"The Village Schoolmaster" is a poem by Oliver Goldsmith that reflects an earlier period in British life before the start of the Industrial Revolution. Its main theme is one of nostalgia for villages, which were slowly being displaced as economic centers. The lands previously held as commons were being enclosed to support large scale agriculture and Goldsmith objected to the concentration of wealth and displacement of the peasantry.
The Schoolmaster himself was an extremely important figure in the village. Normally, the schoolmaster, vicar, and possibly a lord of the local manor were the only people in the village with advanced literacy and numeracy skills. The schoolmaster and the vicar would normally help the villagers in any tasks that required literacy and numeracy (thus the abilities to "write and cipher") such as letter-writing, contracts, surveying, etc. Although Goldsmith is gently satirizing the rustics' overestimation of the village schoolmaster, there is a certain nostalgia and affection for him. Even though the village has disappeared, the basic knowledge the schoolmaster imparted remains in the memories of the children he once taught.
"The Village Schoolmaster" by Goldsmith is a lighthearted reflection of a village schoolmaster, but a more serious comment on a public policy.
"Enclosure" was a policy that allowed the wealthy to fence off their land. This prevented villagers, lower class workers and those who didn't own land, from grazing cattle and letting pigs forage, etc., and led to many small villages becoming deserted. The fence in the poem has been neglected, and the gorse has been allowed to grow wild, instead of being collected for fuel, all because the village is deserted due to enclosure.
The schoolmaster was beloved, but he should not be misinterpreted as scholarly or brilliant. Students laugh at his jokes so that they don't get in trouble, and he impresses the uneducated villagers with big words, etc. He also continues to argue even after he has lost. In other words, he was stubborn.
Yet, he was well-liked and is remembered. But the village which liked him is no longer inhabited.