early years problem solving

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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Home > Learning & Development

Learning and Development

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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Early Years Guide

Introduction.

The first few years of a child’s life are especially important for mathematics development . For many education experts, no other group represents a greater opportunity to improve mathematical standards than children in the early years.

The more grounded in mathematical concepts young children become, the better their later outcomes. Conversely, research shows that children who start behind in mathematics tend to stay behind throughout their educational journey.

On this page, we’ll examine:

• What do we mean by Early Years?
• What does learning look like in the Early Years?
• Why is Cognitive Load Theory so important?
• What mastery strategies are available for Early Years?

What do we mean when we talk about Early Years?

The UK government published the Statutory Framework for the early years foundation stage in March 2017. It sets standards for the learning, development and care of children from birth to five years old.

Areas of learning

The EYFS framework outlines seven areas of learning :

• Communication and language
• Physical development
• Personal, social and emotional development
• Mathematics
• Understanding the world
• Expressive art and design

Mathematics in EYFS

In the context of mathematics, the framework says children must be given opportunities to develop their skills in the following areas:

• Understanding and using numbers
• Calculating simple addition and subtraction problems
• Describing shapes, spaces, and measure

Revised guidance

The DfE published revised guidance in March 2021 to take effect in September 2021.

The mathematics component now incorporates many elements of the mastery approach.

Specifically, the revised framework says:

Children should be able to count confidently, develop a deep understanding of the numbers to 10, the relationships between them and the patterns within those numbers.

By providing frequent and varied opportunities to build and apply this understanding — such as using manipulatives, including small pebbles and tens frames for organising counting — children will develop a secure base of knowledge and vocabulary from which mastery of mathematics is built.

In addition, it is important that the curriculum includes rich opportunities for children to develop their spatial reasoning skills across all areas of mathematics including shape, space and measures.

It is important that children develop positive attitudes and interests in mathematics, look for patterns and relationships, spot connections, ‘have a go’, talk to adults and peers about what they notice and not be afraid to make mistakes.

Early Learning Goals

The latest framework has the following early learning goals for mathematics:

Children at the expected level of development will:

• Have a deep understanding of number to 10, including the composition of each number
• Subitise (recognise quantities without counting) up to five
• Automatically recall (without reference to rhymes, counting or other aids) number bonds up to five (including subtraction facts) and some number bonds to 10, including double facts

Numerical patterns

• Verbally count beyond 20, recognising the pattern of the counting system
• Compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or the same as the other quantity
• Explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally

Reception class is the first year at primary school in England, generally for children ages four to five. Unlike every other school year, it’s not compulsory for children to attend Reception, though it’s a good way to introduce them to life at school.

Multi-academy trusts

Looking for impactful maths provision across your multi-academy trust?

Learning in the early years

The first few years of a child’s life are especially important for mathematics development , says the National Center for Excellence in the Teaching of Mathematics.

Research shows that early mathematical knowledge predicts later reading ability and general education and social progress.

As young as eight months old, children are developing an awareness of number names , and include these in their speech, as soon as they begin to talk. As children listen to the talk around them, they are introduced to numbers through opportunities that occur in everyday life, and experience a variety of number rhymes. This supports their growing knowledge of number names.

According to the NCETM, there are:

Six key areas of mathematical learning

Cardinality and counting, composition.

• Shape and Space

Looking briefly at each in turn:

When children understand the cardinality of numbers , they know what the numbers mean in terms of knowing how many things they refer to.

Comparing numbers involves knowing which numbers are worth more or less than each other.

Learning to ‘see’ a whole number and its parts at the same time is a key development in children’s number understanding.

Developing an awareness of pattern helps young children to notice and understand mathematical relationships.

Shape and space

Mathematically, the areas of shape and space are about developing visualising skills and understanding relationships, such as the effects of movement and combining shapes

Measuring in mathematics is based on the idea of using numbers of units in order to compare attributes , such as length or capacity.

Learning to count in the early years is a fundamental skill and key to mastering mathematical concepts in the future, but there’s more to it than you might think, says Sabrina Pinnock, a primary school teacher in Yorkshire.

According to researchers Rochel Gelman and C.R. Gallistel, these are the steps needed to successfully count :

• The one-to-one principle: children must name each object they count and understand there are two groups: the one that has been counted and the one that hasn’t yet been counted
• The stable order principle: children must know how to count in the right order
• The cardinal principle: children need to understand the last number in the set is the total amount
• Counting anything: children need to realise that anything can be counted, not just objects that can be touched, but also things like claps and jumps
• Order of counting doesn’t matter: children need to understand that the order of counting in the set is irrelevant and will still lead to the same amount

Assessing children to find out which step they are struggling with is key to helping them overcome difficulties and become confident counters.

How do children develop counting skills?

Very young children start to count spontaneously and later begin to refine their skills by pointing their finger at the objects they are counting.

They will often try to get all the names of the numbers they know into their count as they pass their finger along the objects. They also reuse numbers. If they have not finished and they have used up all their known numbers, they will begin using the same numbers again. For example, a child might decide to count eight shells she collects at the beach. She might line them up carefully, tag numbers to them by pointing as she slides her finger along the shells, quickly counting out loud, “one, two, three, four, five, one, two, three, four, five, one, two, three.”

In their drive to make meaning, children are eager to experiment as they acquire new small bits of mathematical knowledge. It is extremely important to respect their developing understanding and not expect “perfect” counting sequences.

By valuing children’s partial understanding, children will develop enthusiasm for numbers and become confident mathematicians.

Activities to boost number sense in Reception Year

Children need lots of opportunities to develop number sense and deepen their conceptual understanding. Here are some simple activities to get your Reception Year learners counting:

Crowd control

Display the number of children allowed in each area using pictorial representations of cubes on a 10 frame. Once the children begin to realise how many are allowed in the area, they start to discuss the meaning of more and less. For example, “no more children are allowed in,” or “you can come in because one more than three is four.”

Encourage children to show numbers using their fingers above their head. “Bunny ears six” means they place their fingers above their head to show six. They may decide to use three fingers on each hand. As they become more confident, you could introduce swapping, where they show the same number but with a different configuration of fingers, in this case two and four, or five and one.

Grouping straws

Each morning, drop different amounts of art straws all over the carpet. Say something like, “oh no class, I can’t believe it. I’ve dropped all my straws again. They were all in 10s. Can you help me?” This activity helps children consolidate counting objects and gets them to think about stopping after they have made 10. Providing elastic bands helps them to keep track of their groups of 10.

Fastest 10 frames

This game can help distinguish between those who have developed a good understanding of number sense and those who need further support. Give each child their own frame and cubes. Tell them a number and observe how they place the cubes on the frame. If the children are working with the number eight, do they say each number name as they place the cube on the frame, or do they realise eight is two less than 10? If so, they should be able to place the cubes down faster than other children.

What do they do when you say the next number? For example, for the number five, do they automatically remove three cubes, or do they remove all of the cubes and start over counting from one to five?

Everyday questions to develop number sense

These questions for children aged five to six help develop their number sense and let them practice using mathematical terms.

When prepping lunch or a snack, count out the different types of food with your child, and as you lay the table, count out the different items. Ask your child questions like:

• How many grapes are there?
• How many tomatoes are there?
• How many plates are there?

Practice using the terms more than, fewer than and as many as by asking:

• Are there more grapes than tomatoes?
• Are there fewer tomatoes than grapes?
• Are there as many plates as people eating?

Remember to practice each sentence:

• There are more grapes than tomatoes
• There are fewer tomatoes than grapes
• There are as many plates as family members eating

When counting, make sure that you count one number for one item to strengthen your child’s sense of one-to-one correspondence.

Number Rhymes

Carefully select number rhymes to include those that children are familiar with from home. Make sure the rhymes include:

• Counting back and counting forward
• “No” or “none” (Five little ducks went swimming one day)
• Counting in pairs (two, four, six, eight, Mary at the cottage gate)
• Counting to five, 10 and beyond

Problem solving, reasoning and numeracy

The EYFS requires children to be supported in developing their understanding of problem solving, reasoning and numeracy in a broad range of contexts in which they can explore, enjoy, learn, practise and talk about their developing understanding. They must be provided with opportunities to practise these skills and gain confidence.

Young children learn best through play. For their learning to be effective, they need sensitive and informed support from adults.

All children can be successful with mathematics, provided they have opportunities to explore ideas in ways that make personal sense to them and opportunities to develop concepts and understanding. Children need to know that practitioners are interested in their thinking and respect their ideas.

Foundations

Maths — No Problem! Foundations is designed with all the theory and rigor that underpins a true mastery approach. It meets all the requirements of the national curriculum’s Early Years Foundation Stage. But Maths — No Problem! Foundations doesn’t shy away from embedding learning through play in Reception.

Genuine learning through play in the early years is something the team at Maths — No Problem! gets very excited about. What may appear to be simple games are actually carefully designed activities that have a deep maths mastery focus.

Maths — No Problem! Foundations is a complete Reception programme that includes Workbook Journals, Picture Books, and online Teacher Guides with printable resource sheets, all in one package.

The Maths — No Problem! suite of products — including textbooks, workbooks, a revolutionary online assessment tool, world-class teacher training, and much more — is based on the Singapore method, which combines 30 years of international research with painstaking craftsmanship and constant refinement.

Mark making

Research from Carruthers and Worthington into children’s mathematical graphics reveals young children use their own marks and representations to explore and communicate their mathematical thinking. These graphics include:

• Scribble-marks
• Tally-type marks
• Invented and standard symbols including numerals

Young children’s graphical exploration “builds on what they already know about marks and symbols and lays the foundations for understanding mathematical symbols and later use of standard forms of written mathematics,” the researchers said.

In a 2009 publication, the UK Department for Children, Schools and Families, says practitioners should: “Value children’s own graphic and practical explorations of problem solving” and observe “the context in which young children use their own graphics.”

Developing understanding with careful questioning

When children play and interact with other children, there are always opportunities for maths talk to help them develop a deep understanding, says Sabinra Pinnock.

For instance:

• I have made a pattern. What’s your pattern?
• How many blocks taller is my model compared to yours?
• How do we know this area is full?
• I have three cars, how many do you have?
• Do you have more?
• How do you know?

Give learners long enough to think about their answer and give their response, but not so long that it disrupts the flow of play.

Adding maths talk activities to your daily routine

Developing maths talk in your daily routine gives learners a chance to understand concepts while using real-life concepts. It also means that children can consolidate what they have learned.

The following activities can get you started:

How many children are at school?

