It wasn't until years later as a university student that I discovered not only the theory but the theory of continental drift, developed most fully in 1912 by Alfred Wegener. His ideas were superseded by the theory of plate tectonics in the late 1950s (about the time I was in 6th grade). The earth's crust (the lithosphere) is made up of constituent tectonic plates, puzzle pieces which are stronger and less dense than the underlying asthenosphere upon which they 'float'. The asthenosphere is weak, viscous, and molten. It is in constant global slow-motion circulation, carrying the floating plates with it.
Plates may interact in several ways. They may grind against each others' sides, or they may meet head-on, in which case one plate rides up atop the other. That is how the world's mighty mountain ranges were formed, The Andes, the Rockies, the Himalayas. Volcanoes, earthquakes, island formation, and sea-floor spreading are all evidence of plate activity.
The continents are passengers in this merry dance, which proceeds at the speed of roughly 3-6 cm per year (about as fast as your fingernails grow). Looking at the world today, and using tools in the geological record, it is possible to roll the film in reverse. It turns out that the continents have gone through several cycles of clumping together and dispersing. The most recent episode of convergence happened around 300 million years ago ~ all the dry land on the planet was clustered in a supercontinent called Pangea. Surrounding Pangea was a single global ocean, Panthalassa.
We understand the direction and rate of travel of Pangea's components as it dispersed to the position of today's continents ~ which are still in motion, by the way. Here is an animation showing that epic journey. And here is another animation which projects the continents' motion 400 million years into the future, when they form a new Pangea.
All this discussion has been background for the illustration above (click to enlarge), which shows the positions of today's nations as they would have appeared in the most recent Pangea. Political borders would have a very different relevance, with very little water separating countries. One can only hope that mutual aid and cooperation would evolve, as it has in the European Union. Imagine, driving over to Rick's Cafe Americain in Casablanca for an exotic lunch and intrigue, then back to Manhattan for the evening. Could be fun.
Thanks to io9 for the original idea.