Problem-Solving Techniques
The best way to develop your problem-solving abilities is to be open to new ideas, to be willing to experience the suggested activities rather then to be simply a spectator, and to make an honest commitment to the course. That is, you should attend class regularly, complete all your daily work, read the text carefully, and prepare yourself for each examination.
The following are suggested guidelines to use in solving problems. These guidelines were first proposed by George Polya:
1. Understand the problem. You must read the problem
carefully. Identify which quantity the
problem is asking you to solve for.
2. Devise a
plan. Find the connection between the data and the unknown. Look for patterns,
relate to a previously solved problem or a known formula, or
simply the given information to give
you an easier problem.
3. Carry out the plan.
4. Look back. Examine the solution obtained. Does the
answer you found seem reasonable?
Also review the problem and method of solution so that you will
be able to more easily recognize
and solve a similar problem.
Some problem-solving strategies may involve: the use of one or more variables, completing a table, considering a special case, looking for patterns, guessing and testing, drawing a picture or diagram, making a list, solving a simpler related problem, using reasoning, working backwards, solving an equation, looking for a formula, or using coordinates.
Solving an Applied Problem
First convert the problem into mathematics. This is usually the most challenging part of an applied problem. If possible, start by drawing a picture. Label it with all the quantities mentioned in the problem. If a quantity in the problem is not a fixed number, name it with a variable. Identify the goal of the problem. Then complete the conversion of the problem into math, i.e., find equation(s) which describe relationships among the variables, and describe the goal of the problem mathematically.
Solve the math problem you have generated, using whatever skills and techniques you need. Use Polya's method given above.
As a final step, you should convert the answer of your math problem back into words, so that you have now solved the original problem.