Get your class to work out how many children are at school by placing a picture of themselves or a counter representation on large 10 frames. Ask them questions like:

• How do we know this 10 frame is full?
• How many children are absent?
• What can you tell me about number seven?

Sorting and grouping objects as a class

Sorting and grouping objects as a class helps children learn to reason and look for patterns. Give them a variety of buttons each day and ask open-ended questions like, “how can we sort the buttons?” They can use critical-thinking skills to come up with a range of ideas like sorting by size, colour, pattern, and shape.

Vote for a story

First, ask a child to pick two books. Everyone in the class gets to vote (using a piece of lego, for instance) on which of the books should be read. Tally the votes at the end of the day to determine the winner. This can lead to questions such as:

• How many more votes did one book have than the other?

The key to introducing mastery in the early years is to keep activities fun and part of your daily routine. The more learners explore maths through play, the more engaged they become.

Pattern Awareness

Dr. Sue Gifford, emeritus fellow at University of Roehampton, says recent research shows a child’s ability to spot mathematical patterns can predict later mathematical achievement, more so than other abilities such as counting. It also shows pattern awareness can vary a great deal between individuals.

Australian researchers, Papic, Mulligan and Mitchelmore have found pattern awareness can be taught effectively to preschoolers, with positive effects on their later number understanding.

Explicitly teaching pattern awareness links to encouraging “pattern sniffing” with older children in order to develop mathematical understanding and thinking.

What is mathematical pattern awareness?

Patterns are basically relationships with some kind of regularity between the elements. In the early years, Papic et al suggest there are three main kinds:

• Shapes with regular features, such as a square or triangles with equal sides and angles, and shapes made with some equally spaced dots
• A repeated sequence: the most common examples are AB sequences, like a red, blue, red blue pattern with cubes. More challenging are ABC or ABB patterns with repeating units like red, green, blue or red, blue, blue
• a growing pattern, such as a staircase with equal steps

Children who are highly pattern aware can spot this kind of regularity: they can reproduce patterns and predict how they will continue.

Why is pattern awareness important?

Spotting underlying patterns is important for identifying many different kinds of mathematical relationships. It underpins memorization of the counting sequence and understanding number operations, for instance recognizing that if you add numbers in a different order their total stays the same.

Pattern awareness has been described as early algebraic thinking, which involves:

• Noticing mathematical features
• Identifying the relationship between elements
• Observing regularities

The activity Pattern Making focuses on repeating patterns and suggests some engaging ways of developing pattern awareness, with prompts for considering children’s responses. Children can make trains with assorted toys, make patterns with twigs and leaves outside or create printing and sticking patterns in design activities.

Repeating Patterns

It is important to introduce children to a variety of repeating patterns, progressing from ABC and ABB to ABBC.

Focusing on alternating AB patterns can result in some young children thinking that ‘blue, red, red’ can’t make a pattern. They say things like, “That’s not a pattern, because you can’t have two of the same colour next to each other.”

Cognitive Load Theory

Cognitive Load Theory has gained a lot of traction in recent years as educators embrace evidence-based research to inform their evolving practice, says Ross Deans, a KS2 teacher and maths lead in Bournemouth, England.

What is Cognitive Load Theory and why is it important?

Why are new teachers so overwhelmed by tasks that more experienced teachers can juggle alongside multiple other responsibilities?

The answer is simple — new skills demand more attention.

This logic can be applied to any situation. When learning to drive, for example, you focus carefully on every small detail. That mental exertion can be very demanding. Compare that to the feeling of driving after you’ve been doing it for years; you may barely remember the drive, the process is so familiar.

Now put yourself in the shoes of your pupils. Each lesson provides fresh learning and new skills to master. Consider what happens inside your learners’ heads when they encounter new information, new skills and new vocabulary.

Working memory

Cognitive Load Theory , originated by John Sweller, acknowledges that working memory is very limited.

Working memory is the information we hold in our minds while we’re learning. The number of things that we can keep in working memory at one time is approximately four, plus or minus one, and perhaps even less for children.

It’s important to keep this in mind when planning and delivering lessons. If our learners cannot balance more than four things in their working memory, then we need to be very careful about the information we choose to present to them.

Intrinsic versus extraneous load

Intrinsic load includes anything that is necessary to learn a desired skill. In other words, the essential stuff.

Extraneous load is anything that will detract from desired learning. In other words, the stuff that should be reduced as much as possible.

It can be tempting while teaching to embellish lessons with child-friendly imagery and gimmicks. While It’s important to foster enjoyment, we should avoid distracting learners from the essential components of a lesson.

Supporting the transition to long-term memory

While acknowledging the impact of Cognitive Load Theory, we can consider the following to support our learners:

Focused learning objective

First and foremost, we must have a very clear idea of what we want our learners to achieve. Keep the limitations of the working memory in mind and let this guide the content you choose to include in a lesson.

Activate prior learning

At the start of the lesson, you may choose to design a task that encourages learners to retrieve essential skills. This means their working memory can hold on to new learning during the lesson.

Present information clearly

Take time when designing lessons to make sure information is presented clearly. Avoid unnecessary extras which may detract from the learning goal. Keep slides clean and similar in style.

Avoid cognitive overload

In maths, problems are often detailed and complex. Consider breaking questions up into chunks so that learners can digest each part separately. By taking away the final question, you can make a maths problem goal-free.

Maths mastery for Early Years

Given the importance of developing sound mathematical understanding in the early years, the maths mastery approach can be especially useful, considering its focus on problem solving and whole-class learning.

Early Years and CPA

If you’re teaching the Concrete, Pictorial, Abstract (CPA) approach in the early years, it’s best to focus on C and P. Here’s how to use concrete and pictorial representations effectively.

The CPA model works brilliantly in the primary years but for the youngest learners, moving onto abstract concepts too soon causes difficulties. Spending as much time as possible with concrete objects and pictorial representations helps children master number skills.

By the time they reach Key Stage 2, children need to develop their understanding of numbers by being able to visualise what the concrete looks like in their heads. Therefore, it’s positive that the revised EYFS framework focuses on numbers just to 10, from 20 previously.

If learners develop a deep understanding of numbers to 10, their chances of understanding larger numbers increases significantly.

C is for concrete

Concrete is the “doing” stage. During this stage, students use concrete objects to model problems. Unlike traditional maths teaching methods where teachers demonstrate how to solve a problem, the CPA approach brings concepts to life by allowing children to experience and handle physical (concrete) objects.

Spending time with real-life objects

The theorist Jerome Bruner stresses the importance of children spending time learning maths through tangible items. Spending lots of time using real-life objects, solving real-life problems, and manipulating abstract concrete objects (when ready) such as cubes and counters is essential in the early years.

Ideas include counting out fruit for snack time, comparing, sorting and counting a range of different buttons, pasta, and even ‘magic beans’ linked to specific topics.

Early years and number bonds

By mastering number bonds early on, pupils build the foundations needed for subsequent learning and are better equipped to develop mental strategies and mathematical fluency. By building a strong number sense, pupils can decide what action to take when trying to solve problems in their head.

How to teach number bonds

Children are usually introduced to number bonds through the Concrete, Pictorial, Abstract approach . Here’s just one way to introduce and teach number bonds.

Concrete step

Children start out by counting familiar real-world objects that they can interact with. They then use counters to represent the real-world objects. From here, they progress to grouping counters into two groups.

By putting five counters into two groups, children learn the different ways that five can be made. For example, 3 and 2 as illustrated below. With further exploration, children work out other ways to break numbers into two groups.

Pictorial step

Now that they understand the concept with hands-on objects and experience, children progress to writing number bonds in workbooks or on whiteboards. Early number bond explorations might simply reflect the two groups of counters that they created during the concrete step, along with other combinations.

Abstract step

With the concrete and pictorial steps done and dusted, children progress to representing abstract problems using mathematical notation (for example, 3 + 2 = 5).

Early Years and place value

Number and place value are foundational concepts for all mathematics learning. This means we need to address how to teach place value as early as possible so that pupils can secure their knowledge of the concept.

How do you develop an early understanding of place value in the primary school classroom? Let’s start by defining place value. It is a system for writing numerals where the position of each digit determines its value. Each value is a multiple of a common base of 10 in our decimal system.

Here are some teaching strategies I’ve found useful when helping learners develop an early understanding of place value.

Progress through concepts systematically

Developing an understanding of place value requires systematic progression. Each new concept should build on previous learning experiences so that pupils can gain deeper, relational understanding as they go.

This approach ensures knowledge is developed, refined and applied correctly as numbers become meaningful tools for solving problems rather than just a series of symbols on a page. Most importantly, this starts our learners on the path to becoming confident problem solvers and pattern spotters.

Use the CPA approach to establish meaning

The CPA ( Concrete, Pictorial, Abstract ) approach helps pupils connect a physical representation of a number (concrete manipulatives) to that same quantity as shown in drawings or graphics (pictorial), and finally to the actual written name and symbol for that number (abstract).

Concrete resources are meaning makers. They add meaning to abstract representations of numbers so that when learners progress to the abstract phase, they know what those numbers stand for, what they mean, and how they relate to each other.

If a pupil can identify the meaning of each component in a problem, they are far more confident in how they work to solve it.

Teach the ‘10-ness of 10’

At an early level, spend as much time as possible studying the numbers from 0 to 10, as understanding the 10-ness of 10 is crucial for maths attainment, and it cannot be rushed.

Once this understanding is locked-in, follow this with an introduction to number bonds. Start with the additive relationships between numbers less than 10, then progress to adding and subtracting up to 10. This ensures that learners see 10 as an important ‘base’ number in all of their future maths applications.

Progress to 20, then to 40

I make sure to take my time teaching 10 and teen numbers so that a solid understanding of place value with numbers up to 20 is properly established.

I then extend the place value concept by working with numbers up to 40 — followed by addition and subtraction to 40.

Because pupils have learned to make 10 and use number bonds, they are ready to begin working with multi-digit numbers and regrouping. Focusing on numbers to 40 while developing the concept of place value also allows learners to associate numbers with easily-managed, physical quantities (meaning makers).

Use base 10 blocks for 100 and 1000

The work we’ve done building a gradual understanding of place value will have prepared pupils to progress to three-digit numbers. So we can now move on to studying up to 100.

We start here by developing an understanding of numbers in multiple place value representations. For example, one thousand five hundred is 15 hundreds or 150 tens.

Once they get the hang of that, learners then sharpen their counting, reading, and writing skills for numbers up to 1,000. Moving into addition and subtraction with numbers up to 1,000 — with and without regrouping — is the next step.

