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Maths problem-solving – Activities for Early Years settings

• Written By: Judith Dancer
• Subject: Maths

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Critical thinking doesn’t have to be a daunting prospect. There are simple, effective and exciting ways to encourage children’s maths problem-solving skills, says Judith Dancer…

Maths is a subject many adults lack confidence in. Having struggled with it at school they often avoid it, wherever possible, when grown up.

But if maths seems scary for some people, then maths problem-solving can cause even more anxiety. There is no ‘safety net’ of knowing the ‘correct answer’ beforehand. This is because maths problem-solving lends itself to investigation and exploration with lots of possible tangents.

Understandably this is often the area of maths where many practitioners feel least confident. However, young children, who are not restrained by right answers, feel the most enthused and animated.

The non-statutory  Development Matters Guidance , as part of ‘creating and thinking critically’ in the Characteristics of Effective Learning, identifies that practitioners need to observe how a child is learning, noting how a child is:

• thinking of ideas;
• finding ways to solve problems;
• finding new ways to do things;
• making links and noticing patterns in their experience;
• making predictions;
• testing their ideas;
• developing ideas of grouping, sequences, cause and effect;
• planning, making decisions about how to approach a task, solve a problem and reach a goal;
• checking how well their activities are going;
• changing strategy as needed;
• reviewing how well the approach worked.

All of these elements are, at one time or another, part of the problem-identifying and solving process – although not at the same time and in the same problem.

Role of the adult

Maths problem-solving for young children involves them understanding and using two kinds of maths:

• Maths knowledge – learning and applying an aspect of maths such as counting, calculating or measuring.
• Maths thinking skills – reasoning, predicting, talking the problem through, making connections, generalising, identifying patterns and finding solutions.

The best maths problems for children are the ones that they identify themselves. They will be enthused, fascinated and more engaged in these ‘real’, meaningful problems.

Children need opportunities to problem-solve together. As they play, they will often find their own mathematical problems.

One of the key roles of practitioners is to provide time, space and support for children. We need to develop situations and provide opportunities in which children can refine their maths problem-solving skills and apply their mathematical knowledge.

Supporting maths problem-solving

You can effectively support children’s developing maths problem-solving strategies through:

• Modelling maths talk and discussion – language is part of maths learning because talking problems through is vital. Children need to hear specific mathematical vocabulary in context. You can promote discussion through the use of comments, enabling statements and open-ended questions.
• Providing hands-on maths problem-solving activities across all areas of the setting. Children learn maths through all their experiences and need frequent opportunities to take part in creative and engaging experiences. Maths doesn’t just happen in the maths learning zone!
• Identifying potential maths learning indoors and outdoors. Provide rich and diverse open-ended resources that children can use in a number of different ways to support their own learning. It is important to include natural and everyday objects and items that have captured children’s imaginations, including popular culture.

Maths problem-solving possibilities

Spell it out.

This experience gives children lots of opportunities to explore calculating, mark making, categorising and decisions about how to approach a task.

What you need to provide:

• Assorted containers filled with natural materials. This includes leaves, pebbles, gravel, conkers, twigs, shells, fir cones, mud and sand. Include some ‘treasure’ – sequins, gold nuggets, jewels and glitter.
• Bottles and jugs of water, large mixing bowls, cups, a ‘cauldron’, small bottles, spoons and ladles.
• Cloaks and wizard hats.
• Laminated ‘spells’ – e.g. “To make a disappearing spell, mix 2 smooth pebbles, 2 gold nuggets, 4 fir cones, a pinch of sparkle dust, 3 cups of water”.
• Writing frameworks for children’s own spell recipes and a shiny ‘Spell Book’ to stick these in.
• Temporary mark-making opportunities such as chalk on slate.

The important thing with open-ended maths problem-solving experiences like this is to observe, wait and listen. Then, if appropriate, join in as a co-player with children, following their play themes.

So if children are mixing potions, note how children sort or categorise the objects. What strategies do they use to solve problems? What happens if they want eight pebbles and they run out? Observe what they do next.

When supporting children’s maths problem-solving, you need to develop a wide range of strategies and ‘dip into’ these appropriately. Rather than asking questions, it is often more effective to make comments about what you can see. For example, say, “Wow, it looks as though there is too much potion for that bottle”.

Acting as a co-player offers lots of opportunities to model mathematical behaviours. This might include reading recipes for potions and spells out loud, focusing on the numbers – one feather, three shells…

Going, going, gone

We all know that children will engage more fully when involved in experiences that fascinate them. If a particular group has a real passion for cars and trucks , consider introducing maths problem-solving opportunities that extend this interest.

This activity offers opportunities for classifying, sorting, counting, adding and subtracting, among many other things.

• Some unfamiliar trucks and cars and some old favourites. Ensure these include metal, plastic and wooden vehicles that can be sorted in different ways.
• Masking tape and scissors.
• Sticky labels and markers.

Mark out some parking lots on a smooth floor, or huge piece of paper using masking tape. Lining paper is great for this. Line the vehicles up around the edge of the floor area.

Encourage one child to select two vehicles that have something the same about them. Ask the child, “What is the same about them?”.

When the children have agreed on what is the same – e.g. size, materials, colour, lorries or racing cars – the child selects a ‘parking lot’ to put the vehicles in. So this first parking lot could be for ‘red vehicles’.

Another child chooses two more vehicles that have something the same. Do they belong in the same ‘parking lot’, or a different parking lot? E.g. these vehicles could both be racing cars.

What happens when a specific vehicle could belong in both lots? E.g. it could belong in the set of red vehicles and also belongs in the set of racing cars.

Support the children as they discuss the vehicle. Make new ‘parking lots’ with masking tape and create labels for the groups, if you choose.

Observe children’s strategies

It’s really important to observe the strategies the children use. Where appropriate, ask the children to explain what they are doing and why.

If necessary, introduce and model the use of the vocabulary ‘the same as’ and ‘different from’. Follow children’s discussions and interests. If they start talking about registration plates, consider making car number plates for all the wheeled toys outdoors.

Do the children know the format of registration plates? Can you take photos of cars you can see in the local environment?

