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In Amy Tan's The Joy Luck Club, in the chapter called "Two Kinds," the piano symbolizes two very different things to June and her mother. To Suyuan Woo, the piano symbolizes one's ability to achieve the American dream through hard work.

My mother believed you could be anything you wanted to be in America.

In this case, she wants June to become a child prodigy. June notes that her mother is not certain of what kind of prodigy June should be: at first a "Chinese Shirley Temple." Then there are tests to see if she can recite the capitals of every state; then multiplying numbers in her head; card tricks; and, even "predicting the daily temperatures" in major cities across the U.S. 

At first June is very excited about the prospect of being special in some way. But the continuous disappointment on her mother's face changes this, and whatever motivation she had once "began to die." She sees herself as sad and ugly. But while she rails at her reflection in the bathroom mirror one night, she sees another side to herself:

The girl staring back at me was angry, powerful.

With this mindset, June begins to resist her mother's efforts, no longer trying. Her mother seems to give up until she sees a young Chinese girl performing on the piano on The Ed Sullivan Show. Suddenly, June's mother imagines that if June takes lessons and begins to try, she will also be a prodigy—a child pianist. And so June's mother barters housecleaning services for piano lessons with a retired teacher in their building, and the lessons begin. In this way, Suyuan Woo believes her child can be successful, cashing in on the American dream that is out there just for the taking. The piano symbolizes realized opportunity and success to Suyuan. 

However, June hates the piano. She will not practice and resists at every opportunity.

...I...learned I could be lazy and get away with mistakes, lots of mistakes. 

Her piano teacher is so engrossed in teaching her to keep time to the rhythm of the piece that he does not notice her mistakes. June recalls later that she might have learned to play if she had really tried. For June, the time at the piano becomes a way for her to rebel. Suyuan continues to hope June will succeed because June's cousin has become something of a chess prodigy. As June listens to her mother brag about how caught up in her music she is, June decides to put an end to it all:

And right then, I was determined to put a stop to her foolish pride.

Childishly, June believes that she is fighting her mother. However, when the talent show arrives, June has deluded herself: she gets up to play and is terrible. The piano comes to symbolize June's rejection of her mother's plans, and her rebellion against doing what she does not want to. In the end, she embarrasses herself at the recital; her mother is horrified.

June also sees the piano as her mother's attempt to make her what she is not. She knows she is not a genius.

For unlike my mother, I did not believe I could be anything I wanted to be. I could only be me.