4 ideas
Three schoolchildren are transported into Karlikania, a land where numbers live as small personified people, the dwarfs of the title. Over three days they meet these characters and work through arithmetic problems embedded in the plot, so each rule is learned at the point where the story needs it. The book was written by a mathematician as a vehicle for teaching arithmetic.
In positional notation a digit has no fixed value: the same symbol is worth ten times more with each step it moves left. Zero, which means nothing on its own, is a placeholder that pushes other digits into higher places. Treating numbers as characters makes this concrete, because a character's importance comes from where it stands in the row, not from who it is.
When numbers are cast as characters with personalities and relationships, operations become actions the reader can picture, such as joining, splitting or standing in for one another. The learner remembers the rule because it is tied to a scene and a motive rather than to a bare procedure. Personification works as a memory structure, not just as decoration.
Arithmetic rules are easier to learn when the reader meets them as problems the characters must solve to move the plot forward. The narrative supplies the reason a rule is needed before the rule is stated, which turns rote memorization into something closer to discovery. The story also reframes weakness at mathematics as unfamiliarity with the rules, which can be fixed through experience.