In Abacus, we currently link out to a number of NRICH’s enriching mathematical tasks. Whilst these resources are a great “next step” for children who have already grasped key concepts within the core lesson in Abacus, they can also help all children to think mathematically and to become competent problem solvers.

Our first blog introduced you to problem solving with NRICH, and explored how important it is to choose appropriate tasks. This second blog will explore how you can structure the problem-solving process, and embed problem solving into every school day.

Structuring the problem-solving process

The problem-solving process can usually be thought of as having four stages:

• Stage 1 - Getting started: in this stage, teachers can support children by offering strategies to help them engage with the problem. These could be prompts such as telling a partner what they think the problem is about or helping them understand the problem by encouraging them to draw a picture, act it out or use a model to represent the problem.
• Stage 2 - Working on the problem: will usually involve using one or more problem-solving skills such as:
  • Trial and improvement
  • Working systematically
  • Pattern spotting
  • Working backwards
  • Reasoning logically
  • Visualising
  • Conjecturing.
• Stage 3 - Digging deeper: this usually happens when the problem has been explored and it is possible to look for generalisations and proof. 
• Stage 4 - Concluding: in this stage, children learn to explain their findings both verbally and in writing. Teachers can also encourage pupils to compare answers and approaches, so that perhaps they might try another child’s approach next time and therefore become more fluent with a range of skills and methods. 

Providing children with opportunities to problem solve

It will help children to become fluent in the key problem-solving skills (listed in Stage 2 above) if you take every opportunity to explicitly talk about them and use the appropriate language when they occur in games or larger problem-solving activities. You may like to focus on developing one or two at a time.

Even our littlest learners can start thinking about ‘working systematically’ in contexts such as choosing two toppings out of sprinkles, sugar stars or flakes to go on top of iced biscuits they are making. The key question is – ‘how do you know that you have got them all?’. This comes after, ‘I can find some solutions’ and ‘I can recognise ones that are the same’. For example, is having sprinkles and sugar stars the same as having sugar stars and sprinkles on top of my iced biscuit?

In conclusion

Being a competent and confident problem solver is central to the mathematical development of all children. It is also the major aim of the mathematics national curriculum. There are lots of NRICH problems that will help you develop these skills with children. Take a look at our Problem Solving Feature which offers groups of tasks which will give children experience of using specific problem-solving skills.

You can find out more, and read additional articles, on the NRICH website.

The team at NRICH.