It involves understanding the problem, devising a plan, carrying out the plan, and looking back. Problem solvers can learn individual skills and strategies to use within this framework. As they broaden their knowledge, their facility for solving problems will improve. Polya's framework is not fixed. Although problem solvers may approach a solution in the order outlined, they will often return to earlier stages because they encounter an obstacle and it becomes obvious that another approach will work better.
Problem solving is a process which is learned by doing.
Students will become better problem solvers if they think that the activity is important and relevant. When mathematical concepts and operations are introduced, they should often follow rather than precede problem-solving opportunities. Before the formal terms and symbols are presented, students should learn to approach problems in a variety of ways. The problems should consist of a good mix of process, realistic, and translation problems. Realistic problems are not well defined and require some further specification and refinement, often have multiple solutions, require the collection of information, involve collaboration with other people, cannot be solved in a few minutes, and involve some personal commitment on the part of the student.