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)