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

1. Polya’s Problem-Solving Cycle
The Teaching and Learning Group

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. 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. Polya’s Problem-Solving Cycle
How to
Approach
Problem
Solving
Understand
the Problem
Devise a
Plan
Carry Out
the Plan
Look Back

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. 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. 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. 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. For example…
 Solving a complex mathematical problem
 Polya was a mathematician!
 The extended essay!
 Science investigations
 Fulfilling a design-brief
 Writing an essay

10. Over to you….
 Would this work in your subject?
 What might it look like in your subject?

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