Structural Support – How To Teach Problem Solving Strategies at Maths GCSE
A greater emphasis on problem solving for maths GCSE may provide new challenges for teachers and students alike – but Michael McGarvey has some solutions The reform of GCSE content and assessment criteria is underway, with mathematics amongst the first subjects to change. The introduction of new specifications, content and methods of assessment brings new […]
A greater emphasis on problem solving for maths GCSE may provide new challenges for teachers and students alike – but Michael McGarvey has some solutions
The reform of GCSE content and assessment criteria is underway, with mathematics amongst the first subjects to change. The introduction of new specifications, content and methods of assessment brings new challenges for teachers to navigate in this phase of first teaching ahead of the first exams under the new curriculum, which will take place in Summer 2017.
In maths, one of the core changes is the greater emphasis on problem solving, which now accounts for 30% of the Higher Tier assessment and 25% of Foundation. This means students will need to be made comfortable with problem-solving strategies, as well as the key skills of reasoning, interpreting and communicating. These will now also make up 30% and 25% of assessment at Higher and Foundation tier respectively.
So what is the best way for problem solving strategies to be taught, in order for students to get the maximum impact out of their learning?
Step by step
One way to tackle the increased weighting given to problem solving is to begin with a scaffolded approach, equipping students with a set of steps that they can use as a supportive framework to apply to any new mathematical problem. For example:
Step 1 may simply be ‘Work out what you have to do by reading the question carefully’.
Step 2 could then be ‘Assess what information is needed and check that you have it all.’
Step 3 may be to ask, ‘Is there any information given that you don’t need?’, followed by…
Step 4, which can be ‘Decide what maths you can do.’
The final steps will be to set out the working clearly, and to check that you’ve answered the question.
When Professor Malcolm Swan, whom some may know as the driving force behind the Standard Units, developed his Eight Core Principles of Teaching Mathematics, one idea he stressed was the need to emphasise methods, rather than answers. This is exactly what a scaffolding approach aims to do.
Alongside the scaffolded framework, you can help students to build a mental ’toolkit’ of different problem-solving strategies that they can select from when they reach the step ‘Decide what maths you can do.’
For instance, one problem-solving strategy that could be taught is ‘Draw a diagram’. This involves making sure students learn and understand different diagram types – line diagrams, tables, frequency graphs and polygons – and their functions. Students can then choose an appropriate one to apply to their question, depending on what is being asked. This can turn the problem into something more visual, and enable pupils to work through the question in a way that may feel more logical.
Often we find that learners are more focused on getting the answer right than they are on learning the method, and that they see completion as more important than comprehension. Encouraging students to build a base of different problem-solving strategies will help them focus on learning how to start tackling new questions. If students don’t know where to start, there is a risk that they will feel too overwhelmed by new problems and tasks, and that they won’t be confident enough to try. Using different strategies to think around the problem can help these pupils figure out the best way to make the first approach.
Conversely, building different strategic skills can help more advanced students to whom the solution to a task is obvious – because they will still be able to apply the different skills to other, more challenging problems in the future. Emphasising method in this way may mean learners work on fewer problems overall, but pupils should develop a deeper understanding of them by tackling them using more than one strategy.
Having a scaffolding system and a range of different strategies in place means students can gain confidence in a varied framework of techniques. Over the course of the academic year, the scaffolding supporting them can be removed as students become more fluent problem-solvers. Theoretically, this will leave candidates with a range of learned techniques to employ confidently in their final exams.
Combining these new approaches with all the additional content now included in the GCSE may seem like a lot to be faced with at once. However, with a reasoned, supportive approach, teachers can help students build the structures they need to tackle problem solving head on.
Michael McGarvey has over 20 years of experience in the global education sector, and currently works as the Director of UK Education at Cambridge University Press