People work hard only for what they think they can achieve
No corporation puts money or effort into a venture it does not believe will succeed. It may take risks, but only if it thinks the chances of success are good. People are the same. We may try lots of things, but rarely exert any real effort unless we expect success. We usually avoid things we think we'll fail at, and don't practice skills that we fear won't ever develop!
In other words, students need to believe they have a good chance of succeeding before they'll put in the effort that allows them to succeed. Sadly, this means that the students who are most in need of practice -- the ones who have not done well -- are often the least motivated to work, a vicious cycle toward failure.
What motivates people?
It is circular reasoning to say that we can motivate children by making the work "fun." "Fun" is, after all, just another way of saying that something moves (motivates) us to do more of it?
Cats scratch to keep their claws sharp, and they "play" at stalking and pouncing. They're designed to like these activities even when no real prey is around because claws and hunting are their survival skills. People don't survive by strength, speed, teeth, or claws; as a species, we survive by having a brain, and by playing with that brain to sharpen it, as cats play to sharpen their claws and skills. Sudoku has no practical uses, but people like it and other "useless" puzzles so much that these are sold in supermarkets -- not just to academics, but to everybody. People like feeling smart! The pleasure center in human brains rewards us when we use that brain, because being smart is how humans get ahead, and using our brain is how we get smarter.
Intrinsic and extrinsic motivation
Think Math! takes advantage of the way people are designed. The pleasure of solving a puzzle or discovering something surprising is an intrinsic motivator. Think Math! uses puzzles and surprise often. Research has shown that extrinsic motivators -- motivators that do not come from the nature of the task, but from sweets, money, or other "rewards" that are irrelevant to the task -- often have negative effects, actually reducing motivation in the long run.
Think Math! designs many of its activities to get students to "feel smart" (see, e.g., difference of squares), and its many ways of developing attention, focus, and working memory are also designed to build not only the essential skills, but the motivation to develop those skills further.