Many of the steps we use to solve a problem we carry out unconsciously. They are a part of the way we think, and we just seem to know how to do them without thinking about how we go about doing them. This is just like walking were once learned, we no longer need to be consciously aware of the multitude of operations taking place when we decide to walk from one class to another.

It seems that once we have learned the details of some process through conscious effort, this process is still available to us just by evoking the process itself: "walk to the door and open it" or "plug this value into that equation".

When we encounter novel situations in which our current way of thinking does not work, it is important to take conscious control of our thinking -- to begin thinking about our thinking and about our problem-solving process. One way to gain some insight is to have the thinker of your thought ask some explicit questions about your problem-solving activities.

A few examples are:

What quantities are given in the statement of the question? Do I have them all?

Is the quantity that I just calculated the actually quantity requested by the problem?

What physical situation is described in this problem?

How do I turn the information requested into a mathematical statement?

What is implied by this question, but is not explicitly stated in the question itself?

What principles of physics do I need to understand in order to figure out how to obtain an equation that relates the knowns to the unknowns?

Is what I am doing making sense? Is my answer reasonable?

What makes me believe that the equation I am using really applies to this problem?

What does this symbol mean? Does it mean what I think it means?

From what frame of reference shall I choose to observe the action described?

What if ..., what would that imply in this problem?

What would I have needed to understand that would have allowed me to figure out how to solve the problem myself?

By consciously becoming aware of these types of questions before you encounter some difficulty, it is my belief that they will become a part of your intuitive, spontaneous problem-solving ability in the future.