sweetie, thank you for the research

Your high school teacher was right. Grammatically speaking 'than me' in that sentence was not correct (grammar experts think that than should not be used as a preposition in this case). However in spoken english people say it (than me). as for 'than him' such as in 'she is smarter than him', maybe more people would consider it to be wrong (see webster.com and search 'than' and choose preposition).
'than I am' or 'than i' is always correct.
我想在托福题里一定要用标准语法 （我好象以前考托福时语法没有答错的，但听力没有答对的）。