Your students aren't the only ones to disagree over the number of oceans in the world. Depending on who you talk to there are anywhere from three to five major oceans. Everyone agrees about the Atlantic, Pacific, and Indian Oceans, and some geographers also add the Arctic and Antarctic Oceans. Other geographers call the Arctic a 'marginal sea' and consider the Antarctic to be only an extension of the big three. You might ask your students to think about why people argue about the status of the Antarctic. On the one hand, if you look at a globe, there're no obvious land features to separate the Antarctic from the other oceans, so it seems like it shouldn't get separate-ocean status. On the other hand, the Antarctic current (also known as the West-wind Drift) circles around and around Antarctica, and so effectively acts as a fence to separate the Antarctic waters from other ocean waters. So Antarctic waters are much colder and denser than waters from the Atlantic, Indian, and Pacific Oceans.

The definition of oceans is a difficult one because all of the oceans are connected and so one has to find places where the ocean is constricted bytwo land masses coming close to each other. There is also the difficult (and somewhat arbitrary) distinction between an ocean and a sea. All this aside, we can see that the Indian Ocean is fairly neatly separated from the South Atlantic on the west by the (relative) proximity of South Africa and Antarctica. On the east side, it is separated from the Pacific by Australia and Indonesia as well as the (relative) closeness of Australia and Antarctica. In this manner, we can see that the Aleutian Islands separate the North Pacific from the Arctic Ocean and Newfoundland-Iceland-Greenland-Scandinavia provide a boundary between the North Atlantic and the Arctic Oceans. The Atlantic and Pacific Oceans are separated by the Americas and the Straits of Magellan in the south. This gives us four basic oceans, the Pacific, the Atlantic, the Indian, and the Arctic which are sometimes subdivided (rather arbitrarily but possibly in terms of current systems which are different in the northern and southern hemispheres) into North and South Atlantic and North and South Pacific Oceans.

I can see why this would be a confusing concept. The word ocean can mean several different things, just as the word sea. Look both up in the dictionary and see what you find!
Seas are characterized by being bordered on all sides by land masses. Oceans are typically more open and not bordered by land masses. Oceans commonly will have some mixing with other oceans or seas.
According to my calculations there are 5 oceans: the Arctic, the Indian, the Pacific, the Atlantic, and the Southern Ocean (aka the ocean that circles Antarctica).