In "Two Kinds" by Amy Tan the mother lives vicariously through her daughter.
The mother is a Chinese immigrant who lost her first husband and twin daughters in her homeland of China. She made her way to America to begin a new life, which includes aspirations of the American Dream for her daughter. The mother believes you can be anything in America and starts the quest for her daughter by examining the success of child prodigies. She sees how these children are on display in magazines and on television, which makes her believe her daughter must have some talent that would bring her the same success. This is an attempt by the mother to leave the horrors of her past behind and to move forward in her own life.
She is misguided in her understanding of what a child prodigy is by not realizing they have a innate talent that can be cultivated. She longs for her daughter to have the same, but does not find it, so she decides on the piano for her daughter. Although, Jing-Mei is able to pick up piano skills with some ease, she is not a prodigy. The mother learns this lesson the hard way after sitting through her daughter's disastrous piano recital.
The mother's interest in the remarkable children was her attempt to have a remarkable child of her own.