Get to grips with KS2 Maths problem solving: The Ultimate Guide to Problem Solving Techniques
If your Key Stage 2 pupils are still struggling with problem solving in Maths, here are the key problem solving and reasoning techniques to try with your classes; all aligned to Ofsted's suggested primary school teaching strategies.
Solving problems is widely understood to be one of the most important activities in school mathematics. As far back as 1982, The Cockcroft Report, stated:
Thirty plus years later and problem solving is still the beating heart of the Maths curriculum and - along with fluency and reasoning - completes the triad of aims in the 2014 New National Curriculum.
Ofsted's view on problem solving in the Maths curriculum
Despite its centrality, Ofsted report that ‘problem solving is not emphasised enough in the Maths curriculum’. Not surprisingly, problem solving isn’t taught that well either because teachers can lack confidence, or they tend to rely on a smaller range of tried and tested strategies they feel comfortable with but which may not always 'hit home'. If you're looking to provide further support to those pupils who haven't yet mastered problem solving, you probably need a range of different strategies, depending on both the problem being attempted and the aptitude of the pupil.
We've therefore created a free resource aimed at Maths Coordinators and KS2 teachers that teaches you when and how to use 9 key problem solving techniques: The Ultimate Guide to Problem Solving Techniques
The context around problem solving
According to Jane Jones, HMI, National Lead for Mathematics, in her presentation at the Jurassic Maths Hub:
How to approach Maths problems
So what do we do? Well Ofsted advice is pretty clear on what to do when teaching problem solving. Jane Jones says we should:
Perhaps more than most topics in Maths, teaching problem solving to all pupils effectively requires a systematic approach. Pupils can face any number of problems throughout their SATs and they will face them without our help. To truly give pupils the tools they need to approach problem solving in Maths we must ingrain techniques for approaching problems. With this in mind, in below are some methods and techniques for you to consider when teaching problem solving in your KS2 Maths lessons. For greater detail and details on how to teach this methods, download the Ultimate Guide to Problem Solving Techniques
Models for approaching problem solving
Becoming self-assured and capable as a problem solver is an intricate business that requires a range of skills and experience. Children need something to follow. They can’t just pluck a plan of attack out of thin air which is why models of problem solving are important especially when made memorable. They help establish a pattern within pupils so that, when they see a problem, they feel confident in taking the steps towards solving it.
The most commonly used model is that of George Polya (1973), who proposed 4 stages in problem solving, namely:
- Understand the problem
- Devise a strategy for solving it
- Carry out the strategy
- Check the result
Many models have followed the Polya model and use acronyms to make the stages stick. Which model you use can depend on the age of the children you are teaching and sometimes the types of problems they are trying to solve. Below are several examples of Polya model acronyms:
C - Circle the question words
U - Underline key words
B - Box any key numbers
E - Evaluate (what steps do I take?)
S - Solve and check (does my answer make sense and how can I double check?)
R - Read the problem correctly.
I - Identify the relevant information.
D - Determine the operation and unit for expressing the answer.
E - Enter the correct numbers and calculate
I - Identify the problem
D - Define the problem
E - Examine the options
A - Act on a plan
L - Look at the consequences
R – Read and record the problem
I – Illustrate your thinking with pictures, models, number lines etc
C – Compute, calculate and check
E – Explain your thinking
R – Read the question and underline the important bits
U – Understand: think about what to do and write the number sentences you will need
C - Choose how you will work it out
S – Solve the problem
A – Answer
C – Check
Q – Question – read it carefully
U – Understand – underline or circle key elements
A – Approximate – think about the size of your answer
C – Calculate
K – Know if the answer is sensible or not
T – Think about the problem and ponder
E – Explore and get to the root of the problem
A – Act by selecting a strategy
R – Reassess and scrutinise and evaluate the efficiency of the method
The idea behind these models is the same: to give children a structure and to build an internal monitor so they have a business-like way of working through a problem.
The model you choose is less important than knowing that pupils can draw upon a model to follow, ensuring they approach problems in a systematic and meaningful way.A far simpler model - that we use in the Ultimate Guide to Problem Solving Techniques - is UCR: Understand the problem, Communicate and Reflect.
What’s included in the guide?
After reading the Ultimate Guide to Problem Solving Techniques, we guarantee you will have a new problem solving technique to test out in class tomorrow. It provides question prompts and activities to try out, and shows you step by step how to teach these 9 techniques
Open ended problem solving
Using logical reasoning
Drawing a diagram
Drawing a table
Creating an organised list
Looking for a pattern
Acting it out
Guessing and checking
Cognitive Activation: getting pupils in the lightbulb zone
If you need more persuasion, pupils who use strategies that inspire them to think more deeply about maths problems are linked with higher Maths achievement. In 2015 The National Education Research Foundation (NFER) published ‘PISA in Practice: Cognitive Activation in Maths’. This shrewd report has largely slipped under the Maths radar but it offers considerable food for thought regarding what we can do as teachers to help mathematical literacy and boost higher mathematical achievement.
Cognitive Activation isn’t anything mysterious; just teaching problem solving strategies that pupils can think about and call upon when confronted by a Maths problem they are trying to solve. Cognitive It encourages us as teachers to develop problems that can be solved in more than one way and ‘may require different solutions in different contexts’. For this to work, exposing children to challenging content and encouraging a culture of exploratory talk is key. As is:
Sparking cognitive activation is the same as sparking a fire - once it is lit it can burn on its own. It does, however, require time, structure, and the use of several techniques for approaching problem solving. Techniques, such as open-ended problem solving, are usually learned by example so we advise you create several models to go through with pupils, as well as challenge questions for idependent work. Many examples exist and we encourage you to explore more (e.g. analysing and investigating, creating a tree diagram, and using simpler numbers).
That time, effort, and planning will - however - be well spent. Equipping pupils with the tools to solve problems they have never seen before is more akin to teaching for life than teaching for Maths. The skills they gain from being taught problem solving successfully will be skills they use and hone for the rest of their life - not just for their SATs.
For a range of problem solving techniques, complete with explanations, contextual uses, example problems and challenge questions - dont't forget to download our free Ultimate Guide to problem solving and reasoning techiques resource here.