I think the conclusion to the story actually fits well. The idea that the experience of mother and daughter regarding piano ends in a sort of stalemate is appropriate. Both realize that there is more to their own senses of self. The mother begins to understand that the pursuit of the American Dream can contain subterranean demons and these must be acknowledged. The daughter realizes that she crossed a line in resurrecting a memory from the past. Both understand that there might be a component to their identities that will never be fully grasped by the other. The mother will never understand that her daughter is armed with a conception of freedom "to be herself," as opposed to living with the expectations placed on external contingencies. By the very same analysis, the daughter will never understand the level of difficulty her mother endured in the patriarchal and traditional society of China and the pain caused with the abandonment of her two children. This level of disconnect might be why the mother gives the piano to the grown up daughter at the end of the story. While there is an understanding about the gesture, it never is fully realized. I think this speaks well to the generational and cultural experiences of both mother and daughter, making the ending quite valid.