TO bearsback: regarding :than me or than I

from Grammer Girl:
Than is both a subordinating conjunction, as in She is wiser than I am, and a preposition, as in She is wiser than me.... Since the following verb am is often dropped or “understood,” we regularly hear than I and than me. Some commentators believe that the conjunction is currently more frequent than the preposition, but both are unquestionably Standard.
refer the link:
http://grammar.quickanddirtytips.com/than-I-versus-than-me.aspx

**************
I know that almost everybody uses "...than me"
but my high school english teacher told me : grammatically it's wrong .

we can say

"I am smarter than he"
"I am smarter than is he"
"I am smarter than he is"
I am pretty sure that these 3 are grammatically correct but probably you won't hear it a lot