Is AA2 in your formula the cell containing the teacher's initials?

If yes, then the formula should be more like this:

=IF(ISNUMBER(MATCH(AA2,'Student List',$A$1:$A$100,0)),INDEX('Student List'!$B$1:$B$100,MATCH(AA2,'Student List',$A$1:$A$100,0),"")

where Student List!A1:A100 contain teacher's initials and B1:B100 corresponding students.

or:

=IF(ISNUMBER(MATCH(AA2,'Student List',$A$1:$A$100,0)), VLOOKUP(AA2,'Student List'!$A$1:$B$100,2,0),"")