Here is where our work establishing an early understanding of place value is key, because pupils will intrinsically know why these algorithms work for three and four-digit numbers. Base 10 blocks are a great tool to help solidify those earlier place value ideas when working with numbers up to the thousands.

Approach larger numbers the same way

The CPA approach is once again our answer to learning place value in larger numbers. Apply those skills and always be on the lookout for chances to extend number and place value concepts.

For example, you can identify and complete number patterns or find missing digits on a number line.

From there you can explore strategies for mental mathematics as well as addition and subtraction for numbers up to 10,000. Take learners even deeper by having them explore place value with an emphasis on multiplication, division, and decimals.

Mastering maths concepts like place value in the early years is not just key to success in the classroom. It prepares learners for a lifetime of deep mathematical understanding by giving them invaluable real-world tools like resilience and problem-solving ability.

And a confident problem solver in maths is a confident problem solver in life.

Well done on making it to the end of our Ultimate Guide to Early Years.

We’ve looked at the definition of Early Years and what the government recommends in its revised guidance, and we’ve taken a deep dive into some of the most-effective strategies for teaching mathematics mastery in the Early Years.

We’ve also discussed Cognitive Load Theory and what it means for teachers in the Early Years classroom.

If you’d like to learn more about Early Years, we recommend checking out the following links:

• NCETM: How Early Years children develop mathematical thinking (Podcast)
• NRICH: Early Years Foundation Stage Homepage
• The School of School: Episode 17 Play and early years (Podcast)
• Maths — No Problem! CPA approach

Also, don’t miss our other Ultimate Guides:

• The Maths — No Problem! Ultimate Guide to Maths Mastery
• The Maths — No Problem! Ultimate Guide to Assessment

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• August 31, 2022

Problem Solvers: A Free Early Math Curriculum

A Free Preschool and Early Math Curriculum

Research tells us early math skills are a powerful predictor of overall school achievement. but what does “early math” look like for toddlers and young preschoolers it looks like problem solvers..

Problem Solvers is a free, downloadable early math curriculum for children aged 30 to 48 months that includes:

• 22 play-based preschool and early math activities, spanning 7 domains of early math
• 22 specially-composed songs that support early math learning in each activity
• 22 book suggestions and extension activities that nurture early math language through read-alouds
• 22 parent resources (English/Spanish) that build bridges between school and home, and give parents ideas for engaging math play
• A Teacher’s Guide to help educators implement the curriculum

The development of Problem Solvers was made possible by the generous support of the Honda USA Foundation and the Dr. Seuss Foundation. We are deeply grateful to both foundations for allowing us to make this resource available to preschool and early education programs nationwide.

Get the Problem Solvers preschool math curriculum

• Download a sample Problem Solvers activity .
• Download the Problem Solvers Teacher’s Guide.
• Fall Bonus Unit: “Pumpkin Jump”
• Winter Bonus Unit: “Chilly Patterns” 
• Download the entire free Problem Solvers preschool math curriculum at no charge, including songs, by filling out the form below.

What are early educators saying about Problem Solvers?

Problem Solvers helped us connect math to books, music, and free play. That was something new for me—fresh and different.

It’s always been hard to think of different math activities so this curriculum gave us more ideas and resources!

We have a full curriculum and we were still able to add Problem Solvers as an additional piece—and it wasn’t overwhelming. The kids wanted it and asked for it, even if the teachers missed it that day.

We saw the children focusing on this new math language and using it throughout the classroom – Is it longer? Is it more? Making lots of comparisons, doing lots of counting.

More Resources on Preschool and Early Math Activities

• ZERO TO THREE’s  Let’s Talk About Math  video series:  See how early math skills develop from birth to five. Includes free parent resources.
• ZERO TO THREE’s  Math4Littles  resources: Explore this set of 36 math activities for two- to three-year-olds that build math skills through parent-child play.
• Erikson  Early Math  Collaborative : Browse a library of teacher-friendly instructional resources and fun activities for young children aligned to the big math ideas of early childhood.
• Learning and Teaching With  Learning  Trajectories : Early Math Birth to Grade 3:  Learn more about the math skills that children are developing in the early years.
• Early Math  Counts :  Explore resources for creating math-rich early childhood environments.
• Development and Research in Early Math Education (   DREME ):  Check out math-focused children’s book suggestions with activity ideas.
• Finding  Math  from the Institute for Learning & Brain Sciences, University of Washington: Access this suite of resources designed to help you discover early childhood math in your everyday life.

Looking for training or professional development on early math?

Set up a professional development experience for your staff to build knowledge around early math instruction and support the implementation of Problem Solvers.

• Teaching & Learning
• Early Years

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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Mastery Motivation: Persistence and Problem Solving in Preschool

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Mastery motivation is persistence—continuing to do or to try to do something that is difficult—at mastering challenging tasks or activities.

Problem solving is natural for preschoolers. As teachers know, everyday routines can bring difficult challenges, like learning how to zip up a coat or ask for help before frustration sets in. Each challenge builds children’s skills in different areas of development: language, social and emotional, cognitive, and physical. But sometimes a problem can seem too challenging.

You may have seen this scenario play out in your classroom: Two preschoolers are trying to solve the same puzzle. Both make a mistake, but while one child gives up, the other child keeps trying different ways to solve the puzzle. Early childhood researchers call this persistence at mastering challenging tasks  mastery motivation , and it plays a key role in children’s learning and in their later academic achievement. Early childhood teachers are in a great position to help children foster this important skill.

Here are five ways to support mastery motivation:

• Provide lots of different types of challenging activities, like math games that have more than one way to solve a problem.
• Support children’s independence and let them make their own choices in activities or during play.
• Try to resist the urge to fix the problem—it can take away children’s sense that they are capable problem solvers.
• Do provide gentle guidance when frustration starts to set in, such as holding the puzzle board steady while a child adds a puzzle piece or offering a well-timed, “What if you turned that piece the other way?”
• Give children positive feedback by praising the problem-solving process and encouraging them to keep trying.

We know that children who are not provided with challenging activities or who receive negative or harsh feedback tend to show less mastery motivation. The same holds true for children receiving praise like “You’re so smart” and children whose environment is overly controlling.

When teachers appreciate children’s efforts, children learn that working hard and persisting are positive behaviors. As children grow, they will face more and more difficult problems. They need to know that it’s okay to struggle—it’s part of the learning process.

Photo © EDC

Jessica Mercer Young  is a research scientist and developmental and educational psychologist specializing in early learning at Education Development Center.

Kristen E. Reed,  project director at EDC, has worked as a teacher, curriculum developer, professional development facilitator, and researcher. For more ways to make math engaging, challenging, and fun, visit ym.edc.org .  [email protected]

Vol. 11, No. 1

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Research on early childhood mathematics teaching and learning

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• Published: 23 June 2020
• Volume 52 , pages 607–619, ( 2020 )

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This paper reports an overview of contemporary research on early childhood mathematics teaching and learning presented at recent mathematics education research conferences and papers included in the special issue (2020–4) of ZDM Mathematics Education . The research covers the broad spectrum of educational research focusing on different content and methods in teaching and learning mathematics among the youngest children in the educational systems. Particular focus in this paper is directed to what lessons can be drawn from teaching interventions in early childhood, what facilitates children’s mathematical learning and development, and what mathematical key concepts can be observed in children. Together, these themes offer a coherent view of the complexity of researching mathematical teaching and learning in early childhood, but the research also brings this field forward by adding new knowledge that extends our understanding of aspects of mathematics education and research in this area, in the dynamic context of early childhood. This knowledge is important for future research and for the development of educational practices.

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Research in Early Childhood Mathematics Education Today

Mathematics Education in the Early Years

Early childhood mathematics education: reflections and moving forward.

Avoid common mistakes on your manuscript.

1 Introduction

Early childhood mathematics education is a rich field of study and practice that includes the provision of stimulating activities and learning environments, organized and orchestrated by teachers, care-takers and other professionals with the aim of offering young children experiences that extend their knowledge and development of mathematical concepts and skills. Generally, early childhood mathematics education involves children aged 3–6 years, but in many countries even the youngest toddlers go to early childhood centres. Therefore, contemporary research on early mathematics education focuses on children from birth until they enter formal schooling in the first grade. To develop this field of research, a strong foundation of theory and methodology is necessary, along with consideration of the practical settings of young children’s learning as well as the societal needs and relevant educational policy frameworks. Moreover, from a didactical perspective, it also requires consideration of the essence of the mathematics to be taught to young children.

High-quality research grounded in theory is necessary for all areas of mathematics education, in order to move forward and contribute to the generation of new knowledge from which the educational practice can benefit. Since there is much evidence that later development in mathematics is laid in the early years (e.g., Duncan et al. 2007 ; Krajewski and Schneider 2009 ; Levine et al. 2010 ), such high-quality research is especially critical for early childhood mathematics education. Research involving young children entails certain challenges that cannot simply be solved by adopting research designs that are used with older students. The aim of gaining deep knowledge of how young children’s mathematical understanding can be fostered places high demands on research methods. As early as 40 years ago, Donaldson ( 1978 ) stated that children act differently in their everyday situations than they do in experiment situations, and this has been confirmed by many others since then. Thus, gaining knowledge about teaching and learning mathematics in the early years requires research that is conducted in various learning environments and that acknowledges that these learning environments are complex, multifaceted, and dynamic.

Research in mathematics education is a relatively recent scientific discipline beginning in the last century (Kilpatrick 2014 ). Investigating young children’s mathematical learning and teaching became part of this discipline much later. Early childhood mathematics has long been the research field of developmental psychology and cognitive sciences. From the studies of mental abilities and thinking in mathematical problem-solving carried out in these disciplines, we have gained knowledge about the influence of working memory and attention span (e.g., Ashcraft et al. 1992 ; Passolunghi and Costa 2016 ; Stipek and Valentino 2015 ), as well as about the role of innate abilities of numerical awareness in children’s mathematical performance (e.g., Butterworth 2005 ; Wynn 1998 ). Yet, these studies lack a deeper investigation of the mathematics that is performed and how it is developed by children. Neither do such investigations address why certain mathematical competencies are important or why some activities stimulate their development and others do not. Contrary to psychological research, mathematics education research has a didactic perspective, which means that it is linked to the perspective of the learning child, the teaching teacher, and the environment offering learning opportunities in which the teaching and learning take place. Above all, didactic research distinguishes itself from psychological research because it deals explicitly with the question of what the mathematics is in early childhood activities, both within and outside formal education.

