problem solving maths early years

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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Making Math Meaningful for Young Children

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Children are natural mathematicians. They push and pull toys, stack blocks, and fill and empty cups of water in the bathtub. All of these activities allow young children to experience math concepts as they experiment with spatial awareness, measurement, and problem solving (ETFO 2010; NAEYC 2010). Young children easily learn as they describe, explain, and consider the ideas from their immediate environment. Am I as tall as Yancey? How can I find out? I know! We can both stand next to each other in front of the mirror.

Early math is not about the rote learning of discrete facts like how much 5 + 7 equals. Rather, it’s about children actively making sense of the world around them. Unlike drills or worksheets with one correct answer, open-ended, playful exploration encourages children to solve problems in real situations. Because the situations are meaningful, children can gain a deeper understanding of number, quantity, size, patterning, and data management (Grossman 2012). For example, it is easier to understand what six means when applied to a real-life task such as finding six beads to string on a necklace or placing one cracker on each of six plates.

Creating a math-rich classroom

Research suggests that preschool classrooms can be the ideal environment for learning about math (ETFO 2010). Children sort materials into corresponding bins at cleanup time, explore patterns and shapes while creating at the art table, tell time while using the visual schedule to predict which activities come next, and measure when they squeeze their bodies through the climber on the playground (ETFO 2010).

Preschool classrooms also celebrate curiosity and risk-taking as children engage in inquiry-based exploration at various learning centers and outdoors. Interesting items in the environment encourage children to find answers to their questions and solve problems across all curricular domains. Children measure as they clap out the beats to music. They repeat rhythmic patterns as they dance. They describe, sort, and count objects in the discovering science center and look for patterns while on a nature walk. They count the rungs while climbing up the ladder to the loft. Many familiar children’s songs, stories, and poems contain mathematical messages that help familiarize children with counting, measuring, and patterning. For example, children can count along with “One, two, buckle my shoe” and “Ten little monkeys jumping on the bed.”

In addition to offering blocks, buttons, and other loose materials to touch and explore, teachers can ask open-ended questions that promote problem solving and probe and challenge children’s mathematical thinking and reasoning (Ontario Ministry of Education 2010). Such questions are not meant to elicit correct answers but rather to engage children in open-ended conversations that promote high-level thinking, such as What do you notice about these objects? How might we sort the toys? One of the foundations of play-based learning is that the teacher is active in the play, asking questions and adding knowledge and insight. The teacher learns together with children throughout the inquiry process.

Every preschool classroom needs to be rich with materials that encourage math exploration and learning. A well-stocked math and manipulatives center includes found objects such as shells, stones, bread tags, and sticks, as well as purchased materials. The center can include photos of completed geoboard creations or of children sorting coins in the dramatic play center. There might be narratives of children’s learning, such as transcripts of children’s comments and conversations, and artwork featuring pattern or shape exploration. Teachers can post documentation of math learning as a way of encouraging children to reflect on past experiences and motivate them to plan and revise future ones. These visuals can inspire even deeper, more connected learning. They help children maintain their focus on a particular topic, refine and expand their ideas, communicate their learning to others, and reflect on their experiences before making new plans.

Encourage children to play mathematically

Young children need to see themselves as capable mathematicians. Child-guided and child-focused explorations and teacher-guided math activities help children practice and consolidate their learning. This helps them feel confident about what they know and can do. Although many preschoolers learn some math concepts on their own, it’s important for teachers to include math in authentic experiences, resulting in a deeper understanding by children (ETFO 2010).

In addition to creating a rich math and manipulatives learning center, teachers can encourage children to use math tools and strategies in all areas of the classroom. Children might use a set of plastic links to measure their buildings in the block center, use play money to pay for a train ticket in the dramatic play center, and use rulers to measure the growth of spring bulbs in the discovering science center. Take a set of scales outdoors so children can figure out who found the heaviest rock. Using math tools for real-life tasks frees both teachers and children to act spontaneously, resulting in richer interactions and a calmer learning environment (Wien 2004).

In addition to the freedom to use materials in authentic ways, children also need freedom of time and space to deeply engage in math. The preschool schedule should include plenty of time for uninterrupted play so children have the time they need to work on sustained tasks of interest. This allows children to explore materials thoroughly, often resulting in more complex and evolved experiences over time. If a child spends all of his time at one learning center, he is not missing out on learning opportunities elsewhere. Instead, his deep connection to the center is often indicative of rich learning. Teachers can model the use of other materials at the center, such as using writing materials to draw plans for a structure to be built, or pose challenges that encourage the child to think beyond her play, such as How tall can you build this tower before it falls?

To support learning, it is important to encourage children to communicate their explorations and findings. Teachers can establish a routine through which children share their experiences at group time. For example, a child might explain how he built a structure with blocks, do a dance with repeating steps, or share a photo of a complex pattern made with colorful buttons. While circulating through the room, a teacher might notice high-quality work and suggest that a child share it with her peers during group time. The child making the presentation grows in confidence and the onlookers may want to try the experience themselves.

Most children enter preschool knowing a lot about math. In a safe and supportive classroom they will feel comfortable taking risks and engaging in self-directed problem solving. Weaving math into all areas of the curriculum will heighten children’s play experiences and allow all learners to experience success. Children will soon see themselves as capable mathematicians who apply their skills in a number of ways. Their growing math skills, confidence, and interests will serve them well in school and life.

Supporting Dual language learners

Children who are DLLs can learn math concepts and skills without being fluent in their second language. Much of the meaning is found in the right materials. If families send to the classroom familiar items from home, the children will know the name and function of the items in their home language. They can use this prior knowledge as a foundation to help them learn math. For example, young children may not understand how to sort plastic shapes, but they already know it is important to sort the baby’s socks and daddy’s socks in separate piles—a math activity that has real-life meaning in any language.

