I've covered most of these points before, but the article is a fun read. I'll summarize the "myths" and "truths" here, but check out the source.
Note: The six points below state the truth, not the lies. That's a bit confusing.
6 Ridiculous Lies You Believe About the Founding of America
By Jack O'Brien, Elford Alley
Our history books don't really go into a ton of detail about how the Indians became an endangered species. Some warring, some smallpox blankets and ... death by broken heart?
There's a pretty important detail our movies and textbooks left out of the handoff from Native Americans to white European settlers: It begins in the immediate aftermath of a full-blown apocalypse. In the decades between Columbus' discovery of America and the Mayflower landing at Plymouth Rock, the most devastating plague in human history raced up the East Coast of America.
#5. Native Culture Wasn't Primitive
American Indians lived in balance with mother earth, father moon, brother coyote and sister ... bear? ... If the government was taken over by hippies tomorrow, the directionless, ecologically friendly society they'd institute is about what we picture the Native Americans as having lived like.
One of the best examples of how we got Native Americans all wrong is Cahokia, a massive Native American city located in modern day East St. Louis. In 1250, it was bigger than London, and featured a sophisticated society with an urban center, satellite villages and thatched-roof houses lining the central plazas.
#4. Columbus Didn't Discover America: Vikings vs. Indians
America was discovered in 1492 because Europeans were starting to get curious about the outside world thanks to the Renaissance and Enlightenment and Europeans of the time just generally being the first smart people ever.
A bunch of Vikings set up a successful colony in Greenland that lasted for 518 years (982-1500). To put that into perspective, the white European settlement currently known as the United States will need to wait until the year 2125 to match that longevity. The Vikings spent a good portion of that time sending expeditions down south to try to settle what they called Vineland--which historians now believe was the East Coast of North America.
#3. Everything You Know About Columbus Is a Calculated Lie
Columbus discovered America thanks to a daring journey across the Atlantic. His crew was about to throw him overboard when land was spotted. Even after he landed in America, Columbus didn't realize he'd discovered an entire continent because maps of America were far less reliable back then.
The myths surrounding him cover up the fact that Columbus was calculating, shrewd and as hungry for gold as the voice over guy in the Cash4Gold ads. When he couldn't find enough of the yellow stuff to make his voyage profitable, he focused on enslaving Native Americans for profit. That's how efficient Columbus was--he discovered America and invented American slavery in the same 15-year span.
#2. White Settlers Did Not Carve America Out of the Untamed Wilderness
The Pilgrims were the first in a parade of brave settlers who pushed civilization westward along the frontier with elbow grease and sheer grizzled-old-man strength.
In written records from early colonial times, you constantly come across "settlers" being shocked at how convenient the American wilderness made things for them. The eastern forests, generally portrayed by great American writers as a "thick, unbroken snarl of trees" no longer existed by the time the white European settlers actually showed up. The Pilgrims couldn't believe their luck when they found that American forests just naturally contained "an ecological kaleidosocope of garden plots, blackberry rambles, pine barrens and spacious groves of chestnut, hickory and oak."
[In short, the Indians "tamed the wilderness" before the Europeans arrived.]
#1. How Indians Influenced Modern America
After the Natives helped the Pilgrims get through that first winter, all playing nice disappeared until Dances with Wolves. Even the movies that do portray white people going native portray it as a shocking exception to the rule. Otherwise, the only influence the Natives seem to have on the New World and the frontiersmen is giving them moving targets to shoot at, and eventually a plot outline for Avatar.
The fake mystery of Roanoke is a pretty good key for understanding the difference between how white settlers actually felt about American Indians and how hard your history books had to ignore that reality. Settlers defecting to join Native society was so common that it became a major issue for colonial leaders--think the modern immigration debate, except with all the white people risking their lives to get out of American society. According to Loewen, "Europeans were always trying to stop the outflow. Hernando De Soto had to post guards to keep his men and women from defecting to Native societies." Pilgrims were so scared of Indian influence that they outlawed the wearing of long hair.