__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 ?

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