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Polya's Heuristic PD
51
Word Problems
and Polya
By Nicole Thuestad (nthuestad@gmail.com)
The Problem: Students are stumped by word Problems
Solution: Polya's Problem Solving Heuristic
Who Is Polya?
Polya
- In 1945 George Polya published the book How To Solve It
- It sold over one million copies and has been translated into 17 languages
- In this book he identifies four basic principles of problem solving
Overview of his Heuristic
Polya's Principles
1. Understand the problem
2. Devise a plan
3. Carry out the plan
4. Look back
With some guidance this becomes a checklist so no problem goes unsolved
Polya’s First Principle:
Understand the problem
#1
Polya taught teachers to ask students questions such as:
Do you understand all the words used in stating the problem?
• What are you asked to find or show?
• Can you restate the problem in your own words?
• Can you think of a picture or diagram that might help you understand the
problem?
• Is there enough information to enable you to find a solution?
Polya’s Second Principle: Devise a plan
#2
Polya mentions that there are many reasonable ways to solve problems.
The skill at choosing an appropriate strategy is best learned by solving many problems.
You will find choosing a strategy increasingly easy.
Some Strategies
• Guess and check • Look for a pattern
• Make an orderly list • Draw a picture
• Eliminate possibilities • Solve a simpler problem
• Use symmetry • Use a model
• Consider special cases • Work backwards
• Use direct reasoning • Use a formula
• Solve an equation • Be ingenious
Polya’s Third Principle:
Carry out the plan
This step is usually easier than devising the plan.
In general, all you need is care and patience, given that you have the necessary skills.
Persist with the plan that you have chosen.
If it continues not to work discard it and choose another.
Polya’s Fourth Principle: Look back
Polya mentions that much can be gained by taking the time to reflect and look back at what you have done, what worked, and what didn’t.
Doing this will enable you to predict what strategy to use to solve future problems.
Polya’s Fourth Principle: Look back
Once you have a potential solution, check to see if it works.
1. Did you answer the question?
2. Is your result reasonable?
3. Double check to make sure that all of the conditions related to the problem are satisfied.
4. Double check any computations involved in finding your solution.
Summary, Strategies
and Practice
Link to PDF: tinyurl.com/y98chltf
Summary, Strategies
and Practice
First Practice Problem
Every person at a party of twenty-eight people said hello to each of the other people at the party exactly once. How many "hello's" were said at the party?
Kahoot Review
Link for Presenter:
https://tinyurl.com/y7wh722c
Link for Participant: www.kahoot.it