There should be a keyboard shortcut, which is similar to split, but after splitting the screen the working directory of new terminal should be the same as the working directory of the old one.
*** This bug has been marked as a duplicate of bug 169058 ***
Also related to bug 214547.
On second thought bug 214547 is actually a closer duplicate than bug 169058, redupe'ing. *** This bug has been marked as a duplicate of bug 214547 ***