Problems can be generally broken down into two categories; well-defined problems and ill-defined problems.
Well-defined problems have a clear starting and ending point, such as how to make it bright in a room that's currently dark.
This strategy is commonly used in mathematical proofs.
Another example of it is if you've ever done a maze and started at the end and worked your way backwards toward the beginning. What if I gave you these six matches and asked you to use them to draw four equilateral triangles? If you had trouble solving that problem, you're not alone.
If you do get stuck on a problem, you can let it incubate, or just sit in your mind while you're not really thinking about it. It's like when you're trying to think of the name of that actor in a movie you saw, but it only comes to you later that night after you thought you stopped thinking about it.
that all students need to learn more, and often different, mathematics and that instruction in mathematics must be significantly revised." (, page 1).
Most people get stuck on thinking about this problem in a two-dimensional way. The answer, though, requires you to think about the problem in three dimensions.
You need to create a triangle pyramid with the six matches in order to form four equilateral triangles.
You know exactly what you're starting with and exactly how you wanna end up.
Ill-defined problems, on the other hand, have a more ambiguous starting and or ending point, such as how to live a happy life.