In 1945, George Polya published the book How to Solve It in which he outlines a four-step model to use in the solution of problems. It involves understanding the problem, devising a plan, carrying out the plan, and looking back. Although problem solvers may approach a solution in the order outlined, they will often return to earlier stages because they have encountered an obstacle and it becomes obvious that another approach will work better. Students must analyze the problem and combine prior knowledge and experiences into a procedure that will arrive at a solution. Students need to recognize the applicability of mathematics.
Problem solving is the link between mathematics in the classroom and the real world.
The problems should consist of a good mix of translation, process, and realistic 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. Translation problems involve translating written or verbal statements into mathematical expressions and then performing an algorithm. Problem solving is a process that is learned by doing. Students will become better problem solvers if they think that the activity is important and relevant.