I have four girls named Clarke in the rolls of the Mordecai school:
Jane Clarke attended two sessions, from summer 1811 to summer 1812.
Martha Clarke was there for one session in 1815, then for the last four sessions (1817-1818).
Mary R. Clarke of Nottoway Co., VA was there for one session, 1816 (second half).
Nancy Clarke was a student for four years, eight sessions, 1815-1818.
Nancy and Martha are at the school in overlapping times, and they have the same adult name, Col. John Clarke, attached to their accounts. Mary R. Clarke has a different adult's name, Thomas C. Clarke, on her account. But "Col. Clarke" appears in the school ledger in January 1815, for Mary, unless I misread Martha there; "John Clarke" appears for "Miss Nancy" in April 1815; And "Col. J. Clarke" for Nancy in February 1816; so this whole group might be kin. (David Clarke and William Clarke are other names in the ledger, but they seem to be attached to student Olivia Norfleet--still, could be a further connection.) I'm also thinking that "Mary R" and "Martha" might be the same girl--Mary R. would fill in one of the gap sessions for Martha.... hmmm.
Clarke is a fairly common surname, and none of these girls has an unusual first name. But let's see what we can find anyway (acknowledging that Clarke may be Clark, Martha may be Patsy, Nancy may be Ann, etc.).
.... Hm, not too many leads. Will leave this here for now.