Another sparse entry in the rolls of the Mordecai school. Martha Barnes attended the school for one year, 1810. Not much else to go on--no hometown, no adult name attached to the account. The student's name isn't even that uncommon.
One possible candidate, from looking around the family history pages:
Martha "Patsey" Barnes, Mrs. Samuel Gann Jr.; b. 31 March 1796 in Rockingham Co. NC; one of the nine children of Revolutionary War-veteran Chesley Barnes and Mary Means; married c.1819, same county; died c.1870. Generation and location are all dead on. But did Martha Barnes Gann witness a document in 1852 "by mark"--not by signature? Could a girl have spent a year at the Mordecai school without being able to sign her own name forty-two years later? Probably a strike against this as a match, but not a deal-breaker; it could still be her. Or not.