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:

‘The ability to solve problems is at the heart of mathematics. Mathematics is only “useful” to the extent to which it can be applied to a particular situation and it is the ability to apply mathematics to a variety of situations to which we give the name “problem solving”. [...] At each stage [...] the teacher needs to help pupils to understand how to apply the concepts and skills which are being learned and how to make use of them to solve problems. These problems should relate both to the application of mathematics to everyday situations within the pupils’ experience, and also to situations which are unfamiliar.’

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:

• Problems do not have to be set in real-life contexts, beware pseudo contexts.
• Providing a range of puzzles and other problems helps pupils to reason strategically to approach problems, sequence unfolding solutions, and use recording to help their thinking for next steps.
• It is particularly important that teachers and TAs stress reasoning, rather than just checking whether the final answer is correct.
• Pupils of all ability need to learn how to solve problems - not just the high attainers or fastest workers.

#### 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:

• Set problems as part of learning in all topics for all pupils.

• Vary the ways in which you pose problems.
• Try to resist prompting pupils too soon and focusing on getting ‘the answer’ – pupils need to build their confidence, skills and resilience in solving problems, so that they can apply them naturally in other situations.
• Make sure you discuss alternative approaches with pupils to help develop their reasoning.
• Ensure that problems for high attainers involve demanding reasoning and problem-solving skills, not just harder numbers.

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:

1. Understand the problem
2. Devise a strategy for solving it
3. Carry out the strategy
4. 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:

##### CUBES

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?)

##### RIDE

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

##### IDEAL

I - Identify the problem
D - Define the problem
E - Examine the options
A - Act on a plan
L - Look at the consequences

##### RICE

R – Read and record the problem
I – Illustrate your thinking with pictures, models, number lines etc
C – Compute, calculate and check

##### RUCSAC

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
C – Check

##### QUACK

Q – Question – read it carefully
U – Understand – underline or circle key elements
C – Calculate
K – Know if the answer is sensible or not

##### TEAR

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

• Working backwards

• 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:

• Giving pupils Maths problems that require them to think for an extended time.
• Asking pupils to use their own procedures for solving complex problems.
• Creating a learning community where pupils are able to make mistakes.
• Asking pupils to explain how they solved a problem and why they choose that method.
• Presenting pupils with problems in different contexts and ask them to apply what they have learned to new contexts.
• Giving pupils problems with no immediately obvious method of solution or multiple solutions.
• Encouraging pupils to reflect on problems.

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.

#### Looking for support in Maths next year?

Book a 15 minute demonstration of our 1-to-1 Maths intervention to find out how your target pupils can achieve up to 7 months' progress in 14 weeks'.

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