ETFO (Elementary Teachers’ Federation of Ontario). 2010. Thinking It Through: Teaching and Learning in the Kindergarten Classroom . Toronto, ON: ETFO.

Grossman, S. 2012. “The Worksheet Dilemma: Benefits of Play-Based Curricula.” Early Childhood News . www.earlychildhoodnews.com/earlychildhood/article_view.aspx?ArticleID=134 .

NAEYC. 2010. “Early Childhood Mathematics: Promoting Good Beginnings.” A joint position statement of NAEYC and the National Council of Teachers of Mathematics (NCTM). www.naeyc.org/files/naeyc/file/positions/psmath.pdf .

Ontario Ministry of Education. 2010. The Full-Day Early Learning-Kindergarten Program (draft version). Toronto, ON: Queen’s Printer for Ontario. www.edu.gov.on.ca/eng/curriculum/elementary/kindergarten_english_june3.pdf .

Wien, C.A. 2004. “From Policing to Participation: Overturning the Rules and Creating Amiable Classrooms.” Young Children 59 (1): 34–40. www.naeyc.org/files/yc/file/200401/Wien.pdf .

Deanna Pecaski McLennan , PhD, is a kindergarten educator and author in Windsor, Ontario, Canada. She loves exploring mathematics through a play-, inquiry-based approach. She enjoys sharing her classroom practice and connecting with others using social media. @McLennan1977

Vol. 8, No. 1

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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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• February 25, 2016

Help Your Child Develop Early Math Skills

Before they start school, most children develop an understanding of addition and subtraction through everyday interactions. Learn what informal activities give children a head start on early math skills when they start school.

Children are using early math skills throughout their daily routines and activities. This is good news as these skills are important for being ready for school. But early math doesn’t mean taking out the calculator during playtime. Even before they start school, most children develop an understanding of addition and subtraction through everyday interactions. For example, Thomas has two cars; Joseph wants one. After Thomas shares one, he sees that he has one car left (Bowman, Donovan, & Burns, 2001, p. 201). Other math skills are introduced through daily routines you share with your child—counting steps as you go up or down, for example. Informal activities like this one give children a jumpstart on the formal math instruction that starts in school.

What math knowledge will your child need later on in elementary school? Early mathematical concepts and skills that first-grade mathematics curriculum builds on include: (Bowman et al., 2001, p. 76).

• Understanding size, shape, and patterns
• Ability to count verbally (first forward, then backward)
• Recognizing numerals
• Identifying more and less of a quantity
• Understanding one-to-one correspondence (i.e., matching sets, or knowing which group has four and which has five)

Key Math Skills for School

More advanced mathematical skills are based on an early math “foundation”—just like a house is built on a strong foundation. In the toddler years, you can help your child begin to develop early math skills by introducing ideas like: (From Diezmann & Yelland, 2000, and Fromboluti & Rinck, 1999.)

Number Sense

This is the ability to count accurately—first forward. Then, later in school, children will learn to count backwards. A more complex skill related to number sense is the ability to see relationships between numbers—like adding and subtracting. Ben (age 2) saw the cupcakes on the plate. He counted with his dad: “One, two, three, four, five, six…”

Representation

Making mathematical ideas “real” by using words, pictures, symbols, and objects (like blocks).  Casey (aged 3) was setting out a pretend picnic. He carefully laid out four plastic plates and four plastic cups: “So our whole family can come to the picnic!” There were four members in his family; he was able to apply this information to the number of plates and cups he chose.

Spatial sense

Later in school, children will call this “geometry.” But for toddlers it is introducing the ideas of shape, size, space, position, direction and movement.  Aziz (28 months) was giggling at the bottom of the slide. “What’s so funny?” his Auntie wondered. “I comed up,” said Aziz, “Then I comed down!”

Measurement

Technically, this is finding the length, height, and weight of an object using units like inches, feet or pounds. Measurement of time (in minutes, for example) also falls under this skill area.  Gabriella (36 months) asked her Abuela again and again: “Make cookies? Me do it!” Her Abuela showed her how to fill the measuring cup with sugar. “We need two cups, Gabi. Fill it up once and put it in the bowl, then fill it up again.”

This is the ability to make a good guess about the amount or size of something. This is very difficult for young children to do. You can help them by showing them the meaning of words like  more, less, bigger, smaller, more than, less than. Nolan (30 months) looked at the two bagels: one was a regular bagel, one was a mini-bagel. His dad asked: “Which one would you like?” Nolan pointed to the regular bagel. His dad said, “You must be hungry! That bagel is bigger. That bagel is smaller. Okay, I’ll give you the bigger one. Breakfast is coming up!”

Patterns are things—numbers, shapes, images—that repeat in a logical way. Patterns help children learn to make predictions, to understand what comes next, to make logical connections, and to use reasoning skills.  Ava (27 months) pointed to the moon: “Moon. Sun go night-night.” Her grandfather picked her up, “Yes, little Ava. In the morning, the sun comes out and the moon goes away. At night, the sun goes to sleep and the moon comes out to play. But it’s time for Ava to go to sleep now, just like the sun.”

Problem-solving

The ability to think through a problem, to recognize there is more than one path to the answer. It means using past knowledge and logical thinking skills to find an answer.  Carl (15 months old) looked at the shape-sorter—a plastic drum with 3 holes in the top. The holes were in the shape of a triangle, a circle and a square. Carl looked at the chunky shapes on the floor. He picked up a triangle. He put it in his month, then banged it on the floor. He touched the edges with his fingers. Then he tried to stuff it in each of the holes of the new toy. Surprise! It fell inside the triangle hole! Carl reached for another block, a circular one this time…

Math: One Part of the Whole

Math skills are just one part of a larger web of skills that children are developing in the early years—including language skills, physical skills, and social skills. Each of these skill areas is dependent on and influences the others.

