I don't think that Jing- mei sees herself as the prodigy that her mother wishes her to be.  Jing- mei might have talent.  Yet, it is evident that her mother wishes so much more for her daughter.  The mother wishes Jing- mei to embody more and represent more than she did in her own life.  It becomes clear that the mother wishes the daughter a better life, one with more opportunity and promise, than her own life featured.  Jing- mei does not wish for such recognition in her own piano playing.  She becomes convinced that the best approach to her mother's wishes is through passive resistance.  It is evident that the mother longs for such recognition.  In part, this is to compete with Lindo Jong, whose child, Waverly, is the local chess champion.  Yet, another motivation for the mother is the idea that in her life, opportunities were not evident.  Chances for happiness were minimized.  The desire to ensure that her own child has some of these opportunities is what drives her to force her daughter to represents the highest of recognition, something that her own life lacked.