Polya’s Problem-Solving Cycle

The Teaching and Learning Group

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

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

Polya’s Problem-Solving Cycle

How to Approach Problem Solving

Understand the Problem

Devise a Plan

Carry Out the Plan

Look Back

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

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

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

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

For example… Solving a complex mathematical problem

Polya was a mathematician!

The extended essay!

Science investigations

Fulfilling a design-brief

Writing an essay

Over to you….

Would this work in your subject?

What might it look like in your subject?

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