Do you feel it is appropriate or inappropriate to use the pronoun he as a common gender pronoun referring to both males and females?

No, using 'he' as a common gender noun is not only inappropriate, it is poor grammar. If the gender is unknown, some appropriate ways to overcome the problem is:

When the teacher gave you the assignment, what did he or she say?

When the teacher gave you the assignment, what did the teacher say?

When the teacher gave you the assignment, what did they say?