Camping out

Constructing camps and dens outdoors is a good way to give children the opportunity to be involved in lots of maths problem-solving experiences and construction skills learning. This experience offers opportunities for using the language of position, shape and space, and finding solutions to practical problems.

• Materials to construct a tent or den such as sheets, curtains, poles, clips and string.
• Rucksacks, water bottles, compasses and maps.
• Oven shelf and bricks to build a campfire or barbecue.
• Buckets and bowls and water for washing up.

Encourage the children to explore the resources and decide which materials they need to build the camp. Suggest they source extra resources as they are needed.

Talk with the children about the best place to make a den or erect a tent and barbecue. During the discussion, model the use of positional words and phrases.

Follow children’s play themes. This could include going on a scavenger hunt collecting stones, twigs and leaves and going back to the campsite to sort them out.

Encourage children to try different solutions to the practical problems they identify. Use a running commentary on what is happening without providing the solution to the problem.

Look for opportunities to develop children’s mathematical reasoning skills by making comments such as, “I wonder why Rafit chose that box to go on the top of his den.”

If the children are familiar with traditional tales, you could extend this activity by laying a crumb trail round the outdoor area for children to follow. Make sure that there is something exciting at the end of the trail. It could be a large dinosaur sitting in a puddle, or a bear in a ‘cave’.

Children rarely have opportunities to investigate objects that are really heavy. Sometimes they have two objects and are asked the question, “Which one is heavy?” when both objects are actually light.

This experience gives children the chance to explore really heavy things and measures (weight). They also need to cooperate and find new ways to do things.

• A ‘building site’ in the outdoor area. Include hard hats, builders’ buckets, small buckets, shovels, spades, water, sand, pebbles, gravel, guttering, building blocks, huge cardboard boxes and fabric (this could be on a tarpaulin).
• Some distance away, builders’ buckets filled with damp sand and large gravel.
• Bucket balances and bathroom scales.

With an open-ended activity such as this, it is even more important to observe, wait and listen as the children explore the building site and the buckets full of sand and gravel.

Listen to the discussions the children have about moving the sand and the gravel to the building site. What language do they use?

Note the strategies they use when they can’t lift the large buckets. Who empties some of the sand into smaller buckets? Who works together collaboratively to move the full bucket? Does anyone introduce another strategy, for example, finding a wheelbarrow or pull-along truck?

Where and when appropriate, join in the children’s play as a co-player. You could act in role as a customer or new builder. Ask, “How can I get all this sand into my car?”. “How much sand and gravel do we need to make the cement for the foundations?”.

Extend children’s learning by modelling the language of weight:

• heavy/heavier than/heaviest
• light/lighter than/lightest
• about the same weight as/as heavy as
• balance/weigh

Judith Dancer is an author, consultant and trainer specialising in communication and language and mathematics. She is co-author, with Carole Skinner, of  Foundations of Mathematics – An active approach to number, shape and measures in the Early Years .

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Ten of our favourite early years problem-solving activities

A lot of the time when we hear the term ‘problem-solving’, our brain jumps back to the tricky maths teasers from our school days, and we immediately recoil a little. However, problem-solving is much more than number conundrums.   

Problem-solving is a key part of early years development and can support learning across many of the My First Five Years streams. The skill of problem-solving starts developing very early in a child's life and stems from the knowledge of the world that they are constantly building.[1]. For instance, your baby may cry when hungry as they know that crying gets the attention of an adult who can feed them.   

Problem-solving is a part of everyday life for children, from being a baby through to their future adulthood. When children learn how to solve problems, it can support them in building resilience, self-confidence and self-esteem. Taking part in problem-solving activities with others can also help children develop social skills, communication and relationships.[2]   

Psychologist Jean Piaget’s theory of cognitive development also focuses on the importance of problem-solving for early childhood development. In each developmental stage of his theory, the psychologist emphasised the importance of play-based learning for young children when it comes to problem-solving, and in turn building skills across the spectrum.[3]    

Supporting problem-solving  

When thinking about problem-solving activities for your child, it can be difficult to know where to begin.   

To keep children engaged, enabling them to take the lead and follow their interests, is key. Play-based, hands-on learning makes acquiring new skills more interesting and memorable for young children.[4]    

Many activities can support children when developing their problem-solving abilities – the possibilities are wide open. When considering which problem-solving activities are the most effective, it is also important to consider how they can be adapted to multiple interests, abilities and how accessible they are when it comes to using resources and materials.   

To help you out, here are ten of My First Five Years’ favourite problem-solving activities that you can try with your child.   

1) Den-building

Den-building is brilliant for problem-solving as it requires creative and critical-thinking, foresight, and planning. It is also a wonderful way to promote sustained shared thinking with your child. Sustained shared thinking is a way of working together that encourages individuals to evaluate the problem that they are working on and is focused on collaboration, using experiences and prior knowledge.[5]  

When building a den with your child, encourage your child to take the lead. You could provide materials such as boxes and blankets, or you could even ask your child to decide what materials you need before starting, encouraging them to plan out their work. Den-building can also be done both indoors and outdoors and with children from a young age. You may find that people have already started creating these in your local woodland that you can add to, adapt, or just enjoy!  

2) Cooking and baking

Cooking and baking are not only fun activities, but they also focus on mathematical problem-solving. To bring problem-solving into a cooking and baking activity, you can ask your child to count out simple measurements, for instance, cups of flour or sugar. Activities like cooking or baking are great for children to be able to take ownership of what is happening; encourage them to choose what you will make and allow them to do all the elements themselves.   

What’s great about cooking is it really doesn't matter how it turns out! Problems can arise often in cooking or baking, for example, the mixture may turn out too dry, you may be an ingredient short, or your cakes might not rise how you expected them to. If this is the case, talk to your child about what might have gone wrong and how you can rectify it next time! Then when they come to do it again, they can use their prior knowledge to help them.   

3) Playing with patterns

Patterns are a great activity for mathematical problem-solving. You can create patterns of any objects that you can find! For example, with pieces of fruit, pebbles from the garden, building blocks or even snacks! You could encourage your child to continue patterns, fill in the missing pieces or even create their own for you to solve problems with as they grow more confident. 