2 A brief overview of the current field of early mathematics education research

As shown by the many publications on teaching and learning of mathematics in early childhood that have been released in the past few years, this area of mathematics education research has increasingly become a mature discipline. The same is reflected by the special interest groups, working groups, and research fora dedicated to mathematics education in the early years. No self-respecting conference today can afford not to pay attention to the area of early mathematics, and there are now also communities and conferences that focus exclusively on early childhood mathematics education. All these communities and conferences are the epicentres where the latest developments in this field are brought together. To set the scene for research on early childhood mathematics teaching and learning, without it being complete, we first provide a brief overview of recently presented and discussed early mathematics education research. As an orientation point for this overview, we used what has recently been presented by researchers at three international meetings.

2.1 CERME 11 thematic working group (TWG) on early years mathematics

A conference that already has a considerable track record for including early childhood mathematics as a fixed part of its programme is the biennial conference of the European Society for Research in Mathematics Education (ERME). This conference started in 2009 with a Thematic Working Group (TWG) on Early Years Mathematics. Since then, the number of participants in this group has grown consistently. In 2019, this TWG (that is, TWG13) consisted not only of European researchers but also attracted participants from Canada, Japan, and Malawi. The most dominant theme presented there involved studies of children’s emerging number knowledge. Many of these presentations were traditional in design, including giving children tasks that had to be solved both individually when the children were interviewed and when they worked in groups in a classroom setting. Based on these studies, researchers formulated descriptions of the children’s knowledge. Sometimes, learning trajectories could be generated from these empirical observations. However, within this TWG several examples of studies with more innovative designs and research settings were also presented, including different modes of exploring and expressing numbers, which can extend our knowledge of early childhood mathematics education. An example of such research is Bjørnebye’s ( 2019 ) study, in which a dice game including elements of multiple representations and embodiment of counting strategies opened up the possibility of observing how children’s actions and responses reflect their understanding. Other studies investigated how affordances of manipulatives and applications encouraged children to develop new ways of thinking about numbers either by working in a digital environment (Bakos and Sinclair 2019 ) or by using their fingers to represent numbers (Lüken 2019 ; Björklund and Runesson Kempe 2019 ).

A characteristic of the research community gathered at CERME11 TWG13 is that the participants generally had in common an interest in better understanding the mathematical thinking of the child. Therefore, it was considered crucial that research establish clues for how to recognize mathematical thinking in the early years. For this purpose, Sprenger and Benz ( 2019 ) used eye-tracking data, as this platform was considered to contribute to the analysis of children’s perception of structure in the process of determining quantities. Yet, what Sprenger and Benz discovered is that data from technological devices still need to be interpreted, and that other expressions of children’s perceptions and reasoning are necessary assets for drawing valid conclusions.

A further important issue that was present at CERME11 TWG13 was related to teaching practice. Specifically, several presentations addressed the questions of how mathematics education should be orchestrated in early childhood education and what opportunities to learn should be offered to children. For example, Breive ( 2019 ) investigated the link between inquiry-based education and open-ended problem-solving, and the role of the teacher in orchestrating such conditions for mathematical exploration. In her paper, Breive described the teachers’ behaviour in terms of the degrees of freedom offered to the children with respect to their actions related to the mathematical content and context. Based on the data she collected, Breive concluded that teachers’ ways of acting, and the accompanying learning opportunities, should be given more attention within early mathematics education research. Similarly, Vogler ( 2019 ), who observed teacher–child group interactions, concluded that so-called indirect learning (which can be found as a common approach in many preschool settings) may induce an obstacle to learning mathematics embedded in activities if there is not a mutual understanding of what learning content is the aim of the activity. In line with these two studies, other researchers who focused on teachers’ interactions with children also highlighted critical issues for educational practice and supported further research inquiries.

Another source for learning about the latest developments in early childhood mathematics education research is the POEM conferences (Mathematics education perspective on early mathematics learning between the poles of instruction and construction). The latest conference, POEM4, was held in 2018. The presentations published in the conference proceedings (Carlsen et al. 2020 ) all, in one way or another, reflect the question “In what way—and how much—should children be ‘educated’ in mathematics before entering primary school?” This was also the recurring question in the discussions between the participating scholars. Among the contributions, three themes stood out: children’s mathematical reasoning, early mathematics teaching, and parents’ role in children’s mathematical development. There was a strong interest in children’s reasoning abilities and strategies in problem-solving. For example, Tsamir et al. ( 2020 ) investigated how children express their understanding of patterning. For this purpose, the researchers provided preschoolers with patterns to be copied and compared, while observing their strategies. Children’s strategy use was also observed in relation to play situations. Bjørnebye and Sigurjonsson ( 2020 ) observed them in teacher-led outdoor games, while Lossius and Lundhaug ( 2020 ) observed child-initiated play activities. Some researchers used their observations of children’s encounters with mathematical content for theoretical discussions on how to understand children’s meaning-making, for example by taking the semiotic mediation perspective (e.g., Bartolini Bussi 2020 ) or through the lens of attentional processes (Verschaffel et al. 2020 ).

With respect to early mathematics teaching, at POEM4 it was discussed that teachers’ educational work largely concerns how to empower children in the learning process, assuming that children have agency in their learning (Radford 2020 ). Some of the presented studies (e.g., Palmér and Björklund 2020 ) specifically chose children's perspectives and problematized how seriation was made a content for learning in a children’s story. They showed how different manipulatives and tools used in teaching have different implications for what is made possible for the children to learn. A critical but essential notion was expressed by Tzekaki ( 2020 ), who underlined that whether children act and think mathematically and learn mathematical concepts depends on what is defined to be mathematical thinking and acting. In line with this perspective, Keuch and Brandt ( 2020 ) and Bruns et al. ( 2020 ) also raised the issue that teachers’ and student teachers’ knowledge of mathematics in early childhood education affects their readiness to exploit the content in ways that facilitate children’s mathematical learning.

The issue of the knowledge of mathematics in early childhood was also addressed in papers on the role of parents in children’s learning of mathematics. Parents are recognized as young children’s first educators, contributing to their mathematical understanding and skills. One example of this research focus is Lembrér’s ( 2020 ) study. In order to know what experiences children bring with them into preschool education and thus might inform their encounter with mathematics, she investigated what parents value in the mathematics activities in which their children are engaged at home.

2.3 ICME-13 monograph “Contemporary research and perspectives on early childhood mathematics education”

The ICME-13 Monograph “Contemporary research and perspectives on early childhood mathematics education” (Elia et al. 2018 ) is the third source for becoming informed about the state of the art in the field of teaching and learning mathematics in early childhood. This book, which has its foundations in the ICME-13 (International Congress on Mathematical Education) Topic Study Group 1 (TSG1) “Early childhood mathematics education” held in 2016, contains chapters on a broad range of topics grouped into five key themes: pattern and structure, number sense, embodied action and context, technology, and early childhood educators’ professional issues and education.

Within these themes, the domain-overarching theme of pattern and structure played a prominent role. As Mulligan and Mitchelmore ( 2018 ) showed in a series of studies, children’s awareness of mathematical structures turned out to be crucial for acquiring mathematical competence. Particularly children’s structuring skills were found to be critical to developing coherent mathematical concepts and relationships. These findings are in line with Lüken and Kampmann’s ( 2018 ) intervention study with first graders, in which 5 months of explicit teaching of pattern and structure during regular mathematics lessons resulted in significant differences between pre- and post-test arithmetic achievement scores in the intervention group. Moreover, the intervention was most beneficial to the low-achieving children.

The research within the theme number sense examined a large variety of different aspects of number development. For example, there was a study about children’s enumeration skills when making lists for designating and representing collections of objects (Dorier and Coutat 2016 ). Also, attention was paid to the use of numerical finger gestures and other bodily-based communication in order to facilitate the learning process (Rinvold 2016 ), children’s spontaneous focusing on numerosity (SFON) (Rathé et al. 2018 ; Bojorque et al. 2018 ), and the link between writing skills and number development (Adenegan 2016 ). Furthermore, an exploration of children’s ability to operate with numbers revealed that 5-year-olds were able to solve multiplication and division problems when they were presented in familiar contexts (Young-Loveridge and Bicknell 2016 ).

In the theme embodied action and context , Karsli’s ( 2016 ) video-ethnographic research in a pre-kindergarten classroom showed that young children’s hand and body movements hold rich potential for engaging them in mathematics, and underlined the importance of early childhood teachers’ attention to the embodied ways in which children engage with mathematics, with potential for creating teachable moments. Other studies investigated children’s engagement in the context of play. In Henschen’s ( 2016 ) study free play was examined, while Nakken et al. ( 2016 ) compared free with guided play, of which the latter resulted in the children exhibiting deeper mathematical thinking, and engagement with more specific mathematical concepts. Anderson and Anderson ( 2018 ) broadened the scope by investigating children’s learning of mathematics in their home environment. Thom’s ( 2018 ) and Elia’s ( 2018 ) research on geometrical and spatial thinking in early childhood offered further insights into the crucial role of the body and other semiotic resources (language, drawings, and artefacts) by which young children develop and communicate spatial-geometrical thinking. A general conclusion within this theme was that the limited ways in which young children are invited to engage with geometrical, spatial, and measurement concepts undervalue the embodied, gestural, in-context nature of their mathematical thinking.

The theme technology specifically addressed the integration of technology into early childhood mathematics teaching and learning both at school and at home. The focus was mostly on touch-screen tablet-based applications. Because this new technology significantly differs from the traditional physical aid materials, professional development is needed to help educators identify and implement effective uses of these applications. To learn more about the role of the educator (teacher or parent) in the child’s interaction with the software, Baccaglini-Frank ( 2018 ) carried out an analysis of student-software-teacher relations, revealing how the teacher’s goal of helping the children experience success actually limited their development of numerical abilities. The use of technology also opened a window to a new perspective in early childhood mathematics, namely by exposing young children to advanced mathematics such as understanding symmetric transformation (Fletcher and Ginsburg 2016 ) and dealing with large numbers (also in symbolic form) and ordinality (Sinclair 2018 ).

