There is a historical reason for this. When contractions came into the language around 1600, there was a form amn't (which still is used in Ireland and Scotland), which was often pronounced an't because the m and n together are difficult to pronounce. But these contractions were never as commonly used as others.

In some areas, the a in an't was pronounced like ay, which led to ain't. But this form today is not accepted in standard English except humorously in a few fixed phrases ("You ain't seen nothin' yet").

In other areas the a in an't was drawn out so that the word was pronounced much like aren't (where the r is not pronounced), which seems to have led to aren't I. But still the contraction an't was not widely accepted, so that today we say I'm not, but not I an't or I amn't.

So aren't I is the standard tag question. Am I not can be used but sounds very formal. Tag questions are most often used in informal speech, so aren't I is the form you should teach your students.

(Source: Michael Quinion, World Wide Words, http://www.worldwidewords.org/qa/qa-amn1.htm)