Trying to come up with ideas is tough, especially problem solving ideas in math especially. The key to generating truly innovative ideas is learning how to challenge the status-quo, by thinking wrong. It seems to students and parents that math shuts down imagination and that is how these ideas came to be is by someone imagining them. In math it is OK to be wrong and as we get older we associate failing by being wrong. Working within our comfort zone renders us unable to approach problems with a truly fresh perspective.
If teachers create a safe enough environment that is fun and loosely structured and encourage participants to question protocol on problems that require higher-ordered thinking. Then we begin to see totally different equations than the ones in textbooks and possibly better equations that they may be able to use throughout their entire life.
There is a full article here http://www.good.is/post/learning-to-think-wrong-could-be-the-key-to-the-right-answers/utm_source=pulsenews&utm_medium=referral&utm_campaign=Feed%3A+good%2Flbvp+%28GOOD+Main+RSS+Feed%29