In chapter 11, Prudence tells Kit that her father wanted to send her to school, but her mother said she's "too stupid." However, Goodwife Cruff's reasons for keeping her child out of school go beyond that. Prudence also tells Kit, who teaches at the school, that Prudence has been forbidden to even speak to Kit.
In chapter 1, Goodwife Cruff becomes suspicious when Kit jumps out of the boat to rescue Prudence's doll. Nat explains to Kit that Goodwife Cruff thinks Kit is a witch because she can swim. He tells Kit about the water trial:
A true witch will always float. The innocent ones just sink like a stone.
Goodman Cruff could have sent Prudence to school despite his wife's wishes, as men were considered the head of the household. However, he defers to Goodwife Cruff and even seems a little afraid of her. In chapter 2, Prudence is...
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forced to stand behind her parents during a meal rather than sitting at the table with them. She eats the "stingy portion" of food they hand back to her. A few times Kit sees Goodman Cruff "furtively slip the child an extra morsel from his plate, but he was plainly too spineless to stand up for her against his shrew of a wife."
In chapter 19, Prudence tells the magistrate that Kit taught her to read and write and demonstrates that she can do both. Goodwife Cruff is so convinced of her daughter's inability to learn and of Kit's guilt that she continues to insist that Kit has bewitched Prudence. She doesn't back down until her husband finally stands up for the little girl.
Why doesn't Prudence attend school in The Witch of Blackbird Pond?
Prudence Cruff is the daughter of the inappropriately-named Goodman and Goodwife Cruff. This revolting pair treat their daughter like dirt, constantly abusing her both physically and mentally.
When Kit first meets Prudence abroad the Dolphin the little girl comes across as a meek, fragile creature, someone who wouldn't say boo to a goose. After Kit dives into the sea to save Prudence's doll it's notable that the little girl's alleged mother isn't exactly bursting with gratitude. This is because she's thoroughly embarrassed at what she sees as her stupid daughter.
That Mrs. Cruff is so quick to describe her own daughter in such harsh, unflattering terms gives you some idea of how the poor child is treated at home. It also gives us a possible reason for why Prudence's parents don't send her to school, or indeed give her any kind of education. They clearly think she's so stupid that it would be a complete waste of time.
However, as Kit herself subsequently discovers, Prudence is far from being stupid. She's just a quiet child who needs lots of support and encouragement. Although she doesn't get it from her parents she most certainly gets it from Kit, who teaches Prudence to read and write.