Trina (18 months old) was stacking blocks. She had put two square blocks on top of one another, then a triangle block on top of that. She discovered that no more blocks would balance on top of the triangle-shaped block. She looked up at her dad and showed him the block she couldn’t get to stay on top, essentially telling him with her gesture, “Dad, I need help figuring this out.” Her father showed her that if she took the triangle block off and used a square one instead, she could stack more on top. She then added two more blocks to her tower before proudly showing her creation to her dad: “Dada, Ook! Ook!”

You can see in this ordinary interaction how all areas of Trina’s development are working together. Her physical ability allows her to manipulate the blocks and use her thinking skills to execute her plan to make a tower. She uses her language and social skills as she asks her father for help. Her effective communication allows Dad to respond and provide the helps she needs (further enhancing her social skills as she sees herself as important and a good communicator). This then further builds her thinking skills as she learns how to solve the problem of making the tower taller.

What You Can Do

The tips below highlight ways that you can help your child learn early math skills by building on their natural curiosity and having fun together. (Note: Most of these tips are designed for older children—ages 2–3. Younger children can be exposed to stories and songs using repetition, rhymes and numbers.)

Play with shape-sorters. Talk with your child about each shape—count the sides, describe the colors. Make your own shapes by cutting large shapes out of colored construction paper. Ask your child to “hop on the circle” or “jump on the red shape.”

Count and sort.

Gather together a basket of small toys, shells, pebbles or buttons. Count them with your child. Sort them based on size, color, or what they do (i.e., all the cars in one pile, all the animals in another).

Place the call.

With your 3-year-old, begin teaching her the address and phone number of your home. Talk with your child about how each house has a number, and how their house or apartment is one of a series, each with its own number.

What size is it?

Notice the sizes of objects in the world around you: That pink pocketbook is the biggest. The blue pocketbook is the smallest. Ask your child to think about his own size relative to other objects (“Do you fit under the table? Under the chair?”).

You’re cookin’ now!

Even young children can help fill, stir, and pour. Through these activities, children learn, quite naturally, to count, measure, add, and estimate.

Walk it off.

Taking a walk gives children many opportunities to compare (which stone is bigger?), assess (how many acorns did we find?), note similarities and differences (does the duck have fur like the bunny does?) and categorize (see if you can find some red leaves). You can also talk about size (by taking big and little steps), estimate distance (is the park close to our house or far away?), and practice counting (let’s count how many steps until we get to the corner).

Picture time.

Use an hourglass, stopwatch, or timer to time short (1–3 minute) activities. This helps children develop a sense of time and to understand that some things take longer than others.

Point out the different shapes and colors you see during the day. On a walk, you may see a triangle-shaped sign that’s yellow. Inside a store you may see a rectangle-shaped sign that’s red.

Read and sing your numbers.

Sing songs that rhyme, repeat, or have numbers in them. Songs reinforce patterns (which is a math skill as well). They also are fun ways to practice language and foster social skills like cooperation.

Start today.

Use a calendar to talk about the date, the day of the week, and the weather. Calendars reinforce counting, sequences, and patterns. Build logical thinking skills by talking about cold weather and asking your child: What do we wear when it’s cold? This encourages your child to make the link between cold weather and warm clothing.

Pass it around.

Ask for your child’s help in distributing items like snacks or in laying napkins out on the dinner table. Help him give one cracker to each child. This helps children understand one-to-one correspondence. When you are distributing items, emphasize the number concept: “One for you, one for me, one for Daddy.” Or, “We are putting on our shoes: One, two.”

Big on blocks.

Give your child the chance to play with wooden blocks, plastic interlocking blocks, empty boxes, milk cartons, etc. Stacking and manipulating these toys help children learn about shapes and the relationships between shapes (e.g., two triangles make a square). Nesting boxes and cups for younger children help them understand the relationship between different sized objects.

Tunnel time.

Open a large cardboard box at each end to turn it into a tunnel. This helps children understand where their body is in space and in relation to other objects.

The long and the short of it.

Cut a few (3–5) pieces of ribbon, yarn or paper in different lengths. Talk about ideas like long and short. With your child, put in order of longest to shortest.

Learn through touch.

Cut shapes—circle, square, triangle—out of sturdy cardboard. Let your child touch the shape with her eyes open and then closed.

Pattern play.

Have fun with patterns by letting children arrange dry macaroni, chunky beads, different types of dry cereal, or pieces of paper in different patterns or designs. Supervise your child carefully during this activity to prevent choking, and put away all items when you are done.

Laundry learning.

Make household jobs fun. As you sort the laundry, ask your child to make a pile of shirts and a pile of socks. Ask him which pile is the bigger (estimation). Together, count how many shirts. See if he can make pairs of socks: Can you take two socks out and put them in their own pile? (Don’t worry if they don’t match! This activity is more about counting than matching.)

Playground math.

As your child plays, make comparisons based on height (high/low), position (over/under), or size (big/little).

Dress for math success.

Ask your child to pick out a shirt for the day. Ask: What color is your shirt? Yes, yellow. Can you find something in your room that is also yellow? As your child nears three and beyond, notice patterns in his clothing—like stripes, colors, shapes, or pictures: I see a pattern on your shirt. There are stripes that go red, blue, red, blue. Or, Your shirt is covered with ponies—a big pony next to a little pony, all over your shirt!

Graphing games.

As your child nears three and beyond, make a chart where your child can put a sticker each time it rains or each time it is sunny. At the end of a week, you can estimate together which column has more or less stickers, and count how many to be sure.

Bowman, B.T., Donovan, M.S., & Burns, M.S., (Eds.). (2001).  Eager to learn: Educating our preschoolers.  Washington, DC: National Academy of Sciences.

Diezmann, C., & Yelland, N. J. (2000). Developing mathematical literacy in the early childhood years. In Yelland, N.J. (Ed.),  Promoting meaningful learning: Innovations in educating early childhood professionals.  (pp.47–58). Washington, DC: National Association for the Education of Young Children.

