Hi,
I don't have XL 2007 at work to check, but this should do it -
=SUM(COUNTIFS(A2:A4,{"*Language Arts Teacher*","*Science Teacher*","*Math Teacher*"},J2:J4,"MELROSE HIGH SCHOOL"))
Of course, these all have the word "Teacher" in common so if you want all teachers you might be able to reduce it to just "*Teacher*" ?
Hope that helps...