## Sunday, 1 July 2012

### POLYA'S THEORY

POLYA’S FOUR-STEPS PROCESS

In this assignment, we often distinguish between “exercises” and “problems”. Unfortunately, the distinction cannot be made precise. To solve an exercise, one applies a routine procedure to arrive at a answer. To solve a problem one has to pause, reflect and perhaps take some original step never taken before arrive at a solution. This need for some sort of creative step on the solver’s part, however minor, is what distinguishes a problem from an exercise. To a young child, finding 2 + 4 might a problem, whereas it is a fact for you. For a child in the early grades, question “How do you divide 64 apples into 8 baskets?” might pose a problem, but for you it suggests a routine exercise, “find 64 ÷ 8”. These two examples illustrate how the distinction between an exercise and a problem can vary, since it depends on the state of mind of the person who is to solve it.

Doing exercises is a very valuable aid in learning mathematics. Exercises help you to learn concepts, properties, and procedures and so on, which you can then apply when solving problems. This project provides an introduction to the process of problem solving. The techniques that you learn in this project should help you to become a better problem solver and should show you how to help others develop their problem-solving skills.

A famous mathematician, George Polya, devoted much of his teaching to helping students become better problem solver. His major contribution is what has become known as the four-step process for solving problems.

Step 1 : Understand The Problem
1.      Do you understand all the words ?
2.      Can you restate the problem in your own words ?
3.      Do you know what is given ?
4.      Do you know what the goal is ?
5.      Is there enough information ?
6.      Is there extraneous information ?
7.      Is this problem similar to another problem you have solved ?

Step 2 : Device a Plan
Guess and test.
1.      Use  a variable.
2.      Look for a pattern.
3.      Make a list.
4.      Solve a simpler problem.
5.      Draw a picture.
6.      Draw a diagram.
7.      Use direct reasoning.
8.      Use indirect reasoning.
9.      Use properties of numbers.
10.  Solve an equivalent problem.
11.  Work backward.
12.  Use cases.
13.  Solve an equation.
14.  Look for a formula.
15.  Do a simulation.
16.  Use a model.
17.  Use dimensional analysis.
18.  Identify subgoals.
19.  Use coordinates.
20.  Use symmetry.

Step 3 : Carry Out The Plan.
1.      Implement the strategy or strategies that you have chosen until the problem is solved or until a new course of action is suggested.
2.      Give yourself a reasonable amount of time in which to solve the problem. If you are not successful, seek hints from other or put the problem aside for a while.
3.      Do not afraid of starting over. Often, a fresh start and a new strategy will lead to success.

Step 4 : Looking Back
1.      Is your solution correct ? Does you answer satisfy the statement of the problem ?
2.      Can you see an easier solution ?
3.      Can you see how you can extend you solution to a more general case ?