Fromboluti, C. S., & Rinck, N. (1999 June).  Early childhood: Where learning begins.  U.S. Department of Education, Office of Educational Research and Improvement, National Institute on Early Childhood Development and Education. Retrieved on May 11, 2018 from  https://www2.ed.gov/pubs/EarlyMath/title.html

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Early Years Careers

How to promote problem solving in the early years

5th November 2015 by Kelly Leave a Comment

Ways to incorporate problem solving in the Early Years

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

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

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

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

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

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

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10 Simple Activities to Teach Your Preschooler Problem Solving

By: Author Tanja McIlroy

Posted on Last updated: 9 May 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.

• Four wooden jigsaw puzzles: a fish, a dog, a cat, and a bird
• 12-piece puzzles

2. Memory games

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

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. 

(Get your own set of printable memory card games here!)

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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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.

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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 .

• Non-Toxic Formula: Our sidewalk chalk is specially formulated to minimize chalk dust and is safe for indoor...
• Convenient Packaging: Comes in a 20-piece plastic bucket with a lid and handle for easy transport and storage.

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

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Home > Learning & Development

Learning and Development

Sand and water table – Getting hands-on with maths

• Written By: Carole Skinner
• Subject: Maths
• View page as PDF: Download Now

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Early years consultant Carol Skinner explains how to use your sand and water table to stimulate children’s understanding of maths…

Sand and water are wonderful mediums to use to develop children’s maths knowledge, skills and understanding. Playing with them involves, amongst other things, investigating, experimenting, constructing and problem-solving – and, lest we forget, it can be lots of fun.

The maths content in the  Early Years Foundation Stage Framework  is about understanding number and calculation, becoming familiar with measuring and working with shapes and solving problems .

We all know that children are constantly trying to put their ideas and theories to the test by hands-on ‘doing’, and the presence of sand or water gives them the opportunity to do just that.

As they play with the sand and water, children acquire and practise new maths skills – from counting how many plastic fish they managed to net, to deciding the best bucket to use to make the largest sand pie, just the sort of activities that give children opportunities to count and measure, and to find out about shapes in a meaningful way.

As such there need to be plenty of opportunities for children to experiment with the sand and water, and to have opportunities to make decisions about what equipment to use and how to use it.

You will need to spend time preparing the environment, including the physical space, selecting and gathering props and displaying them in a way that invites their use. 

You can encourage children’s independence and responsibility by expecting the children to share equipment and take turns.

Put in place strategies that support children in playing cooperatively and learning to be active members of the group or pair when they are using the sand or water.

You should supply additional materials to extend their experiences as well as model uses for particular props by playing alongside and demonstrating how to use a funnel or a rake.

It’s a good idea to make sure there are at least a couple of small dustpans and brushes or mops and buckets nearby so that children can be involved in clearing up.

Setting up the sand play

Wet and dry sand have very different properties, so the children need to experiment with and experience both types, as well as occasionally adding lots of water to turn the sand into very wet sloppy sand.

Whether the sand is damp or dry it should be deep enough to dig, scoop or sieve with – children really do need to be able to fill two or three containers each without running out of sand.

You should provide a good variety of equipment (hanging close by is better than cluttering up the sand tray). Include some natural materials such as shells, drift wood and small stones that can be mixed into the sand or used to embellish sand constructions.

Make sure there is a range of different-sized plastic combs, shapes and small sticks for pattern making. Introduce lentils, rice, small buttons or counters to make the sand gritty and then sieve them out.

Sometimes children should have access to sand in small containers and shallow trays on a tabletop as well as in a conventional sand and water table. On these occasions, provide miniature equipment such as measuring spoons, tea strainers and egg cups.

Children should be able to experience digging in a large amount of sand in an outdoor sandpit or at the very least a tarpaulin on the ground filled with sand – something they can walk on barefoot. A large tyre or plastic paddling pool filled with sand can make a quick instant outdoor sand pit.

10 maths experiences with sand

The mathematically good things children do when they play with sand include lining things up, counting them, making patterns, comparing sizes and using moulds and containers, burying treasure and digging it up again. You should encourage the following play activities to maximise maths learning:

1. Counting how many spoonfuls, shovelfuls or handfuls it takes to fill a container

2. Lining up and counting how many objects have been found in a sieve

3. Making handprints in the sand and then making one more

4. Arranging a row of full containers and nearly full containers

5. Pressing shapes in damp sand to make a pattern

6. Sieving out beads, small pebbles and large sequins and finding the total

7. Sorting the sand tools into things to dig with and containers to fill

8. Using a stick to draw a very, very long line in the sand

9. Observing how quickly/slowly the sand flows through a sieve

10. Filling and emptying containers and using size language

Adult-directed sand play

● Together make a line of five sand castles and then increase the number to 10 castles.

● Use damp sand and four different shaped containers to make some 3D shapes. Challenge the children to say which container made which shape.

● Make two sand pies and discuss what’s the same and what’s different about them.

● Bury seashells, stones and other small objects in the sand to find, count, sort and classify. Record by drawing or photos how many of each type have been dug up.

Setting up the water play

Children enjoy playing with water. When they are investigating it they will have much more fun, and learn much more, if they have access to water both indoors and outside. The indoor sand and water table should be as large as space allows – transparent trays are a good choice, as children can see changes of water colour and whether objects are really sinking or just hovering halfway between the surface and the bottom of the tray – whilst the outdoor water should include, if at all possible, a hose, some watering cans and plastic guttering and pipes. 

Simple changes can add new experiences such as warm water, ice cubes, chopped jelly, food colouring and sometimes bubbles. Buy a sack of shells from a garden centre to put in the water and add different perfumes with bath salts. 

The properties of water that we want young children to experience, recognise and discuss can also help them develop maths knowledge and skills. Of course, a lot of the activity at the sand and water table will involve pouring and measuring, but ask open-ended questions such as, “I wonder if that amount will fit in this jug?” or “Will the water stay in a sieve?” or “What’s the best way to find out which cup holds the most?”

