In order to answer this question, we first need to establish what round characters and dynamic characters are. Round characters are characters in a story with complex personalities who are portrayed with depth and realistic emotions. A dynamic character is someone who is significantly transformed during the course of the story. I would argue that the first-person narrator, Jing-mei Woo, is both.

Jing-mei's round character is revealed by the angst that she deals with in response to her mother's wishes and expectations for her. The complexity of Jing-mei's character shows itself when she keeps disappointing her mother and finds that "something inside [her begins] to die." The roundness of her character comes to light again when she screams at her mother and announces that she is not a genius and that she can't play the piano. It is also seen in the difficult relationship she has with the chess prodigy Waverly. Her character has real depth, and it's easy to imagine Jing-mei as a real person.

We see evidence of the dynamic nature of Jing-mei's character when she begins to rebel against her mother. At the start, she is affable to her mother's wishes, going along to beauty training school, getting her hair cut, and visualizing herself as becoming a prodigy.

She goes along with her parents' every wish and allows her mother to test her to see how she measures up to the child prodigies discussed in magazines. At first, she tries hard, guessing that Nairobi is the capital of Finland because it is "the most foreign word [she] could think of."

Later, however, "something inside [her begins] to die," and she grows to hate the process of trying to find the area in which she will become a prodigy. By the time piano lessons come around, she has become so disillusioned that she hardly tries at all and takes advantage of her teacher's deafness, which leads to her being humiliated at the talent show. By now, we are seeing the dynamism of her character, and she has changed from being an obedient child to a person with her own strong opinions.