4) Sorting and categorising

Sorting and categorising objects is an activity that supports children in mathematical problem - solving and can be easily adapted to individual children’s abilities . You could encourage your child to sort by shape, size, colour, or better yet , their interests . For example, if they are a dinosaur enthusiast, they could classify them by wh ich is their favourite or least favourite , or order them by the size of their feet. They may even find enjoyment in helping you with daily sorting such as recycling or washing!  

Puzzles are a fun resource that can be used with children from a very young age. There are a wide variety of puzzles for children to access , such as chunky wooden puzzles or traditional shape sorters. When playing with puzzles, children will have to use their prior knowledge and experience of shape, space and measure whil e also experimenting with different angles and placements. They will use trial and error to find the best way to complete the puzzle and then will use this knowledge in future attempts.  

6) Ice rescue

As well as being a great problem-solving activity, ice rescue enables children to explore seasonal changes, temperatures and develop their fine and gross motor skills using tools. To play ice rescue, freeze toys inside ice overnight. This could be in cake moulds or small bowls. Use toys that will motivate your child, for instance, their favourite small figurines.   

Once frozen, place your blocks of ice in a big bowl or tray, and encourage your child to think about how they can get the items out. You could provide tools, or even get your child to find tools themselves.  

7) Obstacle courses

Obstacle courses are versatile and can be made with a wide variety of resources. When setting up an obstacle course for your child, try to include sections where your child will have to stop and think about how they will have to adapt their body to move through it , for example, something that they must climb over or under, or a section where they have to move differently. You could even include them in trying to create the obstacle course and allow them to make it the most challenging they can.  

8) Filling, emptying and investigation

Many children enjoy filling and emptying during play. Investigating this way helps children to get a sense of size, capacity and explore predicting and estimation. For instance, if your child likes playing with sand, you could ask them to guess how many scoops they will need to fill a container, or if they like water play you could challenge them to find a way to move the water between two containers as quickly as possible , or from one tray to another.  

9) Story problems

Stories are an effective way of introducing problem-solving and they can be a highly engaging way to promote creative and critical-thinking. You could use familiar or traditional stories to help scaffold play opportunities for your child. For example, you could try building a house for the three little pigs that cannot be knocked over. You could test out different methods using materials that you can find around your home.   

If you are feeling creative, you could also make up a little story using your child’s favourite toys. An example of this could be figuring out how to share food between their favourite teddies during a picnic and making sure that everyone gets enough.   

10) Playing with loose parts or open-ended resources

Natural materials such as leaves, conkers, sticks, acorns, and pinecones are all brilliant open-ended play opportunities (if supervised). You can also use household objects like bottle caps, curtain rings, tubes, tins, boxes, buttons etcetera in this sort of play. All it requires is a tray of different objects that you've collected and time to explore them. Your child will have to think creatively about how to utilise the objects and in doing so will be challenging their cognitive capacity by problem-solving to achieve the desired outcomes.   

References 

[1]  Rachel Keen. (2011). The Development of Problem Solving in Young Children: A Critical Cognitive Skill. Available: https://www.annualreviews.org/doi/full/10.1146/annurev.psych.031809.130730#_i22 .  

[2] Sheila Ebbutt. (2009). EYFS best practice - All about ... problem-solving . Available: https://www.nurseryworld.co.uk/features/article/eyfs-best-practice-all-about-problem-solving .  

[3] Piaget, J. (1983). Piaget's Theory. In P. Mussen (ed). Handbook of Child Psychology. 4th edition. Vol. 1. New York: Wiley.  

[4] Unicef. (2018). Learning Through Play. Available: https://www.unicef.org/sites/default/files/2018-12/UNICEF-Lego-Foundation-Learning-through-Play.pd .  

[5] Kathy Sylva, Edward Melhuish, Pam Sammons, Iram Siraj-Blatchford and Brenda Taggar. (2004). The Effective Provision of Pre-School Education (EPPE) Project: Findings from Pre-school to end of Key Stage1. Available: https://dera.ioe.ac.uk/8543/7/SSU-SF-2004-01.pdf .  

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Problem-solving in early maths: 3 simple teaching tips

E d has made an enclosure for dinosaurs using four wooden blocks. He wants to make sure the dinosaurs can’t escape.

“Interesting, I can see the dinosaurs are all locked inside the enclosure,” says Ed’s teacher, “but the tyrannosaurus rex is very tall. I think it would be able to climb out? Is there something you could do to stop him escaping?”

Ed fetches four more blocks and stacks them on top of his enclosure, making it taller.

“Good thinking, Ed,” says the teacher, “but we can still see his head, so it might need to be taller. There are no more long blocks for you to use. I wonder what you could use instead?”

“I think lots of these shorter ones might fit on the top,” says Ed.

• What would “phonics for maths” look like?
• Is this the “right” way to teach early maths?
• How to develop number sense

There are frequent opportunities for mathematical problem-solving throughout a typical day in an early years setting. But how can we ensure that we maximise their impact when they arise?

The Education Endowment Foundation’s Early Years Evidence Store identifies approaches that educators can use to support young children’s early maths learning and development, while providing a summary of the evidence behind each approach.

Created as part of the EEF’s work supporting the Department for Education’s Stronger Practice Hubs, the store has been co-developed by researchers and educators.

The newly published Early Mathematics theme recommends five approaches for supporting children’s maths development:

• Teaching the association between number and quantity.
• Promoting fluency with numbers and sequences.
• Teaching problem-solving skills for maths.
• Teaching and modelling how to make comparisons and connections.
• Facilitating mathematical language.

If we look at the third approach, teaching problem-solving skills for maths, this covers how we teach children to apply purposeful thinking, communicate their ideas and use manipulatives to solve problems.

Strategies for teaching early mathematical problem-solving skills

Evidence and experience tell us that explicitly teaching problem-solving skills can be effective when combined with other approaches, especially when matched to children’s level of development.

A multi-pronged approach is particularly important for children from lower-income families or those at greater risk of not meeting expected levels of development. Sequencing learning and breaking tasks down, as well as modelling problem-solving strategies, can also help to improve outcomes.

But what does that look like in practice?

