How Do Children Develop Early Math Skills?

Children are using early math skills throughout their daily routines and activities. This is good news as these skills are essential 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, other math skills are introduced through daily routines you share with your child—counting steps as you go up or down. 

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:

• Understanding size, shape, and patterns
• Ability to count verbally (first forward, then backward)
• Recognising 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)

About Numeracy and Maths Skills

Numeracy is the ability to recognise and apply maths concepts in all areas of life.

Numeracy skills involve understanding numbers, counting, solving number problems, measuring, estimating, sorting, noticing patterns, adding and subtracting numbers, etc.

Children and adults need numeracy and maths skills to do everyday things like:

• Solve problems – for example, have I got time to walk to school?
• Analyse and make sense of information – for example, how many wins does my team need to get to the top of the competition?
• Understand patterns – for example, what number would the next house in this street be?
• Make choices – for example, which bike is the best value?

Your child's everyday experiences are full of learning opportunities that lay the foundations for numeracy.

How Your Child Starts Learning Numeracy Skills

Children start learning numeracy skills from the time they're born. 

This learning happens from watching and experiencing numeracy in action, especially in everyday play and activities. For example, it occurs when your child:

• hears you counting their fingers and toes
• starts to recognise numbers and shapes on objects like clocks and phones or in books
• decides how many slices of apple they want.

As children get older, they learn more numeracy and math skills, including size and measurement. For example, this happens when your child:

• compares things of different sizes – 'big', 'small' and 'medium.'
• groups items together and talks about 'same' and 'different.'
• uses words to describe where things are – 'over', 'under' and 'next to.'
• helps set the table with the correct number of plates, forks, spoons and cups
• fill a water bottle
• helps with the shopping and uses the money to buy things
• divides food into equal shares.

And when you talk with your child about math concepts in your everyday activities, it helps your child understand how and why maths is functional. For example, this happens when you point out:

• big and small (size)
• high and low (height)
• heavy and light (weight)
• fast and slow (speed)
• close and far (distance)
• first, second and last (order)

Essential Math Skills for School

More advanced mathematical skills are based on an early math "foundation"—like a house built on a solid foundation. 

In the toddler years, you can help your child begin to develop early math skills by introducing ideas like: 

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 seeing relationships between numbers—like adding and subtracting.

Representation

They make mathematical ideas "real" by using words, pictures, symbols, and objects (like blocks). 

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.

Measurement

Technically, this is finding an object's length, height, and weight using units like inches, feet, or pounds. Measurement of time (in minutes, for example) also falls under this skill area.

Estimation

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, more significant, smaller, and less than. 

Patterns

Patterns are things—numbers, shapes, images—that repeat in a logical way. Patterns help children learn to make predictions, understand what comes next, make logical connections, and use reasoning skills. 

Problem-Solving

The ability to think through a problem, to recognise there is more than one path to the answer. It means using past knowledge and logical thinking skills to find a solution.

Exploring the Math in Play

Children become intensely engaged in play. Pursuing their purposes, they tend to tackle challenging problems enough to be engrossing yet not totally beyond their capacities. 

Sticking with a problem — puzzling over it and approaching it in various ways — can lead to powerful learning. 

In addition, when several children grapple with the same problem, they often come up with different approaches, discuss various strategies, and learn from one another. 

These aspects of play can promote thinking and learning in mathematics as well as in other areas.

Young children explore patterns and shapes, compare sizes, and count things. But how often do they do that? 

And what does it mean for children's development? When children were studied during free play, six categories of mathematics content emerged.

Classifying. 

One girl, Anna, took out all the plastic bags from the container and sorted them by bug and colour.

Exploring Magnitude

(describing and comparing the size of objects). For example, when Brianna brought a newspaper to the art table to cover it, Amy remarked, "This isn't big enough to cover the table."

Enumerating 

(saying number words, counting, instantly recognising several objects, or reading or writing numbers). Three girls drew pictures of their families and discussed how many brothers and sisters they had and how old their siblings were.

Investigating Dynamics 

(putting things together, taking them apart, or exploring motions such as flipping). For example, several girls flattened a ball of clay into a disk, cut it, and made "pizza."

Studying Pattern and Shape 

(identifying or creating patterns or shapes or exploring geometric properties). For example, Jennie made a bead necklace, creating a yellow-red colour pattern.

Exploring Spatial Relations 

(describing or drawing a location or direction). For example, when Teresa put a dollhouse couch beside a window, Katie moved it to the centre of the living room, saying, "The coach should be in front of the TV."

The range of mathematics explored during free play is impressive. Thus, we can see that free space offers a rich foundation on which to build exciting mathematics. 

These everyday experiences form the foundation for later mathematics. 

Later, children elaborate on these ideas. We call this process "mathematisation." And we recognise that children need both these foundational experiences, as well as specific math activities.

Play does not guarantee mathematical development, but it offers rich possibilities. 

Significant benefits are more likely when teachers follow up by engaging children in reflecting on and representing the mathematical ideas that have emerged in their play. 

Teachers enhance children's mathematics learning when they ask questions that provoke clarifications, extensions, and the development of new understandings.

Tips for Building Numeracy Skills in Toddlers and Preschoolers

Talking, everyday activities, play, and reading help your child develop communication, imagination, and further understanding of math concepts. Here are some ideas.

