You won't be able to follow the following video unless you've already seen Thunderheart.
I went to YouTube to see if I could find the relevant clips, and lo and behold, there was one video with everything I wanted (plus a little more) in it!
I guess I'll talk about things in terms of where they are in the above video.
2:08 -- Ray sees Indians dancing and singing in a circle, and then they disappear. Exactly what this is is debatable, but I'm going with the theory that he is seeing the Indians from long ago. This would fit with the vision/dream he later has where he is running with the old ones.
This vision is the first sign that he's waking up, and is a calling to him to embrace his heritage.
2:20 -- Grandpa has asked to speak with Ray, and when Ray finally arrives has a vision and tells it to Ray (with Crow Horse translating). What Grandpa sees and tells of is apparently Ray's relationship with his father, and then his father's death.
An interesting point is that during this narrative you see the TV twice in the background. The first time is at 2:50 when you see a boy running past an adult, and this is right when Grandpa is describing how the little boy in his vision would pretend to not see his father. The second time is 3:12 when the man in the vision cannot breath, and the man on the TV is stumbling around. I hadn't even noticed this until looking closely at the clip above.
So anyways, how does this contribute to the story, other than to show that Grandpa apparently has some idea of what Ray's history is? Well, it's throwing Ray's history in his face, and forcing him to think about it. Something which he doesn't seem to appreciate. He's buried his father's memory (something which he says elsewhere in the movie...) and in the very beginning he says that his father died when he was a baby. His superior corrected him, and reminded him that his father died when he was seven years old.
If he insists that his father died when he was a baby when in fact he was seven when his father died, that's a form of denying his father's existence, and a way of breaking any connection to his father.
So I guess that this confrontation (which I think it can be called a confrontation, despite there being no raised voices, profanity, or violence) was meant to try to open Ray up just a little more to his heritage by accepting and remembering his father, rather than shutting away his father's memory. After all, how can he accept his father's people if he doesn't accept his father?
4:55 -- Ray has a vision of his father holding him when he was a boy. Ray's mother comes to take Ray away from his father, who is drunk.
It's not a pretty vision, but it forces Ray to acknowledge his father's presence in his early childhood. As such, it also opens Ray up to his father's people, and therefore his own heritage.
6:40 -- The dancing, just like we saw at 2:08. I guess you could say that this is to ascertain that he's awake and open to things?
7:00 -- The big one! This is a dream/vision in which Ray runs away from a cowboy alongside other Indians. Later Crow Horse tells him that he was running with the old ones. Also, the cowboy rides out of a graveyard that Ray later finds (and which we see earlier in the movie, though I don't know in what context...) and it's the one where Thunderheart was buried.
Doubtless I'll have more to say about this particular vision later after I've re-watched the movie and can review what Crow Horse says about it.