1. Thinking aloud

In the example at the start of this article, Ed’s teacher models her mathematical thinking aloud, encouraging Ed to do the same. Deliberate modelling, meanwhile, provides opportunities for the teacher to suggest additional challenges for Ed’s play in manageable chunks.

2. Modelling using representations to solve a mathematical problem

Educators can encourage children to use representations in different contexts to scaffold understanding.

This could be through using drawings, fingers or objects, such as pinecones or cubes. For example:

Ben is playing with a friend in the mud kitchen. They plan to make “fir cakes” for the teddy bears they have set up on the picnic bench.

Their teacher asks them how many cakes they will make. Ben tells her, “Four, so there is one each.” Andrea encourages Ben to use his fingers to check this, as she points to each teddy.

The teacher counts aloud as Ben lifts each finger, stopping at five.

“I need five cakes then,” Ben says.

“Yes,” the teacher agrees, “you need one more cake, and then there is one for each teddy”.

3. Reminding

Educators can prompt children to remember and apply a previous strategy to solve a mathematical problem. For example:

During welcome time, the teacher asks the class how they can find out how many children are here today, using their self-registration board.

“We can count them,” says Amrita.

“Yes, you are right; we can count the children. Is there a way we can do it that helps us count them correctly?”

The children aren’t sure, so the teacher reminds them: “If we move the photos one by one into the basket as we count, it’ll make sure we only count each photo once.”

Amrita then moves the photos one at a time into the basket as the children count in chorus to work out how many children are at nursery today.

Lauren Grocott is an early years specialist for the Education Endowment Foundation (EEF)

For more examples of how to teach problem-solving, including narration and using mistakes as teaching and learning opportunities, visit the Early Maths theme of the Early Years Evidence Store

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10 fun maths activities and games for the EYFS

With Famly since

Maths in the early years is a crucial stepping stone for developing children, which is why it’s so important that the little ones can explore and experience it in an enjoyable way. We’ve carefully chosen some fun maths games and resources to promote early learning of numbers through play.

Want to see how it’s done? Click here to watch the video of our five favourite activities ⏯

1. Combine mathematical skills with fine-motor skills.

Number Hunt in Jelly by Hazeldene Family Centre

This fun maths activity:

First, spread out some plastic numbers in jelly layers. When it’s all set, give out some tongs to children and show them how to pick up the numbers from the wiggly substance ( and practice their fine motor skills along the way! ). This sensory play is a great way of sneaking in number recognition into some sensory play.

What you need:

• Plastic Numbers

2. How do you make maths activities fun? Add Lego!

DIY Lego Pattern Cards by A Crafty Living

This fun maths game:

Lego. Useful in so many different ways , including making mathematics exciting. Prepare some cards with colourful blocks on them and let children discover colour patterns and reproduce them with LEGO bricks. Consider leaving the colouring part to your little learners so they can form their own patterns and include some EAD in the mix too. It's a win-win!

• Paper Cards
• Coloured Pencils
• LEGO Blocks

3. Challenge the children's maths skills to solve a missing number mystery

Missing Number Math Activity by Planning Playtime

This Early Years maths game:

Write number sequences on craft sticks and remember to leave some blanks in between. Next, you write the missing numbers on some clothes pins and give them out to the players. Now the children use their fine-motor skills and clip the pins on sticks and complete the sequence. The best thing about this fun and inexpensive maths game is that you only create the props once and they’re ready to be used as many times as you like.

• Craft Sticks (colour or plain)
• Clothes Pins

4. A simple game of swat the number.

Smack the Number Counting Game by Fun Learning for Kids

Prepare some sticky notes with various numbers and place them in front of the children armed with fly swatters. Roll the dice to get your target number. The goal of this simple yet fun game is for the little ones to identify the number on the dice and match it with the ones written on sticky notes by smacking the correct answer with a fly swatter!

• One or two dice
• Fly swatter
• Sticky notes

5. Playing with pom-poms to promote problem-solving skills

Straw and Pom Poms Counting Game by Nurture Store

Label small containers with some numbers that you’d like your learners to practice and prepare some straws and pom poms. For this fun maths activity, the kids simply put the straw on a pom-pom and suck in, to try and pick it up. Then they drop it over the containers until they’ve got the right number in each one.

• Shallow containers
• Labelled stickers (or any paper, glue and marker)

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6. A fun maths game to drive you dotty!

Number Dots and Easy Touch And Count Activity by Busy Toddler

Tape some paper to the wall and write several numbers, each decorated with dots, to match the quantity the number represents e.g. 4 dots on the number 4. Now, the players can touch each dot with a marker and see the number and the quantity altogether! You can also put the paper on the floor but holding a marker up and out makes this not only a fun game for early years maths but also a good way to strengthen those little arm muscles.

7. A magnetic, mathematical, magical fishing game

Magnetic fishing number game by Messy Little Monster

This Early Years maths activity:

First, you or the children need to cut your paper into fish shapes and add a paperclip. Next, write the numbers on the fish using a pen. For the fishing rod, tie some string (with a magnet on the end) to your stick! Now the whole class can 'fish' for numbers!

• Card/ Paper (or old pieces of artwork) to cut into fish shapes
• Paper clips
• Magnets, preferably some too large to be swallowed.
• Stick or long piece of wood

N.B. Always supervise children very carefully with magnets.

8. Fun maths activities are eggs-actly what we're looking for!

Egg Cracking Counting Activity by Modern Preschool

Looking to 'hatch' a plan for some fun maths games? Create ‘eggs’ by cutting out oval shapes from cardboard and writing different numbers on them. Students identify the numbers and 'crack the eggs' by punching the corresponding number of holes in them - you could always make one first, as an example. This exercise can also help develop muscles in those minute hands.

9. More fun in maths? Make it musical!

Top 10 Counting Songs by Super Simple Songs – Kids Songs

According to the BBC “When children are singing they are taking in information and training the brain but they don’t think they are, they think they are just having fun. Singing is an aerobic activity that boosts oxygenation in the bloodstream, increasing mental alertness”. We agree! Check out these 10 lovely songs to give it a go.

• A way to play music
• Your voice!

