What are the two myths that Annette Kolodny argues exist about the history of Native Americans before the arrival of Columbus?
To add to the excellent answer above by co-pope, I'll mention that the reason Kolodny struggles with evidence is because she seeks to combine textual with archeological evidence as she theorizes that Leif Erikson's expeditions made it much farther south than previously thought (perhaps even to New England). There is little archeological evidence of Viking settlements that far south (maybe because of rising sea levels), but Kolodny looks at two medieval manuscripts together called the Vinland Sagas, in which the Norse travelers landed on and explored a site at the northern tip of Newfoundland ("L’Anse aux Meadows"). From there Kolodny thinks they went south and visited the Mi’kmaq peoples. The trouble is the explorers didn't have either compasses or sextants, and there are no maps included in the manuscripts. Geographic references are few and far between, making the evidence far from conclusive. Kolodny also describes nineteenth- and twentieth-century folklorists and academics who promoted ideas of Norse ancestry (unfortunately they may have had a racial or religious agenda, preferring the Norse Christian Erikson to the Catholic Italian Colombus). Kolodny is upfront about the possibility of biases and hoaxes in previous discoveries; her work doesn't entirely prove her hypothesis, but it's honest.
She argues about the Native Americans not being part of "first contact" with Columbus, rather the Vikings were the peoples that connected with Columbus as he landed. She also argues that Native Americans have similar stories about connecting with peoples "from the East" who were Norse/Basque fishermen rather than Spaniard.
Annette Kolodny argues in her pieces that the Native American peoples that are commonly associated as being the first to interact with Europeans and others who "discovered"and ventured to the Americas, were not actually the very first people to associate with Christopher Columbus. She states that early Vikings that landed in the Northern part of the Americas (modern day Canada and the U.S. North-East), and were originally from Northern Europe (modern day Finland and surrounding islands) were the first to interact with Columbus and his crews. She states that Columbus didn't have any known notes about meeting any Natives that would describe what most scholars consider a Native American. There isn't much available to support her claims of this, however there isn't much evidence to go against her claims as well. The other claim she makes is that there is evidence that the first encounters from people not of the Americas originally who were not Spanish in ethnicity, but rather a nomadic fishing type society known sometimes as Basque or Norse peoples, probably also from a Northern European origin. This claim also seems interesting and may even have somewhat evidence to back it up, but Columbus and most of his crew were not actually Spanish, they were Portuguese. They were contracted by the King and Queen of Spain to sail and adventure in the name of their interest and country. So, these claims of Native people not encountering Spanish people first could actually be seen as true, but for different reasons that Kolodny argues, as these adventures were actually not Spanish in ethnicity,but it's possible they were the people the Natives claimed to be of Norse/Basque influence.