Although she's often called a "lackwit fool" by others, Alyce is actually rather an intelligent young lady. Alyce may be illiterate as with most people at that time, and she may be an abandoned orphan from a dirt-poor background, but she has a certain sharpness about her. This is a young lady with the medieval equivalent of street smarts. And without them, she'd find it hard to survive in such a tough world.
But Alyce's intelligence also helps others to survive. When Will's close to drowning, Alyce thinks fast and crawls onto the tree branch so that it dips in the water and Will can grab hold of it. Although the other boys insist on calling Alyce a nitwit, Will now knows better and calls Alyce by her name.
Alyce further shows her intelligence through her remarkable ability to learn by observing other people's behavior. For instance, closely watching Gilbert Gray-Head carve wood allows Alyce to pick up the trade herself, something that few other girls of her time were able to do. And of course, Alyce's intelligence and capacity to learn quickly allows her to become a skilled, caring midwife, which greatly improves her sense of worth and self-respect.