Support children in developing pouring skills – use funnels where needed. As their skills increase, show how to mark the water level by using an elastic band around the container.

10 maths experiences with water

When children are playing with water there are lots of additional ideas and resources you can provide that will enhance their mathematical play, including collecting and measuring snow and rainwater, looking at reflections in puddles and dissolving substances such as salt, sugar and soap flakes in water. You could also try encouraging the following play activities: 

1. Sorting, counting and comparing objects that float

2. Counting how many pebbles were added to a small bucket of water before it spilt out

3. Netting slimy worms of cooked spaghetti and comparing their lengths

4. Using a hose to make water patterns on the ground

5. Squeezing plastic bottles to empty and fill them up

6. Deciding when a container is nearly half-full

7. Pouring water into a funnel to fill various containers

8. Showing where to hold the hose to make rainbows in the sun

9. Sorting into two sets the objects that float and those that sink

10. Filling containers until the water overflows and discussing what that means

Adult-directed water play

● Put some plastic sea creatures in the sand and water table, add blue food colouring and use aquarium nets or strainers to catch the creatures put them in a bucket and count how many were caught. Release the creatures back to the sea once they have been counted.

● Pour water down a slope or gutter and decide if you make the slope steeper whether the water will run faster or slower

● Add bubble mixture to the sand and water table and sponge numerals. Invite the children to net a number, name it and match it to a plastic-covered number line.

● Pour some water onto a hard surface in the  outdoor area  to make a puddle. Measure how big it is by laying out and counting pebbles around the edge of the puddle. Discuss other ways of measuring its size.

● Investigate the way water spouts out of holes. Use a skewer to pierce holes in an empty plastic drink bottle. Make the holes in a circle around the bottle. Investigate tilting the bottle to switch the holes on and off. Next time make the holes in a different pattern.

Playing pirates

Using sand and water play as part of a cross-curricular mini-project…

• Write letters, put them in plastic bottles and float on the water
• Draw maps to show where the treasure is buried
• Design flags to hoist on the pirate ship
• Investigate materials for boat-making
• Sing pirate songs such as This Way, That Way, Over the Deep Blue Sea and use actions to accompany the words
• Read these books and vote on the best pirate story – The Night Pirates by Peter Harris & Deborah Allwright (Egmont), Pirate Ship Adventure by Nicola Baxter (Armadillo Books), Noisy, Noisy Pirates illustrated by Emma Dodd (Ladybird Books)

Carole Skinner is an independent early years consultant and founder associate of Early Education. She is the co-author of  Foundations of Mathematics: An Active Approach to Number, Shape and Measures in the Early Years .

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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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Research on early childhood mathematics teaching and learning

• Survey Paper
• Open access
• Published: 23 June 2020
• Volume 52 , pages 607–619, ( 2020 )

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• Camilla Björklund   ORCID: orcid.org/0000-0001-5436-537X 1 ,
• Marja van den Heuvel-Panhuizen 2 , 3 &
• Angelika Kullberg 1  

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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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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.

Adenegan, K. E. (2016). An investigation into the writing and computational skills of school pupils of age 3–6: Implications for early childhood numeracy. In Paper presented at the 13th International Congress on Mathematical Education, Hamburg, Germany .

Alpaslan, Z. G., & Erden, F. T. (2015). The status of early childhood mathematics education research in the last decade. In CERME9—Ninth Congress of the European Society for Research in Mathematics Education (pp. 1933–1939). Charles University in Prague, Faculty of Education; ERME, Feb 2015, Prague, Czech Republic.

Anderson, A., & Anderson, J. (2018). Math-in-context: The types of math preschoolers ‘do’ at home. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), Contemporary research and perspectives on early childhood mathematics education (pp. 183–202). Cham: Springer Nature.

Chapter   Google Scholar  

Ashcraft, M. H., Donley, R., Halas, M. A., & Vakali, M. (1992). Working memory, automaticity and problem difficulty. In J. I. D. Campbell (Ed.), The nature and origins of mathematical skills, advances in psychology, vol. 91 (pp. 301–329). Amsterdam: North-Holland.

Askew, M., & Venkat, H. (2020). Deconstructing South African Grade 1 learners’ awareness of number in terms of cardinality, ordinality and relational understandings. ZDM . https://doi.org/10.1007/s11858-020-01132-2 . (This issue) .

Article   Google Scholar  

Aunio, P., & Niemivirta, M. (2010). Predicting children’s mathematical performance in grade one by early numeracy. Learning and Individual Differences, 20 (5), 427–435.

Baccaglini-Frank, A. (2018). What schemes do preschoolers’ develop when using multi-touch applications to foster number sense (and why)? In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), Contemporary research and perspectives on early childhood mathematics education (pp. 223–243). Cham: Springer Nature.

Baccaglini-Frank, A., Carotenuto, G., & Sinclair, N. (2020). Eliciting preschoolers’ number abilities using open, multi-touch environments. ZDM . https://doi.org/10.1007/s11858-020-01144-y . (This issue) .

Bakos, S., & Sinclair, N. (2019). Pips (times) Pods: Dancing towards multiplicative thinking. In Eleventh Congress of the European Society for Research in Mathematics Education (CERME11) , Utrecht University, Feb 2019, Utrecht, Netherlands.

Bartolini Bussi, M. G. (2020). Early years mathematics: Semiotic and cultural mediation. In M. Carlsen, I. Erfjord, & P. S. Hundeland (Eds.), Mathematics education in the early years. Results from the POEM4 conference, 2018 (pp. 1–21). Berlin: Springer.

Google Scholar  

Björklund, C., Kullberg, A., Runesson Kempe, A., Reis, M., Clements, D., Sarama, J., Levenson, E., Barkai, R., Tirosh, D., Tsamir, P., Askew, M., Venkat, H., & Hannula-Sormunen, M. (2018). Learning and teaching of arithmetic skills in early years. (Research Forum). In E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter (Eds.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (vol. 1) (pp. 125–155). Umeå, Sweden: PME.

