Two students named Brander attended the Mordecai school. Ann Elizabeth Brander was at the school from mid-1815 to the end of 1816 (so, three sessions); Maria Brander was there for both 1816 sessions. Both girls have James (or J.) Brander listed as the adult on their account. The Branders might have been from the Richmond area, according to this sentence in a Mordecai family letter:
"This will go to Richmond by a Mr. Brander, who with a Mr. Bott of Manchester is to be out in a few days, each with un petite fille."--Rachel Mordecai to her brother Samuel, 12 June 1815 (Mordecai Family Papers, Southern Historical Collection, Chapel Hill NC)
James Brander appears in the school ledger for June 1815 (paying for "Ann Eliza"), and again in November 1815, January 1816 (paying for Ann Eliza and Maria, "board & musick"), June 1816, and November 1816.
Genealogical websites pretty quickly show Ann Elizabeth Brander (1800-1826), daughter of James Brander (1760-1829), a Scotsman by birth, and Elizabeth T. Harrison, born at Manchester, Chesterfield County, Virginia.* She was the fifth of twelve children born to her parents, and was apparently sent to the Mordecai school shortly after the birth of the twelfth child, her sister Mary Catherine. She only lived to be 26; no indication that she married or had any children. (Her older brother Alexander named his daughter Ann Elizabeth Brander in 1842, probably in her memory.) But here's the surprise: Ann Elizabeth didn't have any siblings named Maria. So... Maria Brander might have been a cousin?
Yes. Found references to a Maria Brander Moore Robertson (1803-1873), daughter of John Brander (also of Scotland) and Martha Field Robertson. She married John Thomson Robertson Sr. (1801-1882, maybe her cousin?) in 1823, at Petersburg VA, and they had six children together, between 1823 and 1841. (She may have had a brief marriage before this one, to account for the Moore in her name.) During the Civil War, one of her daughters, Lelia, died in childbirth (in 1863), her son Stanhope was in the 12th Virginia Infantry, CSA; her son Archibald was a young physician who died from typhoid in 1864. (Another son, James, had died in 1847, age 24; and an newborn infant, Maria, died in 1841.)
So it looks like two Scottish brothers, John and James Brander, both lived in the Richmond/Petersburg neighborhood; James brought his 15-year-old daughter Ann Eliza to the Mordecai school in 1815, then after one session she was joined by her 13-year-old cousin Maria.
*Today in Chesterfield County, Virginia, you can find streets named Branders Creek and Branders Bridge.