows that the mother wants Jing-mei to reconnect with her Chinese heritage and embrace her potential and talents. The piano symbolizes the mother's hopes and dreams for Jing-mei. Through the piano, the mother hopes to pass on the legacy of their cultural heritage and the opportunities that Jing-mei may have missed while growing up in America.