Björklund, C., & Runesson Kempe, U. (2019). Framework for analysing children’s ways of experiencing numbers. In Eleventh Congress of the European Society for Research in Mathematics Education (CERME11) , Utrecht University, Feb 2019, Utrecht, Netherlands.

Bjørnebye, M. (2019). Pre-schoolers’ ability to synchronise multiple representations of numerosity in embodiment of a counting-on-strategy. In Eleventh Congress of the European Society for Research in Mathematics Education (CERME11) , Utrecht University, Feb 2019, Utrecht, Netherlands.

Bjørnebye, M., & Sigurjonsson, T. (2020). Young children’s cross-domain mapping of numerosity in path navigation. In M. Carlsen, I. Erfjord, & P. S. Hundeland (Eds.), Mathematics education in the early years. Results from the POEM4 conference, 2018 (pp. 109–126). Cham: Springer.

Bojorque, G., Torbeyns, J., Hannula-Sormunen, M. M., Van Nijlen, D., & Verschaffel, L. (2018). Ecuadorian kindergartners’ spontaneous focusing on numerosity development: Contribution of numerical abilities and quality of mathematics education. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), Contemporary research and perspectives on early childhood mathematics education (pp. 69–86). Cham: Springer Nature.

Breive, S. (2019). Kindergarten teachers’ orchestration of mathematical learning activities: The balance between freedom and structure. In Eleventh Congress of the European Society for Research in Mathematics Education (CERME11) , Utrecht University, Feb 2019, Utrecht, Netherlands.

Bruns, J., Carlsen, M., Eichen, L., Erfjord, I., & Hundeland, P. S. (2020). Situational perception in mathematics (SPiM)—Results of a cross-country study in Austria and Norway. In M. Carlsen, I. Erfjord, & P. S. Hundeland (Eds.), Mathematics education in the early years. Results from the POEM4 conference, 2018 (pp. 317–332). Cham: Springer.

Butterworth, B. (2005). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, 46 (1), 3–18. https://doi.org/10.1111/j.1469-7610.2005.00374.x .

Cai, J., Hwang, C., Jiang, C., & Silber, S. (2015). Problem-posing research in mathematics education: Some answered questions and unanswered questions. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 3–34). New York: Springer.

Carlsen, M., Erfjord, I., & Hundeland, P. S. (Eds.). (2020). Mathematics education in the early years. Results from the POEM4 conference, 2018 . Berlin: Springer.

Clements, D. H., Sarama, J., Baroody, A. J., & Joswick, C. (2020). Efficacy of a learning trajectory approach compared to a teach-to-target approach for addition and subtraction. ZDM . https://doi.org/10.1007/s11858-019-01122-z . (This issue) .

Cooke, A., & Bruns, J. (2018). Early childhood educators’ issues and perspectives in mathematics education. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), Contemporary research and perspectives on early childhood mathematics education (pp. 267–289). Cham: Springer Nature.

Donaldson, M. (1978). Children's minds . Glasgow: Fontana/Collins.

Dorier, J. L., & Coutat, S. (2016). Conceptualizing order in early school. In Paper presented at the 13th International Congress on Mathematical Education, Hamburg, Germany .

Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., et al. (2007). School readiness and later achievement. Developmental Psychology, 43 (6), 1428–1446. https://doi.org/10.1037/0012-1649.43.6.1428 .

Elia, I. (2018). Observing the use of gestures in young children’s geometric thinking. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), Contemporary research and perspectives on early childhood mathematics education (pp. 159–182). Cham: Springer Nature.

Elia, I., Mulligan, J., Anderson, A., Baccaglini-Frank, A., & Benz, C. (Eds.). (2018). Contemporary research and perspectives on early childhood mathematics education. ICME-13 monographs . Cham: Springer Nature.

Ellemor-Collins, D., & Wright, R. (2009). Structuring numbers 1–20: Developing facile addition and subtraction. Mathematics Education Research Journal, 21 (2), 50–75.

Fletcher, N., & Ginsburg, H. (2016). Teaching symmetry in the early childhood classroom: Using software to facilitate discourse and promote understanding of symmetric transformations. In Paper presented at the 13th International Congress on Mathematical Education, Hamburg, Germany .

Fritz-Stratmann, A., Ehlert, M., & Herzog, A. (2016). From thought to reality— Implementation of an in-school mathematics training in South Africa. In Paper presented at the 13th International Congress on Mathematical Education, Hamburg, Germany .

Grando, R. C., & Lopes, C. E. (2020). Creative insubordination of teachers proposing statistics and probability problems to children. ZDM . https://doi.org/10.1007/s11858-020-01166-6 . (This issue) .

Hannula-Sormunen, M. M., Lehtinen, E., & Räsänen, P. (2015). Preschool children’s spontaneous focusing on numerosity, subitizing, and counting skills as predictors of their mathematical performance seven years later at school. Mathematical Thinking and Learning, 17 (2–3), 155–177. https://doi.org/10.1080/10986065.2015.1016814 .

Henschen, E. (2016). Mathematical content of play activities in kindergarten, exemplified on blockplay activities. In Poster presented at the 13th International Congress on Mathematical Education, Hamburg, Germany .

Hundeland, P. S., Carlsen, M., & Erfjord, I. (2020). Qualities of mathematical discourses in Kindergartens. ZDM . https://doi.org/10.1007/s11858-020-01146-w . (This issue) .

Karsli, E. (2016). Young children’s embodied mathematical practices in a pre-K classroom. In Paper presented at the 13th International Congress on Mathematical Education, Hamburg, Germany .

