I'd say your teacher is having a few problems them teaching-wise. Even if you aren't told specifically what a reading is called, i.e. Marxist, Post-Structuralist, Liberal Humanist, etc. you still have to know how every part of the play can be read differently.
Maybe you should have a look around the net or the notes on this site for some more info. To get ya' started:
Liberal Humanist is the traditional reading of the play. That is, Lear gains knowledge from hardship.
Feminist examines the role of women in the play, how women are portrayed, etc. There are a few articles on the net on the topic I think.
Marxist reading looks at how economic principles dictate how the play operates. Marxism in general links back to everything that happens in history being as a result of the differences between modes of production and those involved in the modes of production. For example, the Industrial Revolution, under Marxism, is said to be as a result of changes in the modes of production and hence a restructuring of social order. In King Lear, Marxist readings are basically that Edmund is the new order - capitalism and Lear represents the old order - fuedalism. Again, there should be a few articles on the net.
Post-structrualism is ludicrously complex and takes a lot of reading to understand (I've read a lot on it and I still don't fully understand it). It's about how the power of signification (that is, the exterior) dictates how things operate and so on. The opening scene is the most powerful representation of this, with the daughters all signifying in different ones, and this interpretation looks at the differences between truth and signification (for example, Cordelia is honest in the way she signifies, but what happens as a result). It's fuckin' complex and I wouldn't recommend doing it. I tried to tackle it in an assessment and it just fucked me up.
There is also the psychoanalytical (Freudian) interpretation which looks at the madness of Lear, and the Fool acting as a consciounce (I've forgotten how to spell there) for Lear...perhaps as the sub-conscious created by the sociopolitical standards of the society around him. Blah blah.
There are a lot of other ways of reading it. You can see it as a traditional Greek tragedy (with everyone dying at the end, etc.) and so on. But the above are the most common ones and I'd DEFINITELY take a look at them.
Anton