10. Matching with maths - a classic game with a mathematical twist.

Valentine Math Activity – Broken Heart Numbers by Fun a Day

Sometimes the most fun games are the classics. A simple matching game for one player, two players, or the whole classroom! Simply cut out some hearts and cut each in half using different zigzags, squiggles and other connecting shapes. Then write a number on one side and draw a corresponding number of hearts on the other. Well done, you’ve just created puzzles! Challenge the children to see who can find the matching hearts card to their number cards.

• Paper or card

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Please note: here at Famly we love sharing creative activities for you to try with the children at your setting, but you know them best. Take the time to consider adaptions you might need to make so these activities are accessible and developmentally appropriate for the children you work with. Just as you ordinarily would, conduct risk assessments for your children and your setting before undertaking new activities, and ensure you and your staff are following your own health and safety guidelines.

Matt Arnerich

Matt Arnerich is Famly's Director of Brand & Comms. He looks after the story of what makes Famly different, helping us to get closer to our mission.

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Marcus Fogg

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The EYFS Activity Library: 50 EYFS Activities

August 18, 2023

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Education is an admirable thing, but it is well to remember from time to time that nothing that is worth knowing can be taught. -Oscar Wilde

Outdoor Maths Activities EYFS – Outdoor Maths Ideas

The following are some of my favourite outdoor maths ideas & activities for EYFS (Early Years – Children aged approximately 2-5). For outdoor maths activity ideas for older children, you may want to see my post,  Outdoor Maths Activities KS1 . 

Young children need to be able to manipulate and use hands-on materials to explore mathematical thinking. Using manipulatives and representing mathematical ideas in many different ways allows children to develop a deeper understanding and to make connections between different areas of maths. Children need to be able to use objects to help them with counting and with the representation of numbers. This will help them begin to solve simple arithmetic problems so that they can develop strong mathematical skills (Anghileri, 2006).  

Children will gain a deeper understanding of mathematical concepts and how different areas interrelate if they are given hands-on opportunities to explore (Carruthers & Worthington, 2004). In the long-term, this will help them develop confidence in maths, as well as allow them to apply their learning to problem solve. These outdoor maths activities for EYFS will help make connections and reinforce classroom learning.

Outdoor Maths Activities & Ideas EYFS

I have grouped theses outdoor maths activities & ideas based on different areas of learning for EYFS (Early Years Foundation Stage).  They are primarily for children ages 2-5, but they can be adapted for older children as well.

*Please note that this post contains affiliate links to help with the running cost of this website. Thank you for your support so that we can keep writing!

Number & Place Value (including counting)

Cardinality.

• Counting natural objects  –counting out how many you have in total and matching the total to a numeral (you may use numicon to help scaffold counting).

• Nature hunt – Children can search for a set number of different natural objects. Ex. Children might search for 5 pinecones, 4 sticks, 3 stones, 2 leaves and 1 feather. 
• Number hunt  – children can search for numerals, groups of objects, and/or dice or other value representations of numbers hidden outside. They can then match different representations of the same number together (and even order them).

• Tens frame – Children can use an outdoor ten frame to count objects (and begin to subitise). They can place the same number on the frame in different ways (and recount). Doing this will help them see that 5, for example, may look different but still be 5. How many do you have? What if you place them like this- how many are there now? How do you know?
• Stone stacking  – Children can make stone towers and count the total. It is also an excellent way for children to explore balance and centre of gravity.

• Games – Children can play games such as ‘What’s the time Mr Wolf’ to practice counting steps.
• Counting in play – Adults can encourage children to count as they play and explore. For example, How many steps does it take to cross a bridge? Can you count how many hops it takes to get from one point to another? How many steps to the top? Etc. Alternatively, you could roll large dice and children can count/do that many claps, hops, etc. 
• Transient art & counting – Get children to create a picture using 5 or 10 objects. They can do this individually, or they can work collaboratively.

• Mathematical language – Find ways to use mathematical language with children as you are out and about- e.g. how many bowls are in the mud kitchen? How many tomato plants are growing? Can you count how many flowers/peapods/squash/tomatoes, etc. are growing? Are there lots/few/5 trees in the woods? How do you know? How can you check?
• Counting songs – Children can sing counting songs (ex. 5 little ducks , 5 little speckled frogs , etc.) and use props to help them count and act it out.

• Ordering numbers – Children can use  number rocks  or number logs to practice ordering numbers. They may even go on to practice counting in 2’s (skip counting). What comes first? Which number is larger? How do you know? 
• Number games – Children can play number games with rocks – ex.  Swapping numbers  or  missing number games .

• Free play with numbers – Allow children to play with  number rocks  or stump numbers in their play. This can lead to finding creative ways to use numbers.
• Hopscotch – Children can use or even help make a hopscotch board. They can practice counting and identifying numbers as they play.
• Nature number line – Hang rope between trees (or along a fence if you are concerned about children running into the rope) and provide pegs. Children can hang up and order numbers to make a number line. They might collect things like leaves to pin up on the line to correspond with the value. What number comes next? How do you know? What is one more than…?

• Minibeast hunt – Children can go on a minibeast hunt counting and keeping track of what they find with tally marks or tally chart. You may want to discuss why tally marks work well for this (rather than writing down numbers). You could come together as a large group at the end and create a pictograph using their findings. How many ladybirds have you found?  

Identifying & writing numbers

• Numbers on the ground – Children can play a game of calling out numbers and having to run to stand on that chalk number. To challenge them, you could have them hold up the corresponding value on their fingers. Where is number 4? Can you show me 4 on your fingers?

• Numbered cars and parking spaces – Children can play with cars labelled with numbers and park them in ‘parking spaces’ with a corresponding number, dice value or tally marks.
• Numbers & bikes – In a school with several bikes, cars, etc. for children to ride, they can be labelled with numbers and parked in ‘parking spaces’ with a corresponding number, dice, tally marks or other values. Children can take turns on the bikes, signing their names on a list corresponding with the number of the vehicle, and then using a sand timer to take turns.
• Writing numbers – Children may write numbers in the sand or the dirt with sticks or their fingers. They could  write numbers on the pavement with chalk or with paintbrushes using water or trace over numbers written in chalk with water paintbrushes. They could also use sticks, stones or other natural objects to create numerals.

