Math And Code Design

I was reading about the debate on math education reform in Scientific American and the argument for giving kids more context in which to apply theory is similar to applying the re-factoring approach to software development. Trying to design perfect software the first time around is an exercise in futility. Better to quickly bang something out that works, then go back and re-factor the code so that it is better designed. This way, you have a real-world context as well as real-world constraints in which to design your existing code. Maybe this approach isn't suited well for learning math concepts but it certainly couldn't hurt in introductory programming classes.