EYFS best practice - All about ... problem-solving

Mathematics in the EYFS is called Problem Solving, Reasoning and Numeracy. It's an odd title, probably chosen because it has a rhythmic assonance with Knowledge and Understanding of the World and Communication, Language and Literacy. It's odd, first because problem-solving and reasoning are applicable across all learning, not just maths, and second, because maths is about more than numeracy.

My dictionary defines being 'numerate' as 'able to perform arithmetical operations'. But 'mathematics' has a much wider definition: 'the science dealing with measurements, numbers, quantities, and shapes'. That's a gripe of mine, but let's focus on problem-solving and reasoning. Each of the areas of learning could have had 'problem solving, reasoning and ...' added to their titles.

UNPICKING THE EYFS

The Early Years Foundation Stage has a mixture of very clear, brief descriptions of learning development and more complex general ones.

Simple and brief:

'Continue a rhyming string'; 'respond to simple instructions'; 'handle books carefully'; 'recognise numerals 1 to 5'; 'say the number that is one more than a given number'; 'select a particular named shape'; 'use simple tools competently and effectively'; 'notice and comment on patterns'; 'sing a few familiar songs'; 'go backwards and forwards as well as sideways'.

Complex and general:

'Have an awareness and pride in self and as having own identity and abilities'; 'question why things happen, and give explanations'; 'use language for an increasing range of purposes'; 'use talk to connect ideas, explain what is happening and anticipate what might happen next'; 'use writing as a means of recording and communicating'; 'use developing mathematical ideas and methods to solve practical problems'; 'describe solutions to practical problems, drawing on experience, talking about own ideas, methods and choices'; 'explain own knowledge and understanding, and ask appropriate questions of others'; 'collaborate in devising and sharing tasks, including those which involve accepting rules'; 'talk about personal intentions, describing what they were about to do'; 'work creatively on a large or small scale'.

Approach

It is easy to allocate the simple descriptions to particular curriculum areas, and these are recognisable discrete skills that we know we have to teach. 'Continue a rhyming string' is language and 'recognise numerals 1 to 5' is maths.

The general descriptions are harder to allocate, unless there are clues like 'mathematical' and 'writing'. These complex statements have embedded in them a problem-solving approach. How do you teach 'question ...', 'collaborate ...', 'pride ...', 'personal intentions ...'? Well, you don't. You have to set up the environment and the ethos that will encourage these things, and support the children with planned interventions.

It's difficult working with such a mix of complex concepts. You know how to approach 'begin to form recognisable letters' and 'select a particular named shape'. You show children how to form letters. You teach them the names of the shapes. But how do you ensure that this develops into 'use writing as a means of recording and communicating' and 'use developing mathematical ideas and methods to solve practical problems'?

What are the children learning?

Clearly, children are learning about shapes and how they move and fit together; about how to manipulate large objects; about relative heights; about hollow and solid shapes; about filling spaces; about the properties of materials. But they are also learning about collaboration and working to a common goal, and about perseverance; and above all, they are setting themselves problems that they have to solve.

The work in the case study below involved a problem-solving chain, each one with its own goal to be set, obstacles to be overcome, and the solution to be found. One goal is to build a tower with tyres, but the problem is how to lift and place the tyres.

Another goal is to fetch the tyres to add to the tower, but the problem is how to get the tyres to the tower. Another goal is to make the tower as tall as possible, but the problem is how to reach the top of the growing tower - and so on.

Seeking solutions to the problems involves analytical reasoning, conscious or unconscious. How do I move the tyre? Turn it into a wheel by putting it on its edge and rolling it.

Later, during circle time, the children talked about their play with the tyres. Although there was not a lot of talk during the activity, just brief and necessary instructions and comments, the children were able to put into words what they had been doing.

THE NATURE OF PROBLEM-SOLVING

Problem-solving is an integral part of everyday provision, an expectation rather than an added extra, and it relies on a 'have a go' ethos. Successful problem solvers have these kinds of strategies:

- setting themselves a goal
- recognising there are obstacles in the way of the goal
- getting a feel for the nature of the obstacles
- having a sense of possible ways of overcoming the obstacles
- planning ahead, and predicting what will happen
- checking progress as they go
- trying out different possibilities in a systematic way
- trying different approaches to see which will work best
- looking for even better solutions.

Children who feel confident and secure in their surroundings, and free to make choices, are better able to solve problems, both on their own and collaboratively.

Problems can be minor and arise incidentally, or they can be major projects. But the most important thing is for children to set themselves a challenge, or to engage with the challenge that is there, and then to know that they can choose their own ways of solving it. If children are told the problem and then told the method to use to solve it, they are not problem-solving.

To become confident, proficient problem solvers, it stands to reason that children must have access to a wide range of appropriate resources they can use independently.

The ethos of the setting must support their investigations and allow them to move resources between areas of provision. For example, the children working with the tyres knew with confidence that they could move the tyres around, they could fetch a chair, and they could empty into the tower a range of objects at their disposal, without adult intervention. One of the important things about problem-solving is that it involves choice and that children have opportunities to reason and make decisions.

WHY IS PROBLEM-SOLVING IMPORTANT?

Two highly influential thinkers have stressed the importance of problem-solving as a vehicle for learning: Piaget and Vygotsky.