Keuch, S., & Brandt, B. (2020). ‘You are already bigger than the giraffe!’ The use of adjectives in measurement activities in Kindergarten. In M. Carlsen, I. Erfjord, & P. S. Hundeland (Eds.), Mathematics education in the early years. Results from the POEM4 conference, 2018 (pp. 369–384). Cham: Springer.

Kilpatrick, J. (2014). History of research in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education . Dordrecht: Springer. https://doi.org/10.1007/978-94-007-4978-8_71

Krajewski, K., & Schneider, W. (2009). Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a four-year longitudinal study. Learning and Instruction, 19 (6), 513–526.

Kullberg, A., & Björklund, C. (2020). Preschoolers’ different ways of structuring part-part-whole relations with finger patterns when solving an arithmetic task. ZDM . https://doi.org/10.1007/s11858-019-01119-8 . (This issue) .

LeFevre, J.-A., Skwarchuk, S.-L., Smith-Chant, B. L., Fast, L., Kamawar, D., & Bisanz, J. (2009). Home numeracy experiences and children’s math performance in the early school years. Canadian Journal of Behavioural Science, 41 , 55–66. https://doi.org/10.1037/a0014532 .

Lembrér, D. (2020). Parents’ valuing of mathematics for young children. In M. Carlsen, I. Erfjord, & P. S. Hundeland (Eds.), Mathematics education in the early years. Results from the POEM4 conference, 2018 (pp. 403–420). Cham: Springer.

Levine, S., Suriyakham, L. W., Rowe, M., Huttenlocher, J., & Gunderson, E. (2010). What counts in the development of young children’s number knowledge? Developmental Psychology, 46 (5), 1309–1319.

Li, L., Zhou, X., Gao, X., & Tu, D. (2020). The development and influencing factors of Kindergarteners’ mathematics problem solving based on cognitive diagnosis assessment. ZDM . https://doi.org/10.1007/s11858-020-01153-x . (This issue) .

Lossius, M., & Lundhaug, T. (2020). Mathematical problem-solving visualised in outdoor activities. In M. Carlsen, I. Erfjord, & P. S. Hundeland (Eds.), Mathematics education in the early years. Results from the POEM4 conference, 2018 (pp. 127–141). Cham: Springer.

Lüken, M. (2019). Using finger patterns—The case of communicating age. In Eleventh Congress of the European Society for Research in Mathematics Education (CERME11) , Utrecht University, Feb 2019, Utrecht, Netherlands.

Lüken, M., & Kampmann, R. (2018). The influence of fostering children’s patterning abilities on their arithmetic skills in Grade 1. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), Contemporary research and perspectives on early childhood mathematics education (pp. 55–66). Cham: Springer Nature.

McMullen, J., Hannula-Sormunen, M. M., & Lehtinen, E. (2015). Preschool spontaneous focusing on numerosity predicts rational number conceptual knowledge 6 years later. ZDM, 47 (5), 813–824. https://doi.org/10.1007/s11858-015-0669-4 .

Mulligan, J. T., & Mitchelmore, M. C. (2018). Promoting early mathematical structural development through an integrated assessment and pedagogical program. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), Contemporary research and perspectives on early childhood mathematics education (pp. 17–33). Cham: Springer Nature.

Mulligan, J., Oslington, G., & English, L. (2020). Supporting early mathematical development through a ‘pattern and structure’ intervention program. ZDM . https://doi.org/10.1007/s11858-020-01147-9 . (This issue) .

Nakken, A., Grimeland, Y., Nergard, B., & Thiel, O. (2016). Young children’s play in a mathematics room. In Poster presented at the 13th International Congress on Mathematical Education, Hamburg, Germany .

Paliwal, V., & Baroody, A. J. (2020). Cardinality principle understanding: The role of focusing on the subitizing ability. ZDM . https://doi.org/10.1007/s11858-020-01150-0 . (This issue) .

Palmér, H., & Björklund, C. (2020). Preschoolers’ ways of using fingers in numerical reasoning. In M. Carlsen, I. Erfjord, & P. S. Hundeland (Eds.), Mathematics education in the early years. Results from the POEM4 conference, 2018 (pp. 93–107). Cham: Springer.

Palmér, H., & Van Bommel, J. (2020). Young students posing problem-solving tasks: What does posing a similar task imply to students? ZDM . https://doi.org/10.1007/s11858-020-01129-x . (This issue) .

Passolunghi, M. C., & Costa, H. M. (2016). Working memory and early numeracy training in preschool children. Child Neuropsychology, 22 (1), 81–98.

Pruden, S., Levine, S., & Huttenlocher, J. (2011). Children’s spatial thinking: does talk about the spatial world matter? Developmental Science, 14 (6), 1417–1430.

Radford, L. (2020). Play and the production of subjectivities in preschool. In M. Carlsen, I. Erfjord, & P. S. Hundeland (Eds.), Mathematics education in the early years. Results from the POEM4 conference, 2018 (pp. 43–60). Cham: Springer.

Rathé, S., Torbeyns, J., De Smedt, B., Hannula-Sormunen, M. M., & Verschaffel, L. (2018). Kindergartners’ spontaneous focus on number during picture book reading. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), Contemporary research and perspectives on early childhood mathematics education (pp. 87–99). Cham: Springer Nature.

Rathé, S., Torbeyns, J., De Smedt, B., & Verschaffel, L. (2020). Are children’s spontaneous number focusing tendencies related to their home numeracy environment? ZDM . https://doi.org/10.1007/s11858-020-01127-z . (This issue) .

Reikerås, E. (2020). Relations between play skills and mathematical skills in toddlers. ZDM . https://doi.org/10.1007/s11858-020-01141-1 . (This issue) .

Reikerås, E., & Salomonsen, T. (2019). Weak mathematical skills at an early age: Persistent or temporary? Children with weak mathematical skills and their development from toddlers to preschoolers. Early Child Development and Care, 189 (4), 670–682. https://doi.org/10.1080/03004430.2017.1337753 .

