# Using NRICH Tasks to Develop Key Problem-solving Skills

In her article Developing Excellence in Problem Solving with Young Learners, Jennie Pennant suggests that as teachers we can help children get better at problem solving in three main ways, one of which is through 'explicitly and repeatedly providing children with opportunities to develop key problem-solving skills'.

This article builds on Jennie's. In particular, it explains what we mean by 'problem-solving skills' and aims to give further guidance on how we can help learners to develop these skills by highlighting relevant NRICH tasks.

#### What do we mean by 'problem-solving skills'?

In the aforementioned article, Jennie outlines four stages of the problem-solving process:

Stage 2: Working on the problem

Stage 3: Digging deeper

Stage 4: Reflecting

By explicitly drawing children's attention to these four stages, and by spending time on them in turn, we can help children become more confident problem solvers. Jennie outlines different ways in which learners might get started on a task (stage 1), but it is once they have got going and are working on the problem (stage 2) that children will be making use of their problem-solving
skills.

Here are some useful problem-solving skills:

- Trial and improvement
- Working systematically (and remember there will be more that one way of doing this: not just the one that is obvious to you!)
- Pattern spotting
- Working backwards
- Reasoning logically
- Visualising
- Conjecturing

The first two in this list are perhaps particularly helpful. As learners progress towards a solution, they may take the mathematics further (stage 3) and two more problem-solving skills become important:

- Generalising
- Proving

Having reached a solution, stage 4 of the process then involves children explaining their findings and reflecting on different methods used.

For the purposes of this article, we will think of 'problem-solving skills' as *those skills that learners need in order to work on the mathematics of a task,* during stages 2 and 3 of the problem-solving process.

#### How can we help children get better at these problem-solving skills?

In order for learners to develop their problem-solving skills, they will need to experience lots of contexts in which to practise each one and to be given lots of opportunities to talk about each one. Having a skills-based focus to a lesson or series of lessons can work well and it would be worth focusing on one or two skills at a time.

This takes us back to the Developing Excellence in Problem Solving with Young Learners article, where Jennie also suggests that our choice of task can affect learners' confidence and competence as problem solvers. So, I shall now take each problem-solving skill in turn and suggest groups of NRICH tasks which might help develop it.*Trial and improvement*

There are two collections of NRICH tasks which are good starting points if you wish to focus on this skill:

Trial and Improvement at KS1

Trial and Improvement at KS2

**Working systematically**We have gathered together a collection of tasks and further guidance which lend themselves to systematic working.

**Pattern spotting****Working backwards**

Working Backwards at KS1

Working Backwards at KS2

**Logical reasoning**In addition to the Reasoning Feature, there are two collections of activities on the site which focus specifically on logical reasoning:

Reasoning and Convincing at KS1

Reasoning and Convincing at KS2

**Visualising**Visualising at KS1

Visualising at KS2

**Conjecturing, generalising and proving**These two collections of activities encourage children to conjecture and generalise, and in some cases, go on to prove:

Conjecturing and Generalising at KS1

Conjecturing and Generalising at KS2

**In summary**

One of the main ways to help children become confident and competent problem solvers is by offering them plenty of opportunities to practise key problem-solving skills and, importantly, to talk about the skills in context. In this article, I have outlined what we mean by these skills and suggested groups of NRICH tasks which focus on each. Once learners have had experience of these different problem-solving skills, they may like to tackle some of the following activities which each draws upon a range of skills:

Noah

Pairs of Numbers

Poly Plug Rectangles

Play to 37

Bracelets

Planning a School Trip

Dice in a Corner

*Here is a PDF version of this article.*