In Amy Tan's short story "Two Kinds," what sacrifice does the mother make for her daughter?

In Amy Tan's short story "Two Kinds," the mother makes many sacrifices for her daughter, the protagonist in the story. The mother has come to San Francisco from China, where she lost all of her family, and she tries to teach her daughter that she can be anything she wants to be. The mother has sacrificed her own life, while contending with painful memories of her dead children in China, to try to make her daughter's life great.

The mother does not make much money cleaning houses, but she is able to gather magazines from the houses she cleans to find stories of amazing children to motivate her daughter to achieve greatness. Later, the mother is convinced her daughter can be a musical prodigy, and she manages to have her daughter take piano lessons, even though she has no money. Tan writes, "She had talked to Mr. Chong, who lived on the first floor of our apartment building. Mr. Chong was a retired piano teacher, and my mother had traded housecleaning services for weekly lessons and a piano for me to practice on every day, two hours a day, from four until six." The mother works hard to provide music lessons to her daughter. 

The daughter is worried that her mother wants her to be a genius, but the mother responds, "'Who ask you to be genius?...Only ask you be your best. For you sake.'” The mother wants her daughter to work as hard as she can--something the daughter has a hard time doing. After the daughter does badly at a recital after failing to practice her piece, the mother wants the daughter to continue to practice piano. However, the daughter refuses, and that's the end of her lessons. It's only many years later, after the daughter inherits the piano from her parents, that she realizes that she has cheated herself by not working hard enough and that what her mother wanted was only hard work, not perfection.