Over the years, I have met with countless students who at first believed they were ‘no good at maths’. Imagine their delight when we helped them discover their inner ‘problem solver’.

Many would describe maths as ‘logical, black and white, right or wrong’; for there can only ever be one correct answer. While this may be true, there can often be several ways to solve the same problem, suggesting that mathematics is perhaps a far more creative endeavour than we have previously given it credit for.

The ability to solve problems, mathematical or otherwise, often requires us to think outside the box, to be original and to identify a way forward that others may not have considered.

It engages a creativity that is often not normally associated with the logic inherent in finding a solution, particularly as it applies to numbers.

However, some would argue that Mathematical problem solving is in the same realm as writing music or playing an instrument, in that while it is bound by laws and limitations, it is also a natural expression of our mind’s unique and infinite capacity to form patterns and ideas.

Everyone of us is a problem solver, in a multitude of ways and in a vast array of daily contexts.

When children see themselves as problems solvers and see maths as a way to ‘create’ solutions, it can help to break down the barriers that prevent them from trying in the first place.

Problem solving involves three key things:

- What is the problem asking for? i.e. be sure to identify the unit of measurement and record this near the bottom of the working out page before you have even done the calculations.
- What operation/ operations will be required? i.e. look for language in the text that indicates whether you will be adding, or dividing and think of a reasonable estimate.
- What strategy is going to be most efficient?

When it comes to Problem Solving of more complex worded problems, it is important that children are adept at using a range of strategies, as it will enable them to discern what will be the best approach to use for any given problem.

For example, if a problem involves finding the area of a compound shape, ‘drawing a picture’ and writing measurements as described, will allow the child to visually understand the task and keep track of each step.

In another instance, it may be more efficient to ‘work backwards’ and in another, perhaps a ‘guess and check’ approach.

Below is a list of effective Problem Solving strategies that you and your child can explore when presented with a mathematical problem.

1. Read the problem aloud – *By reading the problem aloud, they can help to clarify any confusion and better understand what’s being asked.*

2. Summarise the information – *Using dot points or a short sentence, list out all the information given in the problem. *

3. Create a picture or diagram – *By drawing a picture, can better understand what’s being asked and identify any information that’s missing.*

4. Act it out – *It can enable students to see the problem in a different way and develop a more intuitive understanding of it. *

5. Use keyword analysis – *Keyword analysis involves asking questions about the words in a problem in order to work out what needs to be done. *

6. Look for a pattern – *This could be a number, a shape pattern or even just a general trend that you can see in the information given. *

7. Guess and check –* Simply make a guess at the answer and then check to see if it works. If it doesn’t, you make another systematic guess and keep going until you find a solution that works.*

8. Working backwards – *Regressive reasoning, or working backwards, involves starting with a potential answer and working your way back to figure out how you would get there. *

9. Use a formula – *There will be some problems where a specific formula needs to be used in order to solve it. *

10. Use direct reasoning – *By breaking the problem down into smaller chunks, you can start to see how the different pieces fit together and eventually work out a solution.*

12. Solve a simpler problem –* Or if you’re struggling with the addition of algebraic fractions, go back to solving regular fraction addition first. *

*Published 22-July-2023*