One common farming technique used in the Mississippian period (Southeastern US 1050 CE-1500 CE) was called slash and burn or Swidden agriculture. This entailed burning a large swatch of ground and mixing the ash into the dirt by tilling. Instead of planting rows of one crop, like corn, crops would be mixed. Corn, beans, squash, gourds, and so on would all share a field. This had a few key benefits. The nutrients were more slowly sapped out of the ground. The crops were less susceptible to pests and a bad crop of one plant wouldn't necessarily spell doom (of course, a really bad crop wouldn't be ideal, but these people were still adept hunters and gatherers despite being more sedentary than than their ancestors). Of course, it has some drawbacks as well. Some of the land still has to lie fallow, but it loses and regains its nutrients much faster than a pure cornfield. Today's cornfields rely on extensive fertilizer use to stay viable. Because of this, the land is cycled over a few decades. Therefore, it requires a massive amount of land for a smaller number of people. Swidden is still practiced today in pockets around the world, from Bangladesh and Thailand to the Amazon. Here's a link on the practices today.