Resnick, L. B. (1983). A developmental theory of number understanding. In H. Ginsburg (Ed.), The development of mathematical thinking (pp. 109–151). New York: Academic Press.

Rinvold, A. R. (2016). The difficulty of learning the three first numerosities. In Poster presented at the 13th International Congress on Mathematical Education, Hamburg, Germany .

Sinclair, N. (2018). Time, immersion and articulation: Digital technology for early childhood mathematics. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), Contemporary research and perspectives on early childhood mathematics education (pp. 205–221). Cham: Springer Nature.

Skwarchuk, S.-L., Sowinski, C., & LeFevre, J.-A. (2014). Formal and informal home learning activities in relation to children’s early numeracy and literacy skills: The development of a home numeracy model. Journal of Experimental Child Psychology, 121 , 63–84. https://doi.org/10.1016/j.jecp.2013.11.006 .

Sprenger, P., & Bentz, C. (2020). Children’s perception of structures when determining cardinality of sets: Results of an eye-tracking study with five-year-old children. ZDM . https://doi.org/10.1007/s11858-020-01137-x . (This issue) .

Sprenger, P., & Benz, C. (2019). Perceiving and using structures in sets—The contribution of eye-tracking in a three-level evaluation process. In Eleventh Congress of the European Society for Research in Mathematics Education (CERME11) , Utrecht University, Feb 2019, Utrecht, Netherlands.

Stipek, D., & Valentino, R. A. (2015). Early childhood memory and attention as predictors of academic growth trajectories. Journal of Educational Psychology, 107 (3), 771–788. https://doi.org/10.1037/edu0000004 .

Thom, J. S. (2018). (Re)(con)figuring space: Three children’s geometric reasonings. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), Contemporary research and perspectives on early childhood mathematics education (pp. 131–158). Cham: Springer Nature.

Tirosh, D., Tsamir, P., Levenson, E. S., & Barkai, R. (2020). Setting the table with toddlers: A playful context for engaging in one-to-one correspondence. ZDM . https://doi.org/10.1007/s11858-019-01126-9 . (This issue) .

Tsamir, P., Tirosh, D., Barkai, R., & Levenson, E. (2020). Copying and comparing repeating patterns: Children’s strategies and descriptions. In M. Carlsen, I. Erfjord, & P. S. Hundeland (Eds.), Mathematics education in the early years. Results from the POEM4 conference, 2018 (pp. 63–78). Cham: Springer.

Tzekaki, M. (2020). Mathematical activity in early childhood and the role of generalization. In M. Carlsen, I. Erfjord, & P. S. Hundeland (Eds.), Mathematics education in the early years. Results from the POEM4 conference, 2018 (pp. 301–313). Cham: Springer.

Van den Heuvel-Panhuizen, M. (2018). Theories, methodologies, results in early arithmetic research. In Presented at PME 42, in Research Forum: Learning and teaching of arithmetic skills in early years , Umeå, Sweden, 3–8 July, 2018.

Van den Heuvel-Panhuizen, M., & Elia, I. (2020). Mapping kindergartners’ quantitative competence. ZDM . https://doi.org/10.1007/s11858-020-01138-w . (This issue) .

Verschaffel, L., Rathé, S., Wijns, N., Degrande, T., Van Dooren, W., De Smedt, B., et al. (2020). Young children’s early mathematical competencies: The role of mathematical focusing tendencies. In M. Carlsen, I. Erfjord, & P. S. Hundeland (Eds.), Mathematics education in the early years. Results from the POEM4 conference, 2018 (pp. 23–42). Cham: Springer.

Vogler, A-M. (2019). Chances and obstacles of ‘indirect’ learning processes in situations with preschool teachers. In Eleventh congress of the European Society for Research in Mathematics Education (CERME11) , Utrecht University, Feb 2019, Utrecht, Netherlands.

Vygotsky, L. S. (1987). The collected works of L.S. Vygotsky, Vol. 1: Problems of general psychology, including the volume Thinking and Speech. Edited by R. W. Rieber and A. S. Carton; translated by N. Minick. New York: Plenum.

Wang, A., Firmender, J., Power, J., & Byrnes, J. (2016). Understanding the program effectiveness of early mathematics interventions for prekindergarten and kindergarten environments: A meta-analytic review. Early Education and Development, 27 (5), 692–713.

Watts, T. W., Duncan, G. J., Clements, D. H., & Sarama, J. (2018). What is the long-run impact of learning mathematics during preschool? Child Development, 89 (2), 539–555. https://doi.org/10.1111/cdev.12713 .

Wynn, K. (1998). Numerical competence in infants. In C. Donlan (Ed.), The development of mathematical skills . Hove: Psychology Press.

Young-Loveridge, J., & Bicknell, B. (2016). Tens awareness: A framework for early place value learning. In Poster presented at the 13th International Congress on Mathematical Education, Hamburg, Germany .

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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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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.

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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.

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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.

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Outstanding Maths Lesson for Interview/Lesson Observation Problem Solving - Years 5 and 6

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Last updated

10 May 2024

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An exceptional maths problem solving lesson, complete with written lesson plan and interactive slides. Crafted to engage and challenge high-ability Year 5/6 students, this lesson offers a rich tapestry of activities and tasks designed to ignite mathematical thinking.

Perfect for a lesson observation or job interview, these comprehensive materials will impress all observers and demonstrate your expertise in delivering high-quality maths education.

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Number and algebra

• The Number System and Place Value
• Calculations and Numerical Methods
• Fractions, Decimals, Percentages, Ratio and Proportion
• Properties of Numbers
• Patterns, Sequences and Structure
• Algebraic expressions, equations and formulae
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Geometry and measure

• Angles, Polygons, and Geometrical Proof
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• Measuring and calculating with units
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Probability and statistics

• Handling, Processing and Representing Data
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Working mathematically

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For younger learners

• Early Years Foundation Stage

Advanced mathematics

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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