This stone stands on the village green in Greatham.
I have found a reference in the 1856 book “History, topography, and directory of the county palatine of Durham” by William Whellan that states.
‘The Barrington School, situated in the centre of the village, was erected in 1831 ; it is efficiently conducted, and well attended. There is also an Infant School, which was erected by subscription in 1831’