Wow, I love your teacher; this is like something I'd ask my class to do:
Here are some suggestion questions that your thesis might answer:
Why did the Aztec Empire fall?
Why did American Indians take different sides in wars between white nations (Civil War, American Revolution, French and Indian War?)
Why were Native American technologies so far behind European technologies when the two cultures met?
How did the introduction of the horse (or the gun. or distilled liquor.) by Europeans impact the lives of Native Americans?
Hope those help.