Adam never misses an opportunity to sing "The Farmer in the Dell." His father told him the song was written for their family (although we find out later that Farmer isn't even their real last name). Adam is always happy when he's singing this song: with his parents, both before and after he finds out the truth about his past (Chapters 5 and 30); by himself, throughout his bike ride; and even in the hospital, thinking about his parents:
I'm not so sad anymore although I know [my father] is dead and my mother's dead, too. I keep singing, I keep singing. [...] I am too busy singing, [...] and I smile as I sing. (31.35-38)
The song seems to take Adam to a happy time. And what time was happy for him? His past. He was singing this song long before he knew of all the trouble his life would involve. Singing it seems to take him back to this time when he was a child and the world was as it should be.