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# Polya problem solving cycle

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An introduction to George Polya's approach to solving problems.

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• Great presentation I can benefit from these questions to enhance critical thinking of my students. thank you.u

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• Thank you, mrjdfield:) This will help me ask the right questions to scaffold students' thinking!

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### Polya problem solving cycle

1. 1. Polya’s Problem-Solving Cycle The Teaching and Learning Group
2. 2. Objectives  Understand Polya’s Problem-Solving Cycle  Share some practical ideas for what this might look like in various subjects.  Think about how this might be applied in your own subject
3. 3. What is this about?  Explicitly teaching students how to solve problems using the method developed by George Polya  This is not about problem-based learning
4. 4. Polya’s Problem-Solving Cycle How to Approach Problem Solving Understand the Problem Devise a Plan Carry Out the Plan Look Back
5. 5. Understanding the Problem  The obvious first step, but often not done.  Ask students questions such as:  Do you understand all the words used in the problem?  What are you being asked to do/show/find out?  Can you put the problem into your own words?  Can you draw a diagram/picture that would explain what you have to do?  Is there enough information to enable you to find a solution?  What do we know already, and what do we need to find out? How to Approach Problem Solving Understand the Problem Devise a Plan Carry Out the Plan Look Back
6. 6. Devising a Plan  Use a model  Consider special cases  Work backwards  Use direct reasoning  Use a formula  Solve an equation  Be ingenious  Guess and check  Look for a pattern  Make an orderly list  Draw a picture  Eliminate possibilities  Solve a simpler problem  Use symmetry  There are many ways to approach solving a problem  Below is a list of just some of them  You may need to help the students identify a suitable approach How to Approach Problem Solving Understand the Problem Devise a Plan Carry Out the Plan Look Back
7. 7. Carrying Out the Plan  This is too often where students start!  Students need persistence and patience (and perhaps encouragement)  All the while the students should be keeping the next step in the cycle at the back of their minds How to Approach Problem Solving Understand the Problem Devise a Plan Carry Out the Plan Look Back
8. 8. Look Back  Key questions to ask here include:  Is the plan working?  If not, go back round the cycle and develop a new plan  Students too often keep going with things that clearly aren’t working  Does the solution make sense?  What worked and what didn’t?  Have a solved the problem successfully?  What have I learnt?  These questions are critical to helping students solve future problems How to Approach Problem Solving Understand the Problem Devise a Plan Carry Out the Plan Look Back
9. 9. For example…  Solving a complex mathematical problem  Polya was a mathematician!  The extended essay!  Science investigations  Fulfilling a design-brief  Writing an essay
10. 10. Over to you….  Would this work in your subject?  What might it look like in your subject?
11. 11. References and Further Reading  ‘How to Solve It’, George Polya, 1945  ‘Polya’s Problem Solving Techniques, http://math.berkeley.edu/~gmelvin/math110sp14/polya.pdf  Wikipedia article: http://en.wikipedia.org/wiki/How_to_Solve_It