How To Solve It

Of course, problem-solving is a major activity in any mathematics course. A sound approach to the problem-solving process is a necessity for mathematics students. The approach outlined here is essentially the one from the classic book on the subject, How To Solve It by George Pólya¹.

• The first step is understanding the problem. The student must be able to state what needs to be solved, and what supporting conditions are given as information to be used in solving the problem. Once these are understood, it can be helpful (when possible) to draw a picture representing the unknown quantity to be solved and the other given information. If the unknown quantities are given in verbal form, it is necessary to introduce a suitable notation for these variables, and for the given conditions. Once we understand what we are given, and what we are looking for, we can proceed to the next step.

• We need to devise a plan for the solution of the problem. This plan should arise from a connection between the given information and the unknown. If an immediate connection isn't apparent, the student may have to explore other auxiliary connections to develop a chain which will link the given information to the unknown.

• Once a plan has been developed, the student must carry it out. It is especially important to check the validity and the accuracy of each step in the plan.

• Finally, the student should look back on the solution obtained and examine it. This means checking the work, and also stepping back to get an overview of the entire process. The solution to this problem then becomes part of the student's problem-solving library, which should be available for application to similar problems in the future.