Introduction to Problem Solving

1
Chapter 1

• Introduction to Problem Solving

2
Problem Solving Process and Strategies

• George Polya (1887 1985)
• How to Solve It
• Understand the problem
• Devise a plan.
• Carry out the plan.
• Look Back.

A great discovery solves a great problem but
there is a grain of discovery in the solution of
any problem. Your problem may be modest but if
it challenges your curiosity and brings into play
your inventive faculties, and if you solve it by
your own means, you may experience the tension
and enjoy the triumph of discovery.
3
Problem Solving

1. Preparation Understand problem situation
   terminology, notation, properties. Draw
   pictures, give examples BE ACTIVE!
2. Incubation Solving rarely happens quickly. If
   solution doesnt materialize, put it aside and
   come back later.
3. Illumination Light Bulb!! Relate to other similar
   problems youve seen or solved previously. Look
   at it from a different angle.
4. Verification Does your answer make sense? Is
   your answer reasonable?

4
Problem Solving Process
Original problem
Mathematical Version of the problem
Translate
Solve
Check
Solution to the mathematical version
Interpret
Answer to original problem
5
Problem Solving Strategies

1. Guess and Test.
2. Use a Variable.
3. Draw a Picture.
4. Look for a Pattern.
5. Make a List.
6. Solve a Simpler Problem.

6
Suggestions

1. Accept the challenge of solving a problem.
2. Rewrite the problem in your own words.
3. Take time to explore, reflect, think,
4. Talk to yourself. Ask lots of questions.
5. Allow time to incubate.
6. Look at the problem in a variety of ways.
7. Be organized.
8. Do not be afraid to change your approach.
9. Do not be afraid to make mistakes.
10. Develop good problem-solving helper skills. Do
    not give out solutions instead, provide
    meaningful hints.
11. Stay positive!

7
Ten Commandments for Teachersby George Polya

1. Be interested in your subject.
2. Know your subject.
3. Try to read the faces of your students try to
   see their expectations and difficulties put
   yourself in their place.
4. Realize that the best way to learn anything is to
   discover it by yourself.
5. Give your students not only information, but also
   know-how, mental attitudes, the habit of
   methodical work.
6. Let them learn guessing.
7. Let them learn proving.
8. Look out for such features of the problem at hand
   as may be useful in solving the problems to come
   try to disclose the general pattern that lies
   behind the present concrete situation.
9. Do not give away your whole secret at once let
   the students guess before you tell it let them
   find out by themselves as much as is feasible.
10. Suggest do not force information down their
    throats.