C is right to suggest a look further afield.
The Earsdon of 1840s cannot be easily compared to the village of Earsdon of today.
In the relevant era Earsdon was three different entities...
1) a village, lying within
2) a "township" lying within
3) a Parish.
The Parish consisted of eight "townships".
Burradon, Seghill, Backworth, Holywell, Seaton Delaval, Hartley, South Blyth and Earsdon ( the parish HQ)
After many population shifts and boundary shifts over the years, the communities of Seqhill, Backworth, Holywell and Earsdon, lie within the modern
unitary authority of North Tyneside.
The remainder of Seaton Delaval, Hartley and Blyth now lie within modern-day county of Northumberland.
So a school in Blyth , or other areas, in 1800s could have been categorised
as Earsdon, mother parish.
Trade Directories are a good source of schools of the day, usually listed under master/mistress.
Several directories are on line. Michael