In the theme early childhood educators’ professional issues and education , Cooke and Bruns ( 2018 ) provided a comprehensive overview of the various contributions in TSG1, for which they proposed to distinguish conditions at three levels that influence opportunities for young children to develop mathematical understanding and skills. At the macro level, curricula provide a framework (aims, content to learn, and activities) for mathematics teaching and learning in early childhood, with varying views. Several papers mentioned the tensions regarding new curricula and frameworks that may impose mathematical content rather than allowing the child to develop understanding of mathematical concepts through play. At the meso level, with focus on the teachers’ competence, all involved papers agreed as to the importance that the teacher possess a fundamental understanding of mathematics as the basis for high-quality early mathematics education. However, different studies used different conceptualizations and instruments to measure teachers’ mathematical competence. The micro level refers to the mathematics educational programmes and materials, as well as to the required training for teachers to develop their ability to effectively select and implement such programmes that address children’s mathematical needs (Fritz-Stratmann et al. 2016 ).

In sum, the common themes that stand out from the three international meetings are children’s learning through play, and concerns regarding how to apply content-focused teaching, with or without technology. We found that a great deal of the research is on children’s mathematical thinking and learning, including two main areas concerning children’s emerging number knowledge and children’s learning of patterns. It is noteworthy that in both areas, how children perceive structure or how they manifest structuring abilities were analysed in several of the studies. There were also a number of studies that focused on how finger patterns, gestures, or bodily-based communication may facilitate children’s learning of numbers.

Children’s learning through free or guided play is also a main issue that was discussed. Teachers’ guiding interaction with children in play was shown to contribute more to deeper mathematical thinking and engagement with specific mathematical content. How teaching affects children’s learning opportunities in preschool was furthermore of great concern in several of the studies. A conclusion drawn from this research is that teachers’ ways of acting and the learning opportunities created for children should be given more attention. In what way, and how much, children should be educated before entering primary school remains a central issue.

3 The contributions of this special issue

In this special issue of ZDM Mathematics Education (Issue 2020–4), contemporary research on early childhood mathematics teaching and learning is discussed by researchers from all over the world. The initiative emanated from the 42nd PME conference in Umeå, Sweden (July 2018), where we had the opportunity to organize a Research Forum in which researchers involved in the field of early childhood mathematics education gathered to present and discuss theoretical and methodological challenges and outcomes of studies on learning and teaching arithmetic skills in early years (Björklund et al. 2018 ; Van den Heuvel-Panhuizen 2018 ). The conclusion of the Research Forum was that early childhood mathematics education research is key, but that more efforts are needed to bring together the state of the art within this field as a foundation for moving early childhood mathematics education research forward. This special issue again provides a window into the contemporary field of research on early childhood mathematics teaching and learning. To discuss what this special issue adds to this field and reflect on the challenges that lie ahead for research on early childhood mathematics education, in the next section we synthesize the themes that emerge from the 15 papers included in this special issue. Each theme highlights the papers’ shared knowledge and contributions to research methods. Many papers are related to several themes, but for our discussion we chose those papers that predominantly belong to a particular theme. In total, we identified three recurring themes: the early interventions and their effects, the facilitating factors for learning and development, and the mathematical key concepts that can be observed in children. Together, these themes bring to the fore aspects that are essential for understanding the learning and teaching of mathematics in the early years.

3.1 What lessons can be drawn from interventions?

Research shows that children’s development of mathematical skills and knowledge is often influenced by socio-economic and curricular factors, and by social interaction in both short- and long-term perspectives (Pruden et al. 2011 ). Thus, there is a raised awareness of the impact early childhood education may have on reducing differences in conditions for learning and on increasing and securing equal opportunities for a good foundation in learning for all children. Based on their meta study of early mathematics education research, Duncan et al. ( 2007 ) stated that early intervention counts and numerous references to the same study indicate that this is an important standpoint in research. Why else indulge in the challenging task of researching learning among the youngest in our education systems, if one does not believe that efforts made through teaching are significant for children’s wellbeing and lifelong learning path?

Research on teaching and learning mathematics often shares a common research design in which interventions are implemented (designed, conducted, and the outcomes assessed) with the aim of finding ways to improve teaching practice for the benefit of the learning child, and often to reduce socio-economic inequality. Intervention studies can be objects of research in different ways, focusing on the children’s learning outcomes or the teaching practices. Nevertheless, the goal is to enhance learning through improved teaching. In the papers in this special issue we find efforts to implement well-designed interventions, explicitly focusing on how to teach. Some implement and analyse fine-grained differences in (teaching) actions and the effects on children’s attention to certain content (Paliwal and Baroody 2020 ; Mulligan et al. 2020 ), while others study the effects of attentiveness to children’s experiences and knowledge and the related choices of tasks (Clements et al. 2020 ; Grando and Lopes 2020 ). Nevertheless, essential to studying intervention success or failure is how learning outcomes are measured and interpreted, which is also an important aspect of early childhood mathematics education research (Li et al. 2020 ).

How teaching is framed to present mathematical content to young children, in order for it to be meaningful to them, and in order to be attentive to children’s experiences and knowledge, is investigated and discussed by Grando and Lopes ( 2020 ). Through narratives provided by early childhood teachers, they find insights into how teachers chose to frame the subjects of statistics and probability in ways that engaged children and were responsive to the children’s own experiences, rather than using materials provided by textbooks. Unconventional teaching methods whereby teachers turned their mathematics classroom into a space of creative insubordination are discussed in this paper in relation to the opportunities they offer children to become equipped with critical thinking. The authors argue that the specific content—statistics and probability—demands problematizing activities and experimentation with uncertain outcomes of problems in order to develop probabilistic thinking. This study highlights an essential issue in didactical research: that the content to be taught is not indifferent to how the teaching is designed. The study particularly raises concerns that the design of teaching cannot be random but rather has to be linked to the educational environment and the students attending that particular environment. Consequently, the generalizability of intervention programmes and teaching methods has to be taken into serious consideration if they are to be implemented in different educational settings.

Clements et al. ( 2020 ) set out to investigate the efficacy of implementing an intervention programme in which instructions and progression are grounded in a research-based learning trajectory. Even though the programme itself had previously been found to have positive outcomes for preschool children’s mathematics learning, the goal of the current study was to investigate how to teach in the most successful way. For this purpose, the authors used the same programme but adapted the choices of the tasks’ difficulty level to the children’s current knowledge levels. How to teach was then related to what to teach individual children. Results indicate that skipping difficulty levels to shorten the steps to the learning goals was not successful. This thorough investigation of teaching by adapting the complexity of the content to the child’s ability to learn best what is intended draws attention to the delicate work of teaching in early childhood education. The study supports child-centred approaches that are sensitive to the individual needs and potential of the child, while simultaneously aiming for the learning goals set by the curriculum.

While Clements et al. investigated the effects of an intervention programme covering broader numerical knowledge, Paliwal and Baroody ( 2020 ) aimed to investigate what conditions for learning the cardinality principle are most effective and how subitizing abilities impact on cardinality knowledge achievement. Their efforts were directed towards a fine-grained analysis of how to teach this aspect of the number concept, and what learning processes different approaches elicit in children. What stands out in their study is that they used a highly advanced research design, which allowed them to examine the effects of different ways of directing children’s attention to seeing numbers’ cardinality. In their paper, they point out the importance of directing children’s attention to various ways of seeing numbers’ cardinality, as follows: as a constructing act by adding units to get a number; as an act starting from naming the whole set with a counting word and then differentiating the added units by counting; and a third condition, attending only to single units in a counting act. Thus, their intervention was designed with explicit rigour as to what was made possible for the children to experience, and their investigation concerned the learning outcomes of the different conditions. While this attention in Paliwal and Baroody’s study to the different conditions can at first glance be considered subtle and far from the instruction children encounter in their mathematics education, the study offers insight into the importance of teachers’ awareness of their way of directing children’s attention to certain meanings of the content.

In another paper focusing on the effects of an intervention programme, Mulligan et al. ( 2020 ) analysed children’s written answers to pattern tasks in order to identify differences and changes in their structural awareness. They found a positive effect on the children’s development of awareness of mathematical pattern and structure (AMPS), and showed how the levels changed as an effect of a 37-week intervention programme. Mulligan et al. add to the field of early childhood mathematics knowledge of a particular ability (structural awareness), how it can be identified among young children, and also how the ability changes over a prolonged period of time (during an intervention), which may provide insight into what children actually learn while taking part in an intervention programme.

Children’s learning is of course at the centre of attention in intervention studies, and Li et al. ( 2020 ) pay explicit attention to how to interpret results from a pre- and post-diagnostic test. In their study, Li et al. investigated the development of mathematics problem-solving skills among kindergarteners by analysing their responses to a cognitive diagnostic test. As in most large-scale analyses, it can be shown in quantitative terms how children develop in producing correct answers that indicate growth in knowledge within certain domains that are tested for. However, Li et al. take a step further in their inquiry and illustrate how two children who scored similarly on the cognitive diagnostic test before an intervention had made different progress during the intervention period. Li et al. suggest that the reason for this difference may lie in how children understand and approach tasks, indicating different understanding even though similar answers are produced. Quantitative measures alone do not reveal such differences. The study thus shows the significance of paying attention to how children reason in order to solve a task. Based on their study, Li et al. recommend that children’s learning outcomes from participating in interventions be seen in the light of how the effects of interventions are measured, as it is observed that some developed skills do not endure over time and similar outcomes among children may conceal different learning paths.

3.2 What facilitates children’s learning and development?

Today, it is undisputed that the development of mathematical skills and the teaching of emerging skills in the early years are essential for mathematics education and developmental progress in the long term (Aunio and Niemivirta 2010 ; Duncan et al. 2007 ; Krajewski and Schneider 2009 ). However, in contrast to this perspective, a recent overview of the long-term effects of preschool mathematics education and interventions (Watts et al. 2018 ) challenges this almost taken-for-granted assumption, as most early interventions have a substantial fadeout effect. Thus, there is a need to revisit our current knowledge of teaching and learning, and scrutinize what seems to make a difference. Some of the papers in the special issue particularly consider this issue in their efforts to ascertain what facilitates children’s mathematical learning and development, and focus on influential aspects found in play settings (Reikerås 2020 ; Tirosh et al. 2020 ), verbal communication in teaching practices (Hundeland et al. 2020 ), and the home numeracy environment (Rathé et al. 2020 ).

Hundeland et al. ( 2020 ) raise the question of how children learn to use and understand the canonical language of mathematics, and study this aspect in terms of mathematical discourses taking place in kindergarten teaching sessions. They take a sociocultural stance (see Vygotsky 1987 ), seeing communication as the link between internal communication (thinking) and external communication (interaction). Therefore, children’s opportunities to contribute ideas and arguments are vital for their (mathematical) learning processes. Earlier research has also shown that care-takers’ talk influences not only children’s vocabulary but also, for instance, their spatial problem-solving (Pruden et al. 2011 ). The deeper knowledge that the study by Hundeland et al. ( 2020 ) provides regarding the quantity and quality of mathematical talk in which children are involved, offers us better opportunities also to organize supportive and stimulating conditions for knowledge growth.

