I think it was Karl, who said that main clause vs. subordinate clause was a more useful terminology than independent vs. dependent clause.  I thinik it is important to realize, however, that there is a good reason for both sets of terms.  Sentences come in several kinds, and the clauses are named for their relation in those sentence types.  These types of sentences, I think, should be part of the introduction to the use of these terms: 

 

1) simple sentence: the term main clause or independent clause are not needed,

2) compound sentence: the term independent lets you distinguish between the clauses at this level,

3) complex sentence: the terms main and subordinate gives a way to distinguish these clauses,

4) compound-complex sentence: here at least two terms are needed, one or more independent clauses may each have dependent clauses.

The way that "main" and "subordinate" would be useful in the last most complicated case, would be in the versions giving them in simple or complex sentence paraphrases.  The analytic paraphrases of compound sentences make them simple sentences. 

 

It's perhaps when "indirect predicates" are called "small clauses" that the terminology can get confused.  Another source can be when it is stated that a clause has the same structure as a sentence.  Indeed, they are very similar constructions, so having these two sets of oppositions is a good way of keeping them straight. 

 

Bruce Despain