Tracing Old Scottish School Records

In search of old school records from Scotland I am searching for old school records (1840s-1860s) in order to find out which school my ancestors attended. I understand that it was not compulsory for parents to send their children to school until 1872 but surely there must be records somewhere in Scotland which references to the pupils. My great grand parents are Robert Stewart who was born at Old Kilpatrick in Dumbartonshire in 1842 and Margaret Cochran(e) who was born at Helensburgh in 1834.