Irving's "The Legend of Sleepy Hollow" is somewhat of a vagrant, and would have been treated as such if it weren't for the fact that he is a traveling educator and valued for his knowledge and career. Since it is Crane's job to travel around to do his job, Irving describes his situation as one where he "boarded and lodged at the houses of the farmers whose children he instructed. With these he lived successively a week at a time." This answers the question of where Crane lived--in the houses of his students! Not only did he live with his students, but he rotated each week, which would have made it a little more difficult to move if he had heavy luggage to worry about in the process. But that wasn't so much the case, either, though. Crane was pretty much poor. Irving says that "all his worldly effects (were) tied up in a cotton handkerchief," which implies that he didn't have much anyway.

Ichabod Crane lives in Sleepy Hollow, in the vicinity of Tarrytown, New York, which is itself located north of New York City, on the Hudson River. It should be noted, this was a region of significance during the Revolutionary War, being that it was in this area that British spy John André was captured by Revolutionary forces (and this historical importance is all the more significant, given that "Legend of Sleepy Hollow" itself is set in the post-Revolutionary War period, at which point these events would still have been well within living memory). John André, the Headless Horseman, the Revolutionary War, and the still much older history of Dutch colonization all go together in forming a historical context from which Washington Irving creates a kind of personality for the place where this story is set.

Ichabod Crane lives in a "sequestered glen... known by the name of Sleepy Hollow."  Sleepy Hollow is located just north of Tarrytown in New York.  It is located in the Hudson River Valley, along the banks of the Hudson River.  Some consider the place to be bewitched.  Legend says that the area is haunted by a Headless Horseman.

It is customary for a schoolmaster in the 1700s to "[board] and [lodge] at the houses of the farmers whose children he instruct[s]."  Typically, a schoolmaster spends a short period of time staying at the house of one student before moving on to board with another.  This is often part of the contribution that parents make toward their children's education in this time period.  As an unmarried schoolmaster, Ichabod does not have a real home.  He does always have a place to sleep at night, even though the location of the bed changes based on which family he is staying with that week.  He stays in various parts of the village with the different families.  He spends a lot of time visiting with the locals in his spare time.

As part of Ichabod Crane's compensation for teaching the children in the Sleepy Hollow area, he gets his room and board, on a rotating basis, from the farmers whose children he is teaching.  Irving notes that "With these [that is, the farmers] he lived alternately a week at a time, this going the rounds of that neighborhood, with all his worldly effects tied up in a cotton handkerchief."  One of the reasons Crane has to alternate lodgings on a weekly basis is that his appetite is so huge that he is undoubtedly a burden on his host.

There are two reasons Irving includes the detail of Crane's belongings being carried in a handkerchief.  As an itinerant (someone who has to move a lot) schoolteacher, he cannot afford to have many belongings, and as a schoolteacher in rural areas, his salary would be so low that he could not afford to buy anything but necessities.  In addition, Irving is reminding us that Crane is a New England Yankee from Connecticut, notorious for not wanting to spend any money.  This is just a gentle dig at the literary stereotype of someone from New England.