4 ideas
Robert is a boy who hates maths because his teacher, Mr. Bockel, sets rote word problems about bakers and pretzels while he munches pretzels himself. Over twelve dreams, a number devil shows him primes, Fibonacci rabbits, infinite decimals and Pascal's triangle by letting him discover the patterns himself. Robert goes from dreading numbers to being admitted into the devil's 'number heaven' of great mathematicians.
The devil argues that arithmetic drills are not mathematics. Machines can do calculation, and many real mathematicians are poor at it. The actual subject is noticing, generalizing and explaining patterns, such as why primes never run out or why rows of a triangle sum to powers of two. Students who are bored by computation may therefore be rejecting drudgery rather than mathematics.
The devil gives formal ideas informal names: primes are 'prima donnas', square roots are 'rutabagas', exponents are 'hopping' and irrational numbers are 'unreasonable numbers.' These nicknames let the learner work with the idea before facing intimidating jargon. The official term can be attached once the concept is already understood.
Pascal's triangle is built by one rule: each number is the sum of the two above it. Yet it contains the counting numbers, the triangular numbers, powers of two in its row sums and Fibonacci numbers along its shallow diagonals. Colouring its odd and even entries also reveals a fractal pattern. Examining a single simple structure from different angles can reveal more than piling up new material.