Problem Solvers Acknowledgements

A problem is a chance for you to do your best.
                                          --Duke Ellington


1-Draw a Diagram

2-Make a List

3-Guess and Check

4-Divide and Conquer

5-Look for a Pattern

6-Start at the End

7-Mixed Problems



1.  Give your students problems that they CAN solve

This is basic!  The joy of problem solving is SOLVING problems.  The misery of problem solving is failing to solve problems.  Students who experience the JOY of solving problems WANT to solve MORE problems.   Students who experience only the misery of failure DO NOT even want to TRY to solve any more problems.  To be good problem solvers, students must BELIEVE that they can solve problems.  Therefore you must give them problems they CAN SOLVE.

2.  Give your students problems that SEEM difficult.

This also is basic!  If ALL the problems that your students solve are EASY problems, they will not believe they can solve difficult problems.  Therefore you must TEACH them to solve problems that SEEM difficult but CAN BE SOLVED--if they try!  Problems only SEEM difficult before they’ve been solved.  After they’ve been solved, problems seem easy.

3.  Teach your students HOW to solve problems that SEEM difficult.

Problems seem difficult when the solution is not obvious.  Usually, difficult problems are solved by a series of logical STEPS that CANNOT BE SEEN—at first!  If all the steps of the solution can be seen immediately, the problem is not difficult.  But good problem solvers START by TRYING to solve the problem.  They take the FIRST STEP, and look for the second step.  If they do not see the second step, they take a DIFFERENT first step.  In other words good problem solvers start by TRYING to solve problems that seem difficult, not by wondering how to solve them. 

4.  Teach your students problem-solving STRATEGIES.

The choice of a problem solving STRATEGY suggests the first step and helps the problem solver to see the next step.  Good problem solvers do not give up; they try a different strategy, a different first step, and then they look for the second step.


5.  At first, tell them which strategy to use, but later, expect them to CHOOSE AND TRY to find an effective strategy for themselves.

Introduce your students to each of the problem-solving strategies. You will find sample problems for each strategy and sample solutions showing you how experienced students have solved them. At first, tell your students which strategy to use. In this way, the problems are made a little easier, and they will get some practice using each strategy in turn. Eventually, you will not tell them which strategy to use, and for this purpose you may select from the “Mixed Problems.”



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