What differs in the study by Hundeland et al. compared to most others with similar research questions is their focus on the kind of interaction that the mathematical discourse induces, which, based on the chosen sociocultural theoretical framework, should be crucial for positive learning outcomes. However, what they study and compare is the impact on the mathematical discourse that a certain in-service training has. This places mathematics in the spotlight of mathematics education research. While psychological and cognitive research provides us with important knowledge of mental processes and developmental advancement, studies like the one by Hundeland et al. have a clear direction towards understanding, and not least improving, the conditions for children’s learning and development, either by implementing teachers’ professional development or through curriculum improvements.

It is commonly agreed that young children’s learning is often situated in play. In a large-scale observation study, Reikerås ( 2020 ) conducted a thorough examination of the kind of play in which toddlers engage, for the purpose of learning how play skills may be related to early mathematical skills. It was found that competencies that allow the child to be active in solitary and parallel play, as well as children’s ability to initiate and remain in a play activity, correlated positively with the toddlers’ mathematical skills. The kind of play skills that showed the highest correlation with mathematical skills was their competence to interact in play. General social play skills thus seem to have an impact on mathematical learning, but Reikerås’ study cannot reveal how these are connected or any causal effects. An effort to better understand the interaction going on in toddlers’ play is made by Tirosh et al. ( 2020 ), investigating the challenges toddlers may face as they practise one-to-one correspondence in a playful context, and how different individuals participate in the playful mathematical context. Here, interaction and social skills become one issue with an impact on the learning opportunities arising in the play.

In many cases, the messy context of children’s play is a methodological challenge. It is not possible to control influencing variables to the same extent as in an experimental design. On the other hand, findings from the messy settings are more likely to bring to the fore aspects that were not anticipated, which raises new questions for research and theory development. Design research supports this kind of knowledge contribution, as several cycles are conducted, each developed based on insights from the previous cycle. These cycles adhere to children’s initiatives such as practising one-to-one correspondence in a setting the table task by putting one spoon inside each cup instead of placing one spoon beside each cup (see Tirosh et al. 2020 ); thus, the child is expressing an understanding of the concept, but is expressing it differently than how the task suggests. This highlights the importance of directing attention to instructions used in research studies, and particularly to the language of mathematics and the spatial aspects of props used in a task, related to the possibilities involved as young children interpret and execute a task.

Children take part in cultural life, where today numerical aspects are an inevitable part of the everyday environment. Nevertheless, there are differences in the extent to which children attend to these aspects, and consequently in how they learn the meaning of numbers, graphical representations of numbers, and how to use numbers. A common assumption is that home numeracy environment is a strong factor (LeFevre et al. 2009 ; Skwarchuk et al. 2014 ), which is reflected not least in the abundance of studies regarding socio-cultural background and demographic factors as a pre-cursor for learning progress. Rathé et al. ( 2020 ) put the common assumption to the test—that home environment has an influence on children’s progress in mathematical development—by comparing young children’s tendency to focus spontaneously on numeracy and numerical symbols in their home numeracy environment. Concerning this specific directionality to numbers, which is assumed to have an impact on children’s arithmetic skills in later years (see McMullen et al. 2015 ), based on their study they propose that the home numeracy environment does not seem to have any significant impact.

3.3 What mathematical key concepts can be observed in children?

A great deal of research in the field of early childhood mathematics education studies what mathematics children understand and how this understanding evolves. This knowledge is crucial in designing teaching that contributes to more advanced thinking and problem-solving strategies that support conceptual growth. Therefore, children’s utterances and how they act are the centre of interest for many researchers. Also, in this special issue, much attention is paid to the mathematical key concepts that can be attributed to children’s thinking, resulting in papers addressing children’s understanding of similarity in mathematical objects (Palmér and Van Bommel 2020 ), their understanding and use of structures (Sprenger and Bentz 2020 ; Kullberg and Björklund 2020 ), their understanding of the concept of cardinality and ordinality (Askew and Venkat 2020 ), and the underlying structure of their quantitative competencies (Van den Heuvel-Panhuizen and Elia 2020 ).

Children’s expressions, and how they are allowed to express themselves, are critical for our understanding of the learning of mathematics. Children’s problem posing is one aspect that can tell us about their understanding of mathematics (Cai et al. 2015 ). In the special issue, this is particularly addressed in the paper by Palmér and Van Bommel ( 2020 ), who investigated children’s understanding of similarity in mathematical objects. They analysed how children themselves created tasks in three-dimensional geometry that were similar to a previous problem-solving task they had worked on. It is suggested that this finding sheds light on the children’s interpretation of the specific mathematical features of the original task.

How children perceive structure has been shown to play an important role in how they, for example, determine a number of objects or solve an arithmetic problem (Ellemor-Collins and Wright 2009 ; Resnick 1983 ). In line with these earlier studies, Sprenger and Bentz ( 2020 ) investigated how 5-year-olds perceive structures in visually presented sets. By having the children determine the number of eggs in a 10-egg box while using an eye-tracking device (and recording the children’s utterances and gestures), they were able to analyse the children’s gaze when determining the cardinality of the set, and thereby gain insight into the process of perception. The eye-tracking data showed, for example, that many of the children were able to see structures (e.g. 4 + 1 or 3 + 2) and use them to determine a quantity without having to count all the objects. The authors argue that children’s ability to perceive structures in sets and use them to determine cardinality is central for their further arithmetic learning, as how children perceive sets (e.g., as individual objects, as a composite whole, or in structured part-whole relations) affects the strategies they use for solving arithmetic tasks.

Similar ideas are found in the study by Kullberg and Björklund ( 2020 ), who studied 5-year-olds’ use of finger patterns to structure number relations while solving an arithmetic problem. They identified two major ways of structuring the task: only structuring, and counting and structuring. In the group that both structured using their fingers and counted on some fingers, some ways were found to be more powerful. Children who solved the arithmetic task (3 + _ = 8) by creating a finger pattern of eight raised fingers and simultaneously identifying (‘seeing’) the missing part (5) on two hands (3 + (2 + 3) = 8) were more successful in solving arithmetic tasks, even in a later follow-up assessment. It is suggested that a possible reason for this later success is that these children were able to see numbers as parts included in other numbers, which has been found in earlier research (Resnick 1983 ) to be important for developing arithmetic skills.

Baccaglini-Frank et al. ( 2020 ) also argue that the appropriate use of fingers can contribute to developing children’s number sense. They studied how 4-year-olds interacted (verbally and using finger patterns) when using the application TouchCounts. The app combines multi-touch with audile, visual, and symbolic representation, and several solution strategies are possible, affording the simultaneous experience of, for example, finger patterns on the screen, with the number both seen and spoken. In their paper the authors emphasize how multimodal affordances may encourage children to use different strategies in response to different tasks, and thus experience a broad range of abilities related to number sense, including both cardinality and ordinality.

Askew and Venkat ( 2020 ) examined children’s understanding of the concept of cardinality and ordinality in connection with their awareness of additive and multiplicative number relations. To investigate this topic, first graders (6- and 7-year-olds) in South Africa were asked to position the numerals 1–9 on a bounded 0–10 number line. The children were able to do this in the correct order, with the fewest errors at the upper and lower ends of the number range. Furthermore, evidence was found that awareness of ordinality and that of cardinality develop alongside each other. However, the logarithmic scale, predicted in earlier research, which is considered to indicate a multiplicative structuring of number relationships, was not confirmed in the South African data. Instead, when the numerals grew larger the intervals became more stretched out rather than compressed. In fact, the children’s responses were closer to the linear model, which is considered to indicate an additive structuring of number relationships. Also, the use of unit sizes that did not take into account the length of the number line, together with the underestimation of the position of 5 on the 0–10 line, offered limited evidence of the children’s awareness of the multiplicative structure of the cardinality of numbers. More research is needed to disclose the deep interconnections between children’s understanding of cardinality and ordinality, and their understanding of multiplicative and additive number relations.

Another effort to unravel the complex nature of children’s early number understanding was carried out by Van den Heuvel-Panhuizen and Elia ( 2020 ), investigating the structure of the quantitative competence repertoire of kindergartners. Based on a literature review, they arrived at a model consisting of two constituent parts: quantification (the ability to connect a number to a given collection of objects) and quantitative reasoning (the ability to think and operate with quantities). Quantification was split up into counting and subitizing, and quantitative reasoning into additive and multiplicative reasoning. Although this model is partly in line with models found in earlier research, it also extends previously developed models by including multiplicative reasoning. Data were collected in the Netherlands and Cyprus. A series of confirmatory factor analyses showed that the hypothesized four-factor model fitted the empirical data of the Netherlands, but not those of Cyprus, which clearly challenges the model’s generalizability. A comparison of the component performances in the Dutch sample revealed that, in accordance with other studies, the lowest scores were found for multiplicative reasoning and that the competence of subitizing seems to develop before counting. This was partly confirmed by a statistical implicative analysis at item level. Although this analysis resulted in different implicative chains in the two countries, in both samples the multiplicative reasoning and conceptual subitizing items were found at the top of the chain and the counting and perceptual subitizing items at the end. Also, more research is necessary here, particularly concerning the generalizability of the model to other countries.

4 Future directions for research on early mathematics teaching and learning

After the Research Forum at PME42 we concluded that to move early childhood mathematics education research forward, more efforts are needed to bring together the state of the art within this field. Thus, we proposed a special issue on the theme Research on early childhood mathematics teaching and learning for the purpose of opening up further discussion and inquiry. In this article, the 15 papers included in the special issue are synthesized and discussed in terms of their contribution to the current field of research in early mathematics teaching and learning along with recent research presented at international mathematics education research conferences. Naturally, these do not cover the worldwide field of research, but they at least give a general idea of the current research interests and challenges.

