Do you think the study of grammar is overemphasized or underemphasized in schools today?Give an example from your own experience.

Your professor obviously wants you to answer from your own
experience, so I would encourage you to do that.  From my experience in five different
schools, both public and private, the teaching of grammar is generally underemphasized. 
One of the reasons for that is that teaching grammar isn't particularly interesting or
glamorous, and neither teachers nor students are eager to do grammar work. Sadly, it's
also true that many teachers aren't confident in their own grammar skills--which means
they probably weren't taught them or they didn't learn them in high
school and/or college.  In college I didn't have any class which taught or reviewed
grammar skills except in context--using proper grammar and mechanics in written work. 
My first six years of teaching were in a private school which did emphasize grammar, and
it was through teaching that I reviewed (and sometimes learned) basic grammar. At my
other schools, grammar was not a major component in the English
curriculum.