Problem solving is at the heart of all creative and higher order intellectual work, but it usually doesn't get the attention it deserves during education. Maybe because it's not that easy to do.
Real problem solving is not just imitation. It's a self-conscious process of analyzing information, sorting, prioritizing, testing, and then reassessing. Some people have a natural gift for problem solving, but most learn over the course of their lifetimes.
Better problem solving skills leads to greater adaptation to changing circumstances, resiliency, personal satisfaction, and achievement (more problems solved!). Problem solving can be encouraged by didactic teaching about 'steps' (examine the evidence, consider the extreme case, etc) and open discussions about blindspots and bias. Problem solving instruction is wonderful when provided one-on-one, socratic style...identifying the source of student's opinions, assumptions, and decision making. Don't forget to model problem solving persistence, the solution of problems over time - whether it be days, months, or years.
Fifty Problem Solving Strategies
Problem Solving Strategies
Critical and Creative Thinking