Teaching a student how to approach a problem means he must learn to be aware of how he approaches a situation. Teaching how to analyze a problem can be done through a text example or with a practical example. A text analysis uses a passage from an essay or a novel while a practical example uses a situation that refers more specifically to the subject matter. A text analysis provides a more abstract and general example that can be applicable to different contexts. A practical example shows that critical thinking is useful and necessary. One way of encouraging analysis is to ask a student why she thinks that something happened rather than giving a mere description. For example, asking "why do you think this took place?" instead of instead of "what happened?"
Using puzzles or games is a good way of teaching students how to problem solve. It makes student learn how to work through a difficult or seemingly impossible problem to reach a goal or achieve success. There are many puzzle books, brainteasers or even logic problems that can help a student learn how to use his analytical skills in everyday or real-life problems.
An important aspect of critical thinking is learning to think for yourself. That means always questioning the legitimacy of seemingly self-evident truths. Learning how to question the context and content of something leads to a deeper and more detailed understanding of a subject. Questioning assumptions and statements also helps to develop a more reasoned and nuanced opinion, one that can take into consideration multiple perspectives. A good way to practice this type of thinking is through group discussion in which you hear different points of view and the reasoning behind them.
Critical thinking about a problem means that you cannot assume the most obvious solution or answer is always the right one. Coming up with alternative solutions to a problem or a puzzle sometimes requires you to go beyond your first assumption about how something should work. Never be afraid to try a new or unconventional solution simply because it isn't standard practice.