What Is Problem Solving?

Age 14 to 18
Article by Steve Hewson

Published 2008 Revised 2011


In this article I model the process of problem solving and thinking through a problem. The focus is on the problem solving process, using NRICH problems to highlight the processes. Needless to say, this is not how problems should be taught to a class!

What is problem solving?

What is the difference between the solution to a problem and the problem solving process ?

How might we break down problem solving into a series of different steps?

What questions and strategies might we use to solve a tricky mathematical problem?

In this activity we shall analyse the problem solving process by looking at three NRICH problems.

We start with System Speak and Sums of Squares

As you strive to solve them can you notice the sorts of problem solving steps that you take at each stage? In this activity being 'stuck' is a good thing! When you are stuck what sorts of things do you try in order to make progress in the problem? Note them down.


Once you have tried the problems, watch these two video clips in which I attempted to solve these problems from start to finish. This shows some of the thought processes I go through when solving problems. Try to focus on the way in which I approached the problem solving process.What questions do I ask? How do I approach the task?

[You can download a transcript of the problem solving steps in Word here:
Sums of squares transcript
System Speak transcript ]

How did my approach relate to yours? Can you see any sense of a 'problem solving structure' emerging? Were any of my approaches sensible? Any not so sensible?

Can you use the ideas you have learned or considered to structure your approach to the more difficult problem Always two ? As you work, make a note of your problem solving process. Even if you do not manage to find the 'answer', you will still be using many problem solving strategies. Can you write these down?

Watch a video of my attempt at solving this problem. Can you identify the key problem solving steps this time?