When asking questions about characters, some areas you might want to focus on are character background, character motivation and how characters influence other characters.
Let’s consider Jing-mei’s mother. What is her motivation for turning her daughter into a prodigy? The answer is partially in the first sentence of the story.
My 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.
Jing-mei (June) is just an ordinary girl, but she is an American-born girl. Suyuan, Jing-mei’s mother, believes that her daughter can grow up to be anyone or anything. This is very important. It is important to not just see her as strict and harsh. She came from a difficult background in China, not all of which we can tell from just this story, but there is enough information from this sentence and the part where she talks about daughters she left behind in China, to tell that she wants more for her daughter.
Another question we might ask is: what does Jing-mei want?
Does Jing-mei really want to be a prodigy? She is a young girl, and all young girls want to please their parents, for the most part. Jing-mei goes through some rebellion, because she doesn’t fit into her mother’s version of herself. She does play along for a while though, trying to become that version.
In fact, in the beginning I was just as excited as my mother, maybe even more so. I pictured this prodigy part of me as many different images, and I tried each one on for size.
However, as she turns out not to have any real prodigy talent, and the will to practice for hours at a time, Jing-mei becomes less and less interested in the prodigy part. She tries many different talents, but none of them stick.
Finally, the third question is: How did Jing-mei’s mother influence her?
The answer to this question is in the song. We see that Jing-mei never turned out to be a piano prodigy. As a child there were two songs: “Pleading Child” and “Perfectly Contented.” As a child, she saw herself as the pleading child. She was never happy, and felt she disappointed her mother. She knew her mother wanted her to be the contented child, and she wanted to make her mother happy. She never saw that song, though. When she grew up, she returned after her mother died, she saw that song. When she went to play the song as an adult, she noticed something.
"Pleading Child" was shorter but slower; "Perfectly Contented" was longer but faster. And after I had played them both a few times, I realized they were two halves of the same song.
Now that her mother was dead, she had the piano tuned “for purely sentimental reasons.” Why was something that was such a source of pain as a child so sentimental? It was meaningful to her because she realized as an adult that her mother made her play the piano because she cared about her and wanted to give her a brighter future.