Arithmetic 

• One more or one less – If you have a group of objects (e.g. 3 stones) help children find one more or one less of the number by adding in one more or taking one away (and then recounting the pile).
• Number line – Children can write out or make a number line to 10 (or hopscotch) and find one more or one less by counting forwards or backwards. It may help children to count objects to go with each number.

• Skittles or bowling – Children can play games such as skittles or bowling. They can identify numbers on the games, count the number of skittles or targets that are hit, add up points, take away how many objects have been knocked over, and see how many are left. There are lots of opportunities for counting, adding and subtracting with these types of garden games.

• Target games – Targets can be put up (or drawn) on walls, or hula hoops hung up on a line. Children can throw balls, beanbags , ‘ rockets ’, etc. to hit the target or throw through the hoop to score. Alternatively, hula hoops or buckets can be placed on the ground and balls or beanbags can be thrown in to score points.
• Counting crops from the garden – As children pick tomatoes or other fruits or vegetables from the garden, get them to count how many they picked from each plant. Then how many have they picked altogether?

• Sharing crops from the garden – Share (pass out) fruit or vegetables grown in the garden. Discuss ways of making it fair. Can children figure out when it is the same value?
• Tic Tac Toe with sticks – This is a simple strategy game that children can play. They can then go on to play more complex strategy games such as Nim.

Geometry (Shape Space and Measure)

• Shape hunt – Children can go on 2D shape hunts outside. What shape is it? How do you know?
• Shapes made out of sticks, rocks, etc . – Children can copy over ones drawn in chalk or create their own freehand.

• Construction – Children can use large blocks, planks of wood and other construction materials to create large 3D shapes and spaces. What have you created? Tell me about it.
• String shapes – They can use loops of string or large bands to make shapes. They can do this in partners/groups and see how manipulating it changes the way the shape looks or perhaps turn it into a different shape. How can you make a triangle, square, rectangle, etc.? Can you show me different ways to make a triangle?

• Transient art – Children can make symmetrical pictures or  mandalas with natural objects .

• Exploring symmetry – They may explore symmetry in nature, perhaps using a mirror to help and even make their own creations (see mandalas above). What do you notice about your picture? If you place this here, is it still symmetrical? Why or why not?
• Nature patterns – Children can also make patterns with natural objects, such as repeating patterns. What comes next? How do you know?
• Dam building / Den building  – Children can use materials such as sticks and rocks to build a fort/den, or to block off or dam a stream. This is an excellent opportunity for children to practice estimating length and using spatial rotation to help them construct.
• Trails and obstacle courses – Children can follow trails or make obstacle courses with logs, sticks, stumps, planks, etc. (Supports the use of vocabulary – over, under, through, around, next to, etc. They can use directional language to help each other get through it. )

• Sorting and ordering – Children can sort /  order (gradient) natural objects  (e.g. leaves, rocks) by a specific feature (ex. shape, size, colour, or other features).
• Music Wall – children and can explore making sounds and patterns with an outdoor music wall.
• Ordering objects by length  – Children usually find it easy to compare two objects but may need more practice when comparing 3 or more objects. I have a post –  ordering sticks by length , which reviews common misconceptions and ways to help children to learn this.

• Measuring with non-standard units – Children can practice measuring objects with non-standard units (e.g. how many stones long is the stick). This activity is the next step after comparing lengths, but before measuring with standard units such as cm or inches.

• Daily routines – Adults can talk to children about what we do at different times of the day to help them notice the changes in the sun at various points in the day. What do you do at the beginning of the day? At the end?
• Mud Kitchen – Children can practice comparing and measuring liquids, solids, etc. using weight, volume, capacity, etc. Adults can introduce vocabulary such as full, half-full, empty, half-empty, nearly full, etc. Which bowl is largest? Which holds the most? How do you know? Can you fill the cup? Can you make it half-full?

• Sand play and water play – Similar to using a mud kitchen, children can use different size containers in a water table or sandpit to fill and empty containers (including pouring through sieves). It provides opportunities to compare volume and the capacity of different containers. Which container holds the most liquid? How can you find out?
• Potions – Children can make up or follow potion recipes. They can follow instructions to measure (with standard or non-standard units) and combine ‘ingredients.’ They might also compare relative measurements such as full, half-full, empty, etc.

• Weighing scales – Children can use balance scales to compare the weights of different objects. How many nuts are equal to the weight of your stick?
• Ramps – Children can race cars, balls etc. down ramps that can be adjusted at different heights and angles to see how changing the slopes changes the speed and distance they go. Lines with numbers (like a non-standard measure) can also be written along the ground to see how far the cars or balls can go. Children might compare different balls or cars – Which went the furthest? How do you know? Can you try anything else?
• Snail races – See how far a snail can go in one minute. Children can help you think of the best ways to measure the snail’s movement. This activity is also a way for children to help count 1 minute and get an idea of how long 1 minute is.

I hope that you find this list of outdoor maths activities & ideas for EYFS helpful. I have also compiled a list of some of my favourite outdoor maths activities & ideas for KS1 , which you may want to explore for some more challenging ideas.

References – Outdoor Maths Activities EYFS & Outdoor Maths Ideas

Carruthers, E. and Worthington, M. (2004).  ‘Young children exploring early calculation’.  Mathematics Teaching , (187), 30-34.

Anghileri, J. (2006).  Teaching number sense , (Ch. 4, pp. 49-70).  London: Continuum.

Arithmetic , Data, Patterns & Sorting , Gardening , Geometry , Maths , Measurement , Natural , Number & Place Value , Preschooler , Rocks , Sticks , toddler

Learning Outdoors , learning outside , Leaves , Mud , numerals , numicon , Nuts , Pinecones , Rocks , Sand , Sticks , Water

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• Maths: Open-ended Investigations
• Mathematical Problem-solving

Reception Maths: Open-ended Investigations Mathematical Problem-solving

Problem-solving tasks develop mathematical skills and problem-solving tactics. These open-ended investigations for Reception or Early Years settings are designed to take advantage of outdoor learning environments, but many of them can be adapted to run inside.

Session 1 Shape

Open-ended investigative tasks provide fun, stimulating contexts in which children can connect previous knowledge with new situations, develop mental flexibility, practise mathematical vocabulary and reason mathematically.

