4 Steps to Problem Solving Adapted from "Science World," November 5, 1993. A FOUR-STEP PROCESS Billstein, Libeskind and Lott have adopted these problem solving steps in their book "A Problem Solving Approach to Mathematics for Elementary School Teachers (The Benjamin/Cummings Publishing Co.). They are based on the problem-solving steps first outlined by George Polya in 1945. 1. UNDERSTANDING THE PROBLEM * Can you state the problem in your own words? * What are you trying to find or do? * What are the unknowns? * What information do you obtain from the problem? * What information, if any, is missing or not needed? 2. DEVISING A PLAN The following list of strategies, although not exhaustive, is very useful. * Look for a pattern. * Examine related problems, and determine if the same technique can be applied. * Examine a simpler or special case of the problem to gain insight into the solution of the original problem. * Make a table. * Make a diagram. * Write an equation. * Use guess and check. * Work backward. * Identify a subgoal. 3. CARRYING OUT THE PLAN * Implement the strategy or strategies in step 2, and perform any necessary actions or computations. * Check each step of the plan as you proceed. This may be intuitive checking or a formal proof of each step. * Keep an accurate record of your work. 4. LOOKING BACK * Check the results in the original problem. (In some cases this will require a proof.) * Interpret the solution in terms of the original problem. Does your answer make sense? Is it reasonable? * Determine whether there is another method of finding the solution. * If possible, determine other related or more general problems for which the techniques will work.
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