Successful problem solving requires having the ability to adaptively and flexibly focus one's attention with respect to the demands of the work. Having a toolbelt of potential methods and combinatorially working through them can be incredibly helpful and we too often forget to explicitly think about doing or how to do that.

This is particularly important in mathematics where students forget to look over at their toolbox of methods. What are the different means of proof? Some mathematicians will use direct proof during the day and indirect forms of proof at night. Look for examples and counter-examples. Why not look at a problem from disparate areas of mathematical thought? If topology isn't revealing any results, why not look at an algebraic or combinatoric approach?

How can you put a problem into a different context and leverage that to your benefit?