Print the sheets and stick them up in suitable play areas. They provide stimulating questions that will enable adults in your classroom to facilitate good mathematical language and learning. Each illustrated activity comes with a list of skills practised that you can use for assessment.

Open-Ended Task

Shape Hunt By looking for and finding shapes, children gain an awareness of similarities of shapes in the environment. They match shapes by recognising similarities and orientation, show curiosity and observation by talking about shapes and begin to use mathematical names for shapes.

More Shapes By looking for and finding shapes formed by windows, children gain an awareness of shapes, practise matching them, and begin to use mathematical names for them. Use language such as ‘square’ to describe the shape of solids and flat shapes.

• More Shapes

Sorting While playing with and arranging twigs, stones, leaves, etc., children can be encouraged to take an interest in shape and space. They can talk about similarity and difference, while sorting objects. Developing mathematical ideas and methods can be used to solve practical problems.

Session 2 Position and Direction

Trails Remember… just about anything you do indoors in maths can be done outside. Some children ‘come alive’ once out of the classroom and may just surprise you with the observations they make or the learning behaviours they show.

Scooters, Bikes, Trikes Riding a scooter, bike or trike prompts counting, consideration of same and different, and position and spatial properties.

• Scooters, Bikes, Trikes
• The Mathematical Journey

Obstacle course Children use everyday language to talk about position, distance and time when running, or walking, an obstacle course. They compare quantities and objects and solve problems.

• Obstacle Course

Milk the Maths: Wellies Encourage children to use everyday language to talk about position whatever they are doing! Putting wellies away is a colourful opportunity.

• Milk the Maths

Session 3 Number and Shape

Holes When digging holes children can use number names in order in familiar contexts. They can use everyday language to talk about size, capacity, position, distance and time. Holes offer fun opportunities to compare quantities and objects and to solve problems.

The Mud Kitchen Ask children questions about shape, space and measure while exploring mud. Consider similarities and differences.

• Mud Kitchen

Planting and Gardening While working in a school garden, children can practise using numbers to identify how many objects there are in a set. They say and use number names in order in familiar contexts, and count everyday objects.

• Planting and Gardening

Hoist Playing with a bucket on a hoist, children can use numbers to identify how many objects there are in a set. They can use everyday language to talk about size, capacity, position, distance and time and compare quantities and objects and to solve problems.

Session 4 Number and the Language of Addition/Subtraction

Leaves When playing with leaves, children have opportunities to see that numbers identify how many objects there are in a set and to say and use number names in order in familiar contexts. They can begin to use the vocabulary involved in adding and subtracting. They can relate addition to combining two and subtraction to ‘taking away’.

Tin Can Alley Play with cans to explore number names in familiar contexts and to.count up to 10 everyday objects. Children can begin to use the vocabulary involved in adding and subtracting and to relate addition to combining two groups of objects and subtraction to ‘taking away’.

• Tin Can Alley

Sand to Sandpit Children can fill a sandpit (or move sand from one place to another) and count up to 10 everyday objects and begin to use the vocabulary involved in adding and subtracting.

• Sand to Sandpit

Logs Put logs onto a trolley and say and use number names in order in familiar contexts. Count and use vocabulary involved in adding and subtracting. Show curiosity and observation by talking about shapes. Begin to use mathematical names for shapes.

More Logs Playing with logs offers countless opportunities to practise counting! Children can also begin to use the vocabulary involved in adding and subtracting and to relate addition to combining two groups of objects and subtraction to ‘taking away’.

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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'.

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.

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.

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Early Years Careers

How to promote problem solving in the early years

5th November 2015 by Kelly Leave a Comment

Ways to incorporate problem solving in the Early Years

Developing problem solving skills is an area of development early years ’ practitioners are familiar with, and the importance of developing these problem solving skills is well known, but what exactly are problem solving skills? And how do we encourage children to develop these?

Within the Early Years Foundation Stage, problem solving comes under the category Mathematical Development, however this does not limit problem solving to just mathematical circumstances! There are opportunities for children in early years to explore problem solving every day, within all aspects of their development. Children are natural problem solvers from birth, all the way from learning to communicate problems through crying, through learning to talk and learning to walk. They develop a natural problem solving process through trial and error, for example, an infant will fall down many times before taking their first steps, but it’s the process of getting back up and trying again which helps them to achieve their goal.

Although problem solving can occur naturally, practitioners should still encourage children to recognise the process of problem solving and become familiar with it.

Shape sorters are a great activity for younger children to explore problem solving through trial and error. The children can get a feel of the shapes and see the holes, but will not yet have the knowledge of shapes to place the correct shape in the correct hole, they will attempt to fit shapes into holes, and when they realise it will not fit, they move onto the next hole. As the children get older, they can apply their knowledge and learning to this activity, understanding that the square shape will fit with the square hole, thus overcoming a problem. Jigsaws are another effective way of children developing problem solving skills in the early years. With younger children larger puzzle pieces can be used made out of tactile materials and they can attempt to solve the jigsaw through trial and error again. Slightly older children can expand onto smaller puzzle pieces, once they have mastered more simple jigsaws. Practitioners should take note of the different strategies children use in order to fit different puzzle pieces together and offer directional help such as matching the colours of pieces together should a child become frustrated.

Early Years practitioners can help children apply problem solving skills to real life situations as well as various activities. For example, practitioners can encourage children to help set up at meal times, but pose them with a problem of not having enough cutlery for each child. Children could be able to recognise this problem, or be guided by the practitioners to realise that not enough cutlery could pose a problem. Practitioners can then encourage and support the children to think of a solution to this problem. Allow children to use their imagination to solve problems, the sky is the limit! If they suggest sharing cutlery or even crafting their own cutlery out of different items, then this is all part of the problem solving process! They are recognising a problem and attempting a solution.

Overall, there are many activities and real life scenarios practitioners can implement in order to help children explore problem solving skills and guide them to create a solution. Using numbers and mathematics are not the only methods of developing problem solving skills as seen from above, but they can be an effective way to develop learning numeracy skills which can help in later life.

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

Sheila Ebbutt, a freelance consultant and was formerly managing director of BEAM (Be A Mathematician) Tuesday, July 7, 2009

Responding to challenges and finding solutions is not confined to mathematics but arises in all areas of learning, says Sheila Ebbutt.