All the papers in this special issue address aspects of early mathematics education and its underlying theories and research methodologies. They share common interests and challenges concerning how to gain knowledge of the youngest children’s mathematical development, and they identify prosperous teaching approaches. Our appeal to researchers participating in the special issue was to cover the broad span of mathematical ideas that are relevant in early childhood education. Nevertheless, we see a strong direction towards research on the learning and teaching of number concepts and basic arithmetic. This is in line with Alpaslan and Erden ( 2015 ) review of early mathematics research published in 2000–2013 in high-ranked scientific journals in the field of mathematics education, in which the most frequently reported research topics were number systems and arithmetic. The same trend is also found in the research addressed in the latest meetings of ICME, ERME, and POEM. We believe further research should widen this scope, and consider and investigate mathematical topics that are currently less highlighted. There is a need for deeper insight into what mathematics means to young children, and also how the foundations can be laid for the domains of spatial and geometric thinking and measurement, as well as for the domains of structures and patterns, data handling, problem-solving and mathematical reasoning.

Moving an educational field forward, however, is not solely based in covering a broad field of content. To strengthen the field, we need to scrutinize the research designs and methods that are used and the knowledge that is generated. Here, new technologies may open up opportunities for designing tools for investigating children’s competencies. However, this initiative goes beyond choosing digital tools or concrete building blocks; it concerns children’s opportunities to express themselves within different environments and make use of tools and manipulatives that may reveal new insights into their competencies and open up for innovative research questions to be posed. What is made available to experience surely has an impact on children’s expressions of knowledge. And expressions in both words and gestures are important keys here to interpreting the youngest children’s knowledge and skills. We can see this in the recent ICME, ERME, and POEM meetings’ presentation of a large variety of research designs and in the papers of this special issue. Many innovative research designs have been developed that allow thorough investigation of children’s mathematical competence and understanding. What we see, for example, is that subtle differences in expression (e.g. gaze, finger use, or ways of posing questions) reveal new and important insights for developing knowledge of children’s mathematical learning. These innovations in methodology allow for the thorough investigation of key features of learning mathematics that go beyond the broad content areas and highlight how mathematical aspects such as cardinality, ordinality, and number structure are experienced by children. Several of the papers in the special issue particularly attend to these aspects, and do so by creating and using new methodologies and technologies.

The consensus in the field of early mathematics education, reflected in the papers and conference presentations, is strong concerning the impact of early interventions on children’s opportunities to thrive as mathematics learners. From longitudinal studies, we know that early knowledge and skills seem to follow through the child’s development; that is, weak mathematical skills in early childhood years are likely to predict weak mathematics performance in later school years (Reikerås and Salomonsen 2019 ; Hannula-Sormunen et al. 2015 ). This means that early intervention and knowledge of how to offer all children a good start for their mathematical learning are essential to the field of early childhood mathematics education. However, it cannot be assumed that simply participating in education, whether it is framed as free or guided play or problem-solving, or stimulating interactive environments, will result in successful learning outcomes, even though most interventions do have a positive impact and most children develop their knowledge to some extent (Wang et al. 2016 ). Common research objectives, therefore, concern intervention implementation, and analyses of children’s learning outcomes from participating in differently designed activities. These studies are of high importance, as they connect the teaching to the learning and provide insights into what seem to be key aspects in the teaching practice. Nevertheless, researching interventions is delicate work, and it is essential to maintain scientific rigor in the design and analysis. Because early childhood education most often takes place in dynamic settings, the conditions under which children learn vary greatly. This diversity is observed in many studies in which children’s engagement in play, both self-initiated and guided, is used as data for analysing their mathematics competencies and learning of mathematics. This phenomenon means that the conditions offered to explore mathematical concepts and principles should be critically examined, along with how learning from interventions is measured and valued. There is a need to determine what works, what seems critical, and what aspects serve as particular challenges. In research, also special attention has to be given to the nature of the teaching practices. What we learn from intervention studies, both those included in the special issue and those in other contemporary research, is the importance of situating research in the current field of knowledge and the context in which the research is conducted. Each study broadens the picture of the teaching–learning relationship, which is by no means one-directional. There are many aspects to consider that potentially influence this relationship, and all of them cannot be included in one study alone.

Early childhood mathematics education research often attends to the opportunities and conditions that are offered for learning. There is no doubt that children’s activities and interaction with others, already from an early age, offer many opportunities to learn mathematical concepts and basic principles, but our ability to discern what children actually learn from the mathematical learning environments offered to them places high demands on the interpretation process. How to understand the processes going on in play and interaction, and what impacts the children’s learning outcomes—what is made possible to learn—often remains an unsolved issue, as the interaction between teacher and children is dynamic, and particularly as play is multidirectional in nature. Studies of interaction in both formal and informal contexts are nevertheless important, as they are conducted in the complex of social and cultural settings that do influence, through norms and individuals’ experiences, what is possible for children to learn.

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Björklund, C., van den Heuvel-Panhuizen, M. & Kullberg, A. Research on early childhood mathematics teaching and learning. ZDM Mathematics Education 52 , 607–619 (2020). https://doi.org/10.1007/s11858-020-01177-3

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10 Simple Activities to Teach Your Preschooler Problem Solving

By: Author Tanja McIlroy

Posted on Last updated: 7 April 2024

Categories Activities for Preschoolers & Kindergarteners

During the first years of a child’s life, an important set of cognitive skills known as problem-solving abilities are developed. These skills are used throughout childhood and into adulthood.

Find out what problem solving is, why it’s important and how you can develop these skills with 10 problem-solving games and activities.

What is Problem Solving in Early Childhood?

So, what exactly is problem solving? Quite simply, it refers to the process of finding a solution to a problem .

A person uses their own knowledge and experience, as well as the information at hand to try and reach a solution. Problem solving is therefore about the thought processes involved in finding a solution.

This could be as complex as an adult working out how to get out of a financial crisis or as simple as a child working out how two blocks fit together.

Problem Solving Skills for Kids

Problem-solving skills refer to the specific thinking skills a person uses when faced with a challenge. Some problems require the use of many skills, while others are simple and may only require one or two skills.

These are some examples of problem-solving skills for preschoolers , as listed by kent.ac.uk .

• Lateral thinking
• Analytical thinking
• Decision-making skills
• Logical reasoning
• Persistence
• Communication skills
• Negotiation skills

The Importance of Developing Problem-Solving Skills in Early Childhood

Problem solving is a skill that would be difficult to suddenly develop as an adult. While you can still improve a skill at any age, the majority of learning occurs during the early years.

Preschool is the best time for a child to learn to problem solve in a fun way. The benefits of learning early will last a lifetime and the beauty of learning anything at a young age is that it is effortless .

It is like learning to play an instrument or picking up a new language – it’s just much easier and more natural at an early age.

Of all the many things preschoolers need to learn , what makes problem solving so important?

There aren’t many situations in life, at work or at school that don’t require some level of problem resolution.

Child’s play itself is filled with opportunity upon opportunity to solve all kinds of tricky situations and come up with solutions to challenges.

Problem Solving in Preschool

During the foundational years, children are constantly solving problems as they play .

Here are just a few examples of problem solving in early childhood :

• Resolving a fight over the same toy
• Reaching a ball that’s stuck in the tree
• Forming a circle while holding hands
• Making a bridge to connect two block towers
• Tying or untying a shoe
• Making up rules for a new game
• Trying to get the consistency of a mud cake right so it stops falling over

The more creative play opportunities and challenges children are given, the more they get to exercise their problem-solving muscles.

During free play , there are non-stop experiences for this, and parents and teachers can also encourage specific problem-solving skills through guided activities .

Problem Solving for Older Children

During the grades, children experience problems in many forms, some of which may be related to their academic, social and emotional well-being at school. Problems may come in the form of dealing with life issues, such as:

• Problems with friendships
• Struggling to understand something during a lesson
• Learning to balance the demands of sport and homework
• Finding the best way to study for a test
• Asking a teacher for help when needed

Problems will also form a large part of academic life as teachers will be actively developing this skill through various activities, for example:

• Solving a riddle or understanding a work of literature
• Working on projects with a friend
• Finding solutions during science experiments
• Solving mathematical problems
• Solving hypothetical problems during lessons
• Answering questions and completing exam papers

Children who have had practice during preschool will be a lot more capable when facing these challenges.

Solving Problems in Mathematics

Mathematics needs to be mentioned separately as although it is part of schooling, it is such a huge part and it depends heavily on a child’s ability to solve problems.

The entire subject of mathematics is based on solving problems. Whether you are adding 2 and 3, working out how many eggs will fit into each basket, or solving an algebraic expression, there is a problem in every question.

Mathematics is just a series of problems that need to be solved.

What we refer to as problem solving in Maths is usually answering word problems .

The reason many children find these so difficult to answer is that the question is presented as a problem through a story, rather than just numbers with symbols telling you what operation to use (addition, division, etc.)

This means a child is forced to think carefully, understand the problem and determine the best way to solve it.

These problems can involve various units (e.g. mass, capacity or currency) as well as fractions, decimals, equations and angles, to name a few. Problems tend to become more and more complex over the years.

My experience in the classroom has shown that many, many children struggle with solving word problems, from the early grades right into the senior years.

They struggle to analyze the question, understand it, determine what information they’ve been given, and what exactly they are required to solve.

The good news is that exposing a child to regular problem-solving activities and games in preschool can greatly help him to solve word problems later on in school.

If you need one good reason to do these kinds of activities, let it be for a smoother experience in mathematics – a subject so many children unnecessarily fear.

Problem Solving in the Workplace

Adults in the workplace seldom thrive without problem-solving skills. They are required to regularly solve problems .

As adults, employees are expected to independently deal with the frequent challenges, setbacks and problems that are a big part of every working environment.

Those who can face and solve their own problems will go further and cope better than those who seek constant help from others or cannot show initiative.

Some  career websites even refer to problem solving as a universal job skill. They also mention that many employees are not good at it. 

Again, although it may seem far removed, learning this skill at a young age will help a child cope right into adulthood and in the working world.

How to Teach Children Problem-Solving Skills

If early childhood is the best time to grow these skills in your young children, then how does one go about teaching them to toddlers, preschoolers and kindergarteners?

Problem solving can be taught in such a way that you expose your child to various opportunities where they will be faced with challenges.

You would not necessarily sit your 3-year-old down and tell or “teach” him all about fixing problems. Instead, you want to create opportunities for your child to grow this skill .

Using the brain to think and find solutions is a bit like working a muscle over time. Eventually, your muscle gets stronger and can handle more “ weight. ” Your child will learn to problem solve in two ways:

• Incidentally – through free play
• Through guided opportunities provided by a parent or teacher

If you make a point of encouraging thinking through games and activities, your child will develop stronger skills than if you let it all happen incidentally.

Problem-Solving Strategies and Steps

If we take a look at the steps involved in solving a problem, we can see that there are many layers involved and different types of skills. Here are the problem-solving steps according to the University of Ken. 

