Ye Hedge School is named after the clandestine schools run by the Irish during the time of the Penal laws which not only forbade the teaching of Catholic catechism, but indeed forbade all education for Catholics. Despite these laws, however, when my great-great-grandfather arrived in the United States from Ireland, he was well educated, knowing arithmetic, algebra, and geometry, history and geography, spelling and writing, and, of course, catechism.

It is simply extraordinary that while the Penal laws prevented the Catholic Irish from voting or holding office, from owning or purchasing land, from engaging in commerce, and forbade them to educate their children in by any means, at home or abroad, education continued. Priests were banned and hunted with bloodhounds and the faithful Irish had nothing but the barest living in their countryside, on lands that had not (yet) been confiscated, yet all the while, priests and other educated Irishmen who were faithful to the Church conducted schools in inaccessible caves or tiny huts, or behind hedges.  The schools were called Hedge Schools. Seumus MacManus, in his book The Story of the Irish Race, describes them thus:

"Throughout those dark days the hunted schoolmaster, with price upon his head, was hidden from house to house.  And in the summer time he gathered his little class, hungering and thirsting for knowledge, behind a hedge in remote mountain glen  where, while in turn each tattered lad kept watch from the hilltop for the British soldiers, he fed to his eager pupils the forbidden fruit of the tree of knowledge.
"Latin and Greek were taught to ragged hunted ones under shelter of the hedges  whence these teachers were knows as "hedge schoolmasters."  A knowledge of Latin was a frequent enough accomplishment among poor Irish mountaineers in the seventeenth century  and was spoken by many of them on special occasions. And it is authoritatively boasted that cows were bought and sold in Greek, in mountain market-places of Kerry."

MacManus also tells of the eighteenth century Irish poet Owen Roe O'Sullivan who was a farm hand until he had the opportunity to help his master's son read a Greek passage; the son had just returned from college on the Continent. 
And he tells us that a friend's father used to hear whole conversations in Latin among the priests and schoolmasters of nineteenth century Ireland.

A good photo of a historic hedge school may be found partway down this webpage:

Ardagh in Limerick has a reference to the "Mass rocks" of the same period in history -- places where Mass was said in secret during the same years as the hedge schools.

The Glenariff website has a wonderful panoramic view of an Irish landscape.  Somewhere in the glen, there is a cave that was used as a hedge school.  The photography does not provide a view of the cave in question, but it gives the flavor of the place and time -- and a flavor of the difficulty the British would have faced trying to destroy the schools:

In our own time, education is legally required and readily available for everyone,  but what an education!  Not only are prayer and catechism forbidden in our schools, as were Mass and Catholic theology in Ireland, but phonics is virtually outlawed, math is neglected, and literature, history, geography, and the biological sciences are so infected with eugenic bias as to be anti-catechetical for Catholics.

Whether you are schooling at home or in public or private schools, Ye Hedge School is committed to developing and promoting materials that will help you bring your children's education in line with eternal truth.

The Hedge School ~ then and now