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'.

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.

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.

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The MacArthur Foundation wants bold solutions to big problems — the prize is $100M

Elizabeth Blair

In 2017, Sesame Workshop and the International Rescue Committee became the first winners of 100&Change for their work with children in the Middle East . Above, Elmo learns how to fly a kite at Azraq Camp, Jordan. Ryan Donnell/Sesame Workshop hide caption

In 2017, Sesame Workshop and the International Rescue Committee became the first winners of 100&Change for their work with children in the Middle East . Above, Elmo learns how to fly a kite at Azraq Camp, Jordan.

Any major challenge, in any field, anywhere in the world.

That's what the MacArthur Foundation is looking to solve with its third round of 100&Change, a $100 million grant competition for proposals that tackle, it says, "one of the world's most critical social challenges."

Chris Cardona, managing director of Discovery, Exploration, and Programs at the foundation, said MacArthur hasn't identified specific challenges it hopes grants will address. "It continues to be a global, athematic competition," he said.

The MacArthur Foundation is soliciting bold ideas to solve one of the world's biggest problems. The winning proposal will receive $100 million. MacArthur Foundation hide caption

Instead, the MacArthur Foundation, which also supports NPR, is looking for feasible, evidence-based proposals that provide a solution with deep impact and that have a clear explanation for how they will measure success.

Community Solutions received $100M from the MacArthur Foundation "to accelerate an end to homelessness in 75 communities." Erica Holmes interacting with Community Solutions' client Andrew Overby. Community Solutions hide caption

The first two winners were a collaboration between Sesame Workshop and the International Rescue Committee for their work helping children affected by conflict and crisis in the Middle East, and Community Solutions for a program aiming to end homelessness in 75 U.S. communities within five years.

The finalists for the 100&Change competition will be announced in the spring of 2025.

This story was edited by Jennifer Vanasco.

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The CEO behind the world's biggest science and engineering fair says the biggest mistake parents make is putting too much pressure on their kids

• The Regeneron ISEF is a huge science fair that attracts top talent from all over the world.
• This year, the competition awarded $9 million in prizes. It has a history of prestigious winners.
• That can make for a stressful competition, but parents shouldn't add to it, CEO Maya Ajmera said.

What's been called the "granddaddy" of science fairs took place last week.

With over $9 million in prizes and heaps of prestige, the Regeneron International Science and Engineering Fair (ISEF) attracts some of the best and brightest students from around the world, like Hawaii and California as well as Kildare, Ireland and Shanghai, China.

Past winners include Nobel Prize recipients , Rhodes Scholars, and MacArthur Foundation genius grant awardees.

With that kind of money and acclaim on the line, it's not surprising that the atmosphere surrounding the competition is intense .

"I think a lot of kids who are here actually — I don't think I'm reading it wrong — are truly excited to be here," said Maya Ajmera, the president and CEO of the Society for Science, which coordinates ISEF. "But they also feel the pressure of wanting to win and the pressure of going to college," she told Business Insider last week.

The biggest mistake that parents with ambitious, curious kids can make is adding to that pressure, she said.

Besides, between addictive social media , the climate crisis, growing up during the pandemic, and feeling lonelier than ever , Gen Z already has more than enough sources of anxiety .

Stepping back and letting the kids do the work

While it can be useful to have a parent invested in helping their kid meet deadlines and make a nice-looking poster, some adults take it too far. Ajmera advises parents to "stand back and let your kid do it."

"Get out of their way," she said, "and don't pressure them too much."

If competing at ISEF is any indication of success, then Ajmera's advice certainly seems to work. Parents of ISEF competitors who spoke with Business Insider shared her philosophy.

"We never pressure them," Maria Estrada, whose two children have both competed and won awards at ISEF, told Business Insider. Estrada said she's never expected her children to have 5.0 GPAs, and that she's even asked her daughter to slow down and be a kid.

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"I accepted my kids for who they are," she added. "I think it's important for parents to know their kids' abilities."

Another parent, Alexa Groff, has a daughter, Taylor, who competes in science fairs and is a competitive dancer. She said that a friend recently told her she'd expected Groff to be an intense "dance mom" who showed up early to everything.

In reality, the friend told her she was "super-duper chill."

"I think it's important for Taylor to explore her passions without my hand in it," Groff said. When her daughter wanted to quit volleyball, for example, she said she let it happen and supported the decision."I want her to figure things out on her own, but know that I'm there for whatever she needs me for," Groff said.

Combining passion and hard work to solve problems

As part of the ISEF competition, nearly 2,000 students from 49 states and 70 countries gathered in Los Angeles to showcase their research to judges. ISEF pulls the finalists from 400 smaller science fairs from around the world, taking the winners from a pool of 175,000 competitors.

While not typically at the same level as peer-reviewed scientific research, ISEF students' topics can be as sophisticated as microbial genetics, bone tumors, and microplastic filtration.

Far from overly involving themselves, parents are often surprised at what their children accomplish with their projects. "They're kind of amazed, actually," Ajmera said.

Students are often inspired to pursue these difficult subjects because of real-world issues and not by their parents' insistence to compete, Ajmera said.

"A lot of kids have their own personal stories to share of something that's affected their families or their communities, and they want to go in and solve it," Ajmera said of the Gen Z competitors.

For example, 18-year-old Maddux Alexander Springer received this year's $10,000 Peggy Scripps Award for Science Communication for his studies on a tumor-causing disease in green sea turtles near his home in Hawaii.

That kind of interest and enthusiasm can carry a student far, which is important since most winning projects are often complex and time-consuming.

For example, 16-year-old Grace Sun won this year's top prize , the $75,000 George D. Yancopoulos Innovator Award, for her project on organic electronic devices. Sun told Business Insider she had to miss hours of school to work in a university lab for her project.

For some kids, though, it's all worth it because the time and effort are investments in what they hope will be their future careers.

"A lot of these kids are going to either land in academia doing research, or they're going to be entrepreneurs and start new companies on the new cutting-edge technologies," Ajmera said.

Watch: How Sesame Street stays relevant to every generation, according to the brand's marketing head

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