When Bloom thinks, "Inishturk. Inishark. Inishboffin," he is probably recalling bits of his school learning to imagine the kinds of memorization drills that the boys in St. Joseph's are being put through. ("Fresh air helps memory. Or a lilt. Ahbeesee defeegee kelomen opeecue rustyouvee doubleyou.") His lilting list records the names of three small islands (inis means island in Irish) off the coasts of County Mayo and County Galway.
Ireland's western islands are sparsely inhabited and remote from urban civilization. Although the ones Bloom names all had inhabitants in Joyce's time (Inishark has since been abandoned), the only access would have been by fishing boat. Like the Aran Islands a bit further south (Inishmore, Inishmaan, and Inisheer), which Joyce visited in 1912 and whose Gaelic-inflected idiom Synge imitated in his plays, they would have figured in the national imagination as bastions of ruggedly authentic Irishness—hence perhaps their inclusion in the curriculum.
Gifford notes that the three islands lie near a part of Galway and Mayo called the Joyce Country, so there may be some overdetermination in their selection. As if to respond to his creator's pride in his family name, Bloom goes on to think of a range of mountains that bears his own surname: "Mine. Slieve Bloom."