Step 1: Identify the problem

Step 2: Define the problem

Step 3: Examine the options

Step 4: Act on a plan

Step 5: Look at the consequences

Therefore, activities at a preschool level need not present complicated high-level problems.

• A simple activity such as identifying differences in a picture can work on the first skill needed – identifying a problem.
• Playing with construction toys can develop a child’s ability to try various solutions and examine the options when faced with a problem such as trying to find the best way to build something.
• Playing Tic-Tac-Toe would make a child predict the consequences of placing their mark in a particular square.

The most basic of activities can work on all these skills and make children competent solution finders.

How to Teach Problem Solving with Questions

The language you use around your child and your questioning technique will also greatly affect their understanding of a problem or challenge as merely something waiting for a solution to be found .

While your child is playing or when she comes to you with a problem, ask open-ended questions that will guide her in finding a potential answer independently. Use the steps listed above to formulate your questions.

Here are some examples of questions:

• What do you think made the tower of blocks fall down?
• If we build it again, how can we change the structure so that it won’t fall down next time?
• Is there a better way we can do it? If you think of a different way, we can both try it and see which works better.
• Did that work? The tower fell again so let’s try another solution.

Resist the temptation to fix every one of your child’s problems, including conflict with friends or siblings. These are important opportunities for children to learn how to resolve things by negotiating, thinking and reasoning.

With time, your child will get used to seeing a problem, understanding it, weighing up the options, taking action and evaluating the consequences.

Problems will be seen as challenges to be faced logically and not “problems.”

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10 Problem-Solving Activities for Preschoolers

Here are 10 simple, easy games and problem solving activities for kids at home or at school. Many of them are the kinds of activities children should have daily exposure to.

Puzzles are one of the best thinking activities out there. Each puzzle is basically one big set of muddled-up things to be sorted out and put back together again. Find out why puzzles are important for development .

Children should have regular exposure to puzzles. They are great for developing thinking skills.

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2. Memory games

Memory games will develop your child’s memory and attention to detail.

Get your own memory game cards by downloading the FREE set of printables at the end of the post.

Use pairs of matching pictures and turn them all face down, shuffled, on a table. Take turns choosing any two cards and turning them face up on the table. If you turn over a matching pair you keep the cards and if the pair doesn’t match, turn the cards back over until it is your turn to try again.

Encourage your child to concentrate and pay attention to where the pictures are and try to find a matching pair on each turn. 

3. Building with Construction Toys

Construction toys such as engineering blocks, a proper set of wooden blocks or Legos (shown below) should be a daily staple in your home.

Everything your child builds is a challenge because it requires thinking about what to build and how to put the pieces together to get a design that works and is functional.

Leave your child to construct freely and occasionally set a challenge and ask him to build a specific structure, with conditions. For example:

• Make two towers with a bridge joining them together
• Build a creature that stands on its own and has 3 arms.

Then watch your child wracking his brain until he finds a way to make his structure work.

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• Special pieces encourage imaginative building with endless possibilities

4.  Activity Books

These activity books are really fun and develop a child’s ability to identify problems and search for information.

• Pomaska, Anna (Author)
• English (Publication Language)

• Handford, Martin (Author)

• Books, Webber (Author)

5. Following Patterns

This simple activity can be played with a set of coloured blocks, shapes or counters.

Simply make a pattern with the blocks and ask your child to continue it. Vary the pattern by changing the colours, shapes or sizes.

This activity will train your child to analyse the given information, make sense of it, recognise the pattern and re-create it.

6. Story Time Questions

Get into the habit of asking questions during your daily story time that develop higher-order thinking skills . Instead of just reading and your child passively listening, ask questions throughout, concentrating on solving problems.

Here are some examples:

• Why do you think the bear did that?
• Do you think his friend will be happy? Why?
• What would you do if you were the monkey?
• How do you think Peter can make things better with his friend?
• If the crocodile had decided not to eat the rabbit, how could the story have ended?

7. Board Games

Board games are an excellent way to develop problem-solving skills.

Start off with simple games like Ludo and Snakes and Ladders to teach the skill of following rules and moving in a logical sequence.

• Double-Header: Enjoy two classic games in Ludo and Snakes and Ladders on this double-faced game board
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Card games like Go Fish are also great for teaching young children to think ahead and solve problems.

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8.  Tic-Tac-Toe

This is a perfect game to teach decision-making skills , thinking before acting and weighing up the possible consequences.

Use a Tic Tac Toe Board or d raw a simple table like the one above on paper or a chalkboard.

• Wooden tic-tac-toe game board with eye-catching red, orange, blue, and green color pattern
• Includes white-framed wooden board with indented squares for mess-free play, 10 colored x and O game tiles,...

Take turns to add a nought or a cross to the table and see who can make a row of three first.

Your child will probably catch on in no time and start thinking carefully before placing their symbol. This game can also be played with coloured counters or different objects.

9. Classifying and Grouping Activities

This activity can be done with a tin of buttons or beads or even by unpacking the dishwasher. The idea is to teach the skill of classifying and categorizing information by learning with physical objects. Here are some other ideas for categorizing:

• Separate the washing – mom’s clothes, dad’s clothes, etc; or socks, tops, shorts, etc.
• Empty out the cutlery drawer for cleaning, mix all the utensils up and then sort into knives, tablespoons, teaspoons, etc.
• Classify and sort out the toys in your child’s bedroom together – all books, construction toys, soft toys, etc.
• Play category games .

Here are more button activities for kids .

10. Building a Maze

This activity is lots of fun and suitable for any age. It is also going to be way more fun than doing a maze in an activity book, especially for younger children.

Draw a big maze on the paving with sidewalk chalk . Make passages, including one or two that end in a dead-end. Teach your child to find her way out .

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As your child gets better at figuring out a route and finding the way out, make the maze more complex and add more dead-end passages.

Are you a preschool teacher or working in Early Childhood Education? Would you like to receive regular emails with useful tips and play-based activity ideas to try with your children? Sign up for the newsletter!

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Friday 3rd of June 2022

hi maam , This Is Uma from India,Can i get this in pdf format or a book. Thank You

Tanja Mcilroy

Monday 6th of June 2022

Hi Uma, thanks for your message. These articles are not available in PDF, but you are welcome to copy and paste them from the website, as long as you add the reference: https://empoweredparents.co/problem-solving-activities-preschoolers/ Thanks for reading!

Wednesday 20th of May 2020

Very very useful content. Good work. Thank you.

Friday 22nd of May 2020

Thanks Ann.

Tuesday 19th of May 2020

Would like to download the free activity pack please.

Hi Kelly, Please download the activity pack on this page: www.empoweredparents.co

Popular searches in the last week:

• 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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Early Years Careers

Problem solving in Early Years Settings

5th January 2016 by Kelly Leave a Comment

  The role of the practitioner in supporting children’s problem solving skills

Some early years practitioners struggle with the definition of problem solving. It is all about the process of working through ideas to reach a solution. It is also about processing information and evaluating ideas and concepts.

As children are constantly learning new ideas, skills and concepts, these will all help them develop their problem solving skills.  For those working in childcare it is important to remember that problem solving is not an activity it is the process in which children go through to find a solution.

Children need to be able to use their thinking skills and practitioner should encourage children think creatively. As well as all this learning the development of children’s language is fundamental as they need to be able to vocalise their thoughts. The development of language allows children interact with other s and share those ideas to help find the right solution

How can adults help support children’s problem solving skills

• Asking questions- adults need to use their skills to ask the right questions as these questions may hold the key to helping children solve that problem.
• Breaking down the task – Adults can help children break the task up to help them solve the problem in smaller steps.
• Scaffold the child’s learning – be careful not to answer the child’s questions yourself, questions should be open ended this will allow the children think, plan, predict, explain and recall as well as ask questions back.
• Listen attentively – practitioners should listen to children’s answers as this will show to the child that what they are thinking is important.
• Try not to overuse questioning.

Acting as an effective model is a key factor when supporting children’s problem solving skills, as children will look to adults for support and guidance.

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Exploring Problem-Solving in Early Years Mathematics | EYFS/KS1

This webinar will provide headteachers, mathematics leads, teachers and teaching assistants with practical guidance and methods they can use to nurture and develop pupils’ problem-solving skills in early years and KS1 mathematics.

• Description
• Learning Outcomes
• Institution

Webinar Duration: 46 minutes (approx.)

This webinar will provide headteachers, mathematics leads, teachers and teaching assistants with practical guidance and methods they can use to nurture and develop pupils’ problem-solving skills in maths.

Problem-solving has long been at the heart of the mathematics curriculum. Teaching children how to problem solve in mathematics can support children’s ability to critically evaluate, encourage independence and develop their skills in reasoning and creativity. It is also an essential part of developing mastery of the subject.

In this webinar the Association of Teachers of Mathematics (ATM), who aim to support the teaching and learning of mathematics in the UK, will explore strategies that schools can use to approach problem-solving in maths with the youngest pupils which are creative and engaging and reflect a better understanding of the needs of the learner.

• Understanding how to introduce learning and problem solving in mathematics which supports children’s ability to problem solve and improve critical thinking skills.
• Recognising successful techniques that can be used in the classroom which improve reasoning in mathematics.
• Appreciating the importance of making maths problem-solving learning tailored towards the needs of children and ensuring continuous sharing and evaluation of different methods used.
• Understanding what is meant by ‘problem-solving skills’ and how to nurture an environment which encourages curiosity and positive attitudes.
• Building a culture which supports teaching and learning through playing and exploring, active learning and creative and critical thinking.

Since 1994, Helen has been an independent educational consultant specialising in developing the teaching and learning of primary mathematics. In July 2014, she completed her doctorate with the University of Roehampton, London. She is interested in engaging all learners mathematically, and how we might nurture effective and supportive learning communities in classrooms in a current educational climate geared to high-stakes testing. Helen is passionate about all children being given opportunities to become confident mathematical thinkers, through the establishment of a classroom culture that nurtures curious learners.

Helen has taught children across the full primary range and has a particular interest and expertise in early years and KS1 mathematics. Her work involves researching and teaching mathematics alongside colleagues in school and contributing to in-service training courses and conferences. Helen is a long-term, active member of the Association of Teachers of Mathematics (ATM).

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Early Years Foundation Stage Activities

Explanation of Our EYFS Format

Here you can find out more about how we structure our EYFS activities.

Early Years Activities - Number

Early Years Activities - Measures

Early Years Activities - Shape and Space

Early Years Activities - Pattern