Before beginning, we should note here that it is important for us to realize that there are many different types of Asians facing very different types of issues in America. For example, Koreans and Japanese face very different issues than Filipinos would.
That said, as with most immigrant groups, Asian Americans face the issue of how much to assimilate into mainstream American society. Many Asian groups are forced to decide whether they will compromise their own ways in order for them or their children to fit in better to American life. Many Asian groups are seen as "model minorities" who have dauntingly strong work ethics. The recent discussion of "tiger moms" illustrates this. Such Asians have to decide whether they will assimilate into American society by reducing their expectations of their children. They have to decide if they will allow their children to live "normal" American lives.