Ideas for Talking

• Use math concepts to describe what you and your child are seeing and doing together. For example, 'Look at the fast cars' or 'This bag is heavy'.
• When you're preparing food, talk about what you're doing. For example, 'I'm cutting this orange in half' or 'Let's share these sultanas – one for me and one for you'.
• Point out and name the numbers you see, like mailboxes, buses and road signs.
• When you're out and about, talk about what's near or further away. For example, 'Let's sit on that bench nearby to have our snack' or 'It's quite far to the lake. Would you like to ride in the stroller?'
• Talk about activities that happen at certain times of the day. For example, 'We eat breakfast at 7 am', or 'Let's go to the park before we have dinner at 6 pm.

Ideas for Everyday Activities

• Make counting part of your everyday life. For example, count shells at the beach, fruit at the shop and trees on the street. Or count toys together as your child packs them away.
• When you're out and about, encourage your child to describe or compare shapes of leaves, colours of flowers or sizes of birds.
• Go for a walk down your street and point out how each house or block has a number in a series. Guess the number of steps between one place and the next.
• Use a growth chart or marks on a wall to measure your child's growing height and describe what you're doing to your child.
• Involve your child in cooking. Your child can help stir, pour, fill and mix. This helps your child get familiar with concepts like counting, measuring, adding and estimating.

Ideas for Play

• Go for a nature walk and let your child gather a mix of leaves, sticks, pebbles and other natural items. Your child can sort them into groups based on size, colour, shape or what they do.
• Sing songs and read books with repeating, rhyming or rhythmic numbers. This will help your child understand patterns.
• Play simple board games, card games and puzzles with shapes and numbers, like 'Snap' or matching pairs of dominoes.
• Play outside games like 'I spy, hopscotch, skittles and 'What's the time Mr Wolf'.
• Play or sing music at different speeds. Your child can dance, jump or shake musical instruments to slow or fast songs. Sing nursery rhymes slowly and then speed up.
• Race toy cars and talk about which came first, second or third.
• Please help your child to arrange their toys in order from shortest to tallest.

What You Can Do

The tips below highlight ways to 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. However, younger children can be exposed to stories and songs using repetition, rhymes and numbers.)

Shape Up

Play with shape-sorters. Talk with your child about each shape—count the sides, describe the colours. 

Make your shapes by cutting large shapes out of coloured construction paper. Then, 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, colour, or what they do (i.e., all the cars in one pile and animals in another).

Place the Call

With your 3-year-old, begin teaching her the address and phone number of your home. Please 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 number.

What Size Is It?

Notice the sizes of objects in the world around you: That pink pocketbook is the biggest. The blue bag is the smallest. 

Ask your child to think about his 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 naturally learn to count, measure, add, and estimate.

Walk it Off

Taking a walk gives children many opportunities to compare (which stone is more significant?), assess (how many acorns did we find?), note similarities and differences (does the duck have fur as the bunny does?) and categorise (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.

Shape Up

Point out the different shapes and colours you see during the day. For example, 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 cold? This encourages your child to link cold weather and warm clothing.

Pass it Around

Ask for your child's help in distributing items like snacks or laying napkins out on the dinner table. 

Help him give one cracker to each child. This helps children understand one-to-one correspondence. 

When distributing items, emphasise 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 relationships (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 relation to other objects.

The Long and the Short of It

Cut a few (3–5) pieces of ribbon, yarn or paper into different lengths. Talk about ideas like long and short. Then, 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 other ways or designs. Supervise your child carefully during this activity to prevent choking, and put away all items when 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 more significant (estimation). Together, count how many shirts. Next, see if he can make pairs of socks: Can you take two socks out and put them in their 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/tiny).

Dress for Math Success

Ask your child to pick out a shirt for the day. Ask: What colour 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, colours, shapes, or pictures: I see a design on your shirt. 

Some stripes go red, blue, red, blue. Or, Your shirt is covered with ponies—a big pony next to a bit of 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 fewer stickers and count how many to be sure.

Promoting Math in Everyday Play

Teachers support math in play by providing a fertile environment and intervening appropriately. Here are some things you can do:

Observe Children's Play

When you haven't seen many new block constructions, share books illustrating different block arrangements or post pictures in the block centre.

When you see children comparing sizes, offer different objects that children can use to measure their structures, from cubes to string to rulers.

Intervene Sensitively

A helpful strategy is to ask if social interaction and mathematical thinking are developing or stalled. 

If they are developing, observe and leave the children alone. Discuss the experience later with the whole class.

Discuss and Clarify Ideas

Children might each argue that their block building is more significant. You may see that one child is talking about height, and another is talking about width. 

You can comment on how you see the buildings as big in different ways, as in "You have a very tall building, and Chris' seems to be very wide."

Schedule Long Blocks of Time for Play

Provide enriched environments and materials, including structured materials, such as blocks and Legos, which invite mathematical thinking.

Young children engage in significant mathematical thinking and reasoning in their play — especially if they have sufficient knowledge about the materials they are using — if the task is understandable and motivating and if the context is familiar and comfortable. 

Math can be seamlessly integrated with children's ongoing play and activities, but it requires a knowledgeable teacher who creates a supportive environment and provides appropriate challenges, suggestions, tasks, and language. 

In classrooms where teachers are alert to all these possibilities, children's play enriches mathematical explorations.