Piaget thought that children under seven saw the world differently from older children and adults, and they need time to explore the world in their own way. These are some of Piaget's key ideas:

- Children need to be in charge of their own learning by choosing their own activities and taking their own time in that exploration.

- We should provide children with materials to explore, such as block play, role-play materials, small-world toys, and so on. We should involve children in planning the uses of these resources, such as setting up a shoe shop or organising a picnic.

- We need to observe children to find out what they are focusing on and what their interests are, and respond to them if they ask for it. Our role as an adult is as a facilitator in their play.

- We should be aware of the stages of learning that children go through so that we can offer appropriate materials and activities for each stage, and note when children become 'ready' for the next stage.

- We should value each child as an individual.

Vygotsky emphasised collaborative and guided problem-solving. He focused on the social aspect of children's learning, and how they develop their thinking skills through shared experiences. This meant that language is a vital tool for thinking and for sharing ideas. He also looked at the roles of older children and adults in influencing learning. These are some of Vygotsky's key ideas:

- Children learn best through active self-directed play.

- Children learn more effectively in collaboration with other children and with adults.

- Our role is to offer help and support in helping children learn how to do things they cannot quite do on their own. Language is very important here.

- We need to observe children to find out where they are on their own learning trajectory.

- We must focus on language, as this is vital in helping children make sense of the world.

- We must be sensitive in how we take part in children's learning. Sometimes we can take the lead and instruct, at other times we will have minimal engagement.

The EPPE (Effective Provision of Pre-School Education) project corroborated Vygotsky's ideas, by finding that quality conversations between adults and children, and children and other children, enhanced children's problem-solving and reasoning skills. The work of the nursery settings in Reggio Emilia also puts into practice Vygotsky's ideas, with children and adults working collaboratively on long and complex projects.

Children's thinking will only develop well if they can spend their time solving problems. As they solve problems, their confidence and self-esteem increases. However, their self-esteem will decline if they fail too often to solve a problem. The role of the adult is so important in providing appropriate help, support, knowledge and skills.

Problem-solving involves reflection and thought. The adult can help by modelling strategies and encouraging children to talk about their methods. Children can develop a range of methods by collaborating with adults and with other children, and by discussing the range of methods.

HELPING CHILDREN BECOME PROBLEM-SOLVERS

- Create an atmosphere where exploration and having a go are more important than getting the right answer or doing the expected thing to please an adult.

- Provide a rich and stimulating environment, with plenty and varied activities, and don't make things too easy for the children.

- Be an opportunist and look for problem-solving possibilities in everyday activities, such as parties, picnics, tidying-up, arriving and leaving, charity events, a new baby, children's own interests.

- Approach everyday activities as problem-solving opportunities. In adult-led guided learning sessions, make sure children have choices within the framework of the objectives of the session. For example, if children are focusing on counting, play an interesting game that involves choices.

- If children ask you to be involved in their problem-solving, prompt them with comments or questions that will help them to continue to grapple with the problem themselves, or supply further resources that will keep the problem with them. A comment or a look can be as effective as questioning. Certainly, asking questions should not be an inquisition, but a collaborative conversation.

What do you think would help you to reach up there?

Mmm ... I don't know ... What have you tried so far?

Why didn't that work? I wonder if there is another way of doing it.

I wonder if we need anything else here to help us.

How does it look now?

I'm not sure I can do it either! Let's have another go.

- In group sessions, encourage children to describe their play, and the problems they tackled and overcame. Invite them to share ideas and thinking to show what they have done.

- If children are becoming frustrated, or if you feel they are on the cusp of new learning, introduce them to a technique or strategy for taking them on to the next step of learning. You can suggest breaking the problem down into smaller steps, or draw their attention to key features or clues.

- On the other hand, also allow children to get into a muddle so they can see that they need to think things through and develop systematic strategies. Don't take the problem away from the children. Healthy confusion is a good starting point for trying to sort things out.

- Make sure that children have long, uninterrupted periods of time at their own self-directed play.

- Observe children regularly to gain insights into their learning. Analyse and interpret these observations to help understand how to support them in their further learning.

For children to engage in and learn from problem-solving, they need to solve problems that they understand, in familiar contexts, where the outcomes matter to them, either on their own or in collaboration with others. They need to have control over the problem-solving process, and the problems should involve knowledge and skills they are confident with. They should have the opportunity to talk about the process, and have adult help to scaffold smaller steps in the process where they need it.

CASE STUDY

Two boys are playing with the tyres in the outdoor area of the setting. Their play leads them to start piling one tyre on top of the other. There are lots of tyres lying around the grassy area, and gradually they collect them and add them to their growing cylindrical tower.

Two more children join them, but in a different activity. They each find a container - one a bucket and spade and the other a dustpan and brush - and they gather up leaves and twigs and stones and empty them into the growing tyre cylinder.

The children building the tower have difficulty manipulating the tyres, as they are big and unwieldy. They have to turn each one on its edge and try to roll the tyre along. Sometimes another child sees this going on and volunteers to help.

Lifting the tyres increasingly higher is also difficult and reqiures two children, at least. As the tower grows, one child runs off and fetches a chair, puts it up against the tower, and lifts each tyre up on top. Meanwhile, the fillers continue to collect material to put into the central cavity.

Now that the hole is deeper, they add larger items such as lumps of wood and bark from the digging area. There are eight or nine tyres, one on top of the other. The children work at this activity for an hour and a half with no adult intervention. There is an adult observing from time to time and making notes.