Explain the poem "The Village Schoolmaster" in full details.

The village Goldsmith is writing about is called "Auburn": it is not  real, but  an imaginary ideal one, possibly one of the villages he had observed as a child and a young man in Ireland and England. Goldsmith, the poet, returns to the village that he knew as vibrant and alive, and finds it deserted and overgrown.

The setting of the particular passage is described in the first three lines. Then Goldsmith discusses the character of the schoolmaster himself.  In his appearance, he is very severe and stern.  The reader would suppose him humourless, except that he likes to tell jokes.  When Goldsmith says "the boding tremblers learn'd to trace/The days disasters in his morning face," the reader comes to understand that the schoolmaster does not mince his words. In the last two lines, he indicates that the schoolmaster was no more.  All of his fame has gone and "the spot/Where many a time he triumph'd is forgot” 

The schoolmaster was a big presence in the village. In an age when literacy and numeracy were powerful the people of the village, looked up to him. He seems a kind of god. The children are fearful of him. They laugh at his jokes, even if they are not funny. “Full well “(9-10)

 The adults are equally impressed with the way he can survey fields ("lands he could measure", 17) and work out boundaries or the times of holy-days like Easter. He can even do more complex calculations ("gauge", 18). This is all ironic: the school-teacher appears knowledgeable to the "gazing rustics" (22).

The poem's jokes are gentle. The tone of the poem is balanced  and gentleness and humour imply a frame of mind that Goldsmith sees as important, as having a moral value in itself.

Goldsmith is quietly mocking the schoolmaster: he is big fish in a small pond. He can impress the villagers with his learning, just because he can read a bit of Latin and knows how to do his sums. The parson, as the religious leader of the village, is of course the most respected man, but the schoolmaster loves a good argument and keeps arguing even when defeated(19-20). On the other hand, this is a loving, endearing portrait. Here's a man who is modest and doing a good job in a quiet and simple place: helping to spread a little literacy and numeracy among the people of the village, helping them in doing calculations about "terms". He is at the centre of a community - and Goldsmith is mourning the passing away of that community, the passing away of the village itself. That is why the lovely yellow flowers on the furze are "unprofitably gay" (2) - there is now no-one about to enjoy their beauty. The schoolmaster is gone long ago, with all the children of his school. A fine community has been lost.

So, this is an affectionate portrait of a community that is no more, and the school-house now deserted. The affectionate portrait of the schoolmaster is a part of this world that has passed away.