Teaching Problem Solving

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How do we improve the teaching of problem solving?

Problem solving is… well… a problem. It is a skill highly prized by employers and a requirement of several of the new GCSE qualifications. However, it doesn’t seem to be a skill that comes easily to pupils.

In the workplace the ability to tackle unexpected issues as and when they arrive, to strategise for your business or department and to find creative solutions for customers are all valuable attributes. They are all problem solving. We therefore need to equip pupils to use these skills when they move on from education as well as needing them to develop these skills to obtain the best exam results possible.

The ACME report on ‘Mathematics in the Workplace and in Higher Education’ (2010) noted the growing global trend within he UK away from low skilled jobs and an increase in those that require ‘management expertise and problem-solving skills’. Their more recent report, ‘Problem solving in mathematics: realising the vision through better assessment‘, also highlighted the importance of teaching problem solving stating, “In the modern world, young people need to be able to engage with and interpret data and information. They need to become flexible thinkers capable of dealing with novel problems and situations and analysing their own and others’ solutions to these. ACME has long recognised the centrality of problem solving in the effective teaching, learning and assessment of mathematics.”

Top 5 Tips For Developing Problem Solving

Teaching problem solving can be frustrating, pupils find it challenging and uncomfortable. However, it can also be an amazing skill to nurture. It brings out the best in pupils’ creativity and allows pupils to develop their own way through a subject or topic that otherwise they might lack confidence in. With various colleagues over the last 3 years I have tried to develop ways to help pupils develop these skills. There is no complete right method that works for everyone but there are some common themes.

The most important two seem to be confidence and time.

Pupils who are confident are more willing to try and solve a problem and to persevere until the problem is solved, and pupils need time to do this – it cannot be rushed. Below are some strategies that have helped build this confidence and resilience in pupils my colleagues and I have worked with.

1. Open Book Tests

We assess pupils at the end of every unit using only problem solving questions. Pupils prepare an A4 page of revision notes and have this with them in the test. They think it is cheating so love it!

From our point of view it gives us a real opportunity to assess the depth of their understanding. The confidence pupils get from having a ‘cheat sheet’ means they are much more likely to attempt a question.

2. Assess Problem Solving Separately to Other Skills

This year we have started to alternate our assessments between one which is heavily problem-solving based and one which assesses fluency and key knowledge. This allows us to diagnose more precisely the pupils who need extra help and support to develop their problem solving skills.

3. Free Writing

Some pupils really struggle with the unknown aspect of problem solving tasks. They don’t want to start if they don’t know how or if they will get to an answer. This can be particularly true for those high attaining pupils who are used to getting things right.

There can be a fear of writing something down which isn’t the actual answer and so to try to combat this I regularly start lessons with 5 minutes of free writing.

Pupils write non-stop for 5 minutes about a number – anything they think is interesting (“5 is odd”, “it is prime”, “half of it is 2.5”, “squared it is 25 and cubed it is 125”). There is no question so there cannot be a right or a wrong answer – they are simply writing something that they know.

4. Teach Explicit Strategies

This is the one tip that has more of a maths bias. We structure our KS3 and KS4 schemes of learning to include early units on problem solving.

We teach pupils about the bar model, arrow diagrams and using algebra and by teaching these as a discrete topic at the start we are then able to refer back to them and interleave these in our practice throughout every other topic.

5. Using Problem Solving as a means of Differentiation

Giving pupils differentiated tasks that differentiate by type of skill rather than content makes problem solving the top level to aim for. With enthusiastic pupils this works wonders as they want to get to the problem solving every lesson. There are some great resources out there that already do this (Access Maths‘ Feedback Sheets structures topics by Fluency, Reasoning and Problem Solving).

As with any wholesale change in focus, it is probably advisable to not try too much too soon.

The 2016 ACME report concluded that, “Changes in the assessment of problem solving should be introduced incrementally. A commitment is required across the community to the gradual increase in the quality of problem solving assessment and a reduction in scaffolding over time. An incremental approach will allow time for schools, teachers and learners to adapt to the changes.”

Have a long term aim but manageable short term goals to get there.

There is no magic wand. Problem solving will continue to be a problem. However, if we put pupil confidence at the heart of strategies we adopt, we may be able to nurture those resilient individuals who can thrive in their exams and ultimately in the workplace.

Lucy Kilgariff

Lucy is currently working as Head of Maths for a successful Devon school. She also works in system leadership as a DLE for the Dartmoor TSA. She has a passion for problem solving and has delivered workshops on the topic for ATM at their annual conference. Teaching is Lucy's second career having previously been a solicitor. She liked the legal world but wanted to do something more rewarding. So far she has not been disappointed!

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