Nothing more quickly disspitates the myth that most people aren't interested in math than hitting them with a good puzzle and watching the instinctive human urge to solve it get to work. To be fair, this doesn't apply to literally all people, but there's certainly a lot more people that enjoy riddles and puzzle games than there are mathematicians.
I've always thought that if I were to teach students at the pre-college level (who we can therefore assume are there because they have to be, not because they already like math), I would use puzzles to get them interested in mathematics, emphasizing that the fascination they (hopefully) feel towards these puzzles is exactly how mathematicians feel about their work.
But does this actually work? Or, if I gave a class of pre-algebra 13 year olds a puzzle like "Given the sum and difference of two numbers, can you work out the numbers themselves?", would I just get a roomful of groans and no attempts at a solution?
My definition of a "puzzle" is roughly as follows:
- A puzzle is not a routine application of the class material, it requires insight and creative thinking.
- A puzzle can be solved using techniques learned in class or about to be learned in class, although the exact connection might not be obvious.
- It may be too hard for the entire class to solve it, the goal is more to get them thinking about the problem (to get them interested in the class, and motivate the techniques you're teaching them).
- The statement of a puzzle is elegant and designed to be inherently interesting (rather than "here is a very specific geometrical scenario, calculate this very specific paramater relating to it").