Kennings are an interesting feature of Anglo-Saxon poetry that modern readers encounter in Old English works like Beowulf, The Wanderer and The Seafarer. To create kennings for "school," you'll need to list some characteristics of school, characteristics that, when heard, would make someone think of "school." One characteristic is (or was) chalk, which is related to the other characteristics of chalkboards and erasers. Another characteristic is playgrounds. Another is the alphabet. Yet another characteristics is arithmetic, and another is bells, and another halls.
The technique used is to combine characteristics to create an image metaphorically representative of "school." We might try "halls of alphabet-speaking," for a prepositional kenning with hyphenation. Or we might try "chalk halls," for a two-word open compound without hyphenation. I'll list a few others, but I'm sure your imagination can produce kennings that are better than mine, maybe using apple or friends or swing set, ball or music or principal, maybe principal-palace.
- eraser bell-halls
- hall of board-erasers
One interesting thing about kennings is that they may have a different structure in Old English than they have in Modern English translation. Some good illustrations of this are given by Kip Wheeler of Carson-Newman College in his definition of kenning. For instance, he shows that Old English banhus is translated as hyphenated bone-house, while goldwine gumena is translated as the hyphenated prepositional gold-friend of warriors. The combined compound beadoleoma is translated as the two-word open compound flashing light, and hyphenated Old English beaga-gifa is translated as hyphenated ring-giver.
There are four types of kenning, as Mr. Dyer of Rockdale County Public Schools of Georgia reminds us. The most well-known is the (1) hyphenated compound, but also used are (2) two-word open compounds as in bear shirt, metaphorically representing a Norse warrior. The third type of kenning is the (3) possessive. It uses an apostrophe in an open compound to denote possession: whale's acre (The Seafarer). The fourth type of kenning is the (4) prepositional kenning. It uses a preposition in an open compound to indicate something's attribute (or someone's attribute). For example, someone, a king, who has the attribute of distributing wealth--or distributing rings of gold--is, in a metaphorical prepositional kenning, a bringer of rings (Beowulf): a king is one who has the attribute of bearing rings to give as gifts.
A kenning, then, creates a metaphorical substitute for something that is named by a noun (e.g., verbs can't be substituted by kennings). The metaphoric comparison presented by the kenning triggers recognition of the unspoken something. For example, if we substitute a kenning for the word ocean, then ocean is unspoken but metaphorically represented by the kenning whale-road (Beowulf). This is because the ocean has the characteristic traits of giving a home to whales (whale-) and of providing transportation (road).