TO TEACH YOUR STUDENTS HOW TO SOLVE 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.