In the west, what did freedom mean to native peoples, and how did that conflict with the interests and values of most white Americans in the second half of the nineteenth century? What did white Americans want? How did they see native peoples? How did different groups of natives (there is variation in their reactions) respond to white encroachment?

In the nineteenth century, the Native Americans held different values of freedom and land ownership than the white settlers did. Native Americans in general hold a very strong belief in the divinity of nature, and that extends to the idea that you cannot "own" land—it is there permanently, and the people that reside on it are only there temporarily. This idea caused a great deal of conflict and strife between the native people and the settlers.
In the late 1800's, the American idea of Manifest Destiny was in full swing, and settlers were taking land further West and North, all the way to the coast and up to the border of Canada, claiming it as their own. This unincorporated territory had largely been populated by Native Americans prior to this time, and they were frequently getting displaced from land they believed the White settlers had no legitimate claim over. The Natives simply wanted to remain on their ancestral land, even if that meant sharing it, because they believed no one should lay claim to land—it was not meant to be taken.
The white settlers saw this as a very backwards and antiquated line of thought and so didn't follow the same observances. The Native Americans were viewed as pests who were preventing the Americans from fulfilling what they viewed as their God-given right to the land.
Some Native American tribes, such as the Sac and Meskwaki, resisted, choosing to fight in order to maintain their place on ancestral lands. This led to much bloodshed and defeat and ended with the same result that the other tribes, who acquiesced much more quietly and quickly, faced. In the end, after the defeat of the Sac and Meskwaki tribes, they were forced to sign a treaty and give up their lands, moving instead to reservations, just as the Cherokee and other tribes had done more peacefully.