Let us remember that symbolism can be shown through an object, character or action. If we think about the symbolic actions that there are in this novel, we can see that one action that is definitely symbolic is what happens to the narrator when he announces that he is leaving the school on the reservation to go to a white school because he is clearly intelligent and academically gifted. This results in him being beaten up on Halloween one night by Indians because of the way that he was being a traitor to his people and to their values. Note what the narrator concludes about the symbolism of this:
They didn't beat me up too bad. I could tell they didn't want to put me in hospital or anything. Mostly they just wanted to remind me that I was a traitor. And they wanted to steal my candy and the money.
This is of course significant because it is the beginning of the ways in which the narrator becomes a "part-time" Indian because he is not accepted by either his own people or the white community that he enters by going to the white school.