The first winter was disasterous - nearly half of the Pilgrims died of starvation, pneumonia and tuberculosis. Many claim that Bradford's first wife perished that first winter, but that is not quite true - she actually fell off the Mayflower quite close to land and drowned, never making it to Plymouth (he later remarried.)
During the first two years the colony lived under what could only be called Communism, enshrined in the Mayflower Compact. Each person was accorded a "share" of the totality of what was produced at the colony, and each person was expected to do their part in working toward the common good. The land, and that upon it, was owned by the colony as a collective.
It not only did not work out, it nearly killed them all.
William Bradford wrote in his diary "For in this instance, community of property (so far as it went) was found to breed much confusion and discontent, and retard much employment which would have been to the general benefit and comfort. For the young men who were most able and fit for service objected to being forced to spend their time and strength in working for other men’s wives and children, without any recompense. The strong man or the resourceful man had no more share of food, clothes, etc., than the weak man who was not able to do a quarter the other could. This was thought injustice.”
After the second winter, realizing that the colony had survived only through the friendship and largesse of the native Americans, and would soon perish if changes were not made, Bradford tore up the Mayflower Compact. He instead assigned each family a plot of land to be their property, to be worked as the family saw fit, and with the fruits of that land to be their own. It was the beginning of private property rights in the New World.
The result? Again, from his diary: "It made all hands very industrious, so that much more corn was planted than otherwise would have been by any means the Governor or any other could devise, and saved him a great deal of trouble, and gave far better satisfaction.”
From the very day that Bradford tore up the Mayflower Compact, Plymouth began to prosper. Within a year the colonists found themselves with more food than they could eat. Flush with a bountiful harvest far in excess of their need for food and having bartered for all the goods they needed to get through the winter, they had a feast of thanks with their Indian trading partners.
Don't hold your breath waiting for the leftist teachers unions to teach this lesson to your children. Better show them this video from Reason: