Helping your child understand maths

Believe it or not, every time your child measures flour for baking, sorts pegs into colours, creates a tower with wooden blocks, sings nursery rhymes, puts a toy in their mouth, pours water in the bath or snuggles up to listen to you read a book, they're building their knowledge of maths. In these early years, children don't need any formal maths teaching – instead, they'll learn the basics by playing, talking and exploring their world. During this time, young children should be introduced to the five main areas of maths – number, geometry, algebra, measurement and statistics – in fun ways. They'll start to learn naturally and without too much formal thinking – and supporting them through this development will help set your child up for a bright mathematical future.

Number

This is where it all starts. Numbers are the foundation of all other mathematical thinking – to understand complex mathematics in the future, we have to be able to count, if your child gets it wrong in the beginning, that's ok. Just enjoy those cute moments while they last, the "one, two, five, seven, nine" mistakes, and those nonsense numbers (like "twenty hundred"). The important thing at this early stage is that they're giving it a go, and they're enjoying it.

You can help your child master numbers by counting forwards and backwards with them, and creating counting experiences – for example, "one arm, two arms, one shoe, two shoes" while you're dressing them.

Numeral recognition is an important part of this phase too. So point out numbers in your environment while you're doing everyday things, like shopping, going for a walk, or reading a book.

Geometry

Space is the very first mathematical concept we explore as human beings. From the day they're born, children will start moving their limbs to gain a sense of the space they're in. Then, as they begin to move deliberately – to roll, crawl, toddle, and then walk – they'll develop their sense of spatial awareness in more depth. This is another reason why giving your baby plenty of time on the floor, to freely explore their environment and their place in it, is so important. Using spatial language, like "under, over, beside, beyond, next to" is also a really great way to enhance your child's understanding.

Geometry is about shape too, but like other areas of mathematics, young children don't need lessons here – they'll gain an understanding of everyday shapes naturally, just by exploring their world. This will then develop into the ability to recognise and name geometrical shapes (triangle, rectangle, square etc.) as they grow older.

Algebra

It's an area of mathematics that's often considered difficult, but when you take it back to basics, algebra is firstly about patterns and symbols. Even in the songs we sing, and the books we read to our children, there are repeating choruses and rhythms that help them learn. Some classic books and songs focus specifically on repetition, ‘Wheels on the Bus' and ‘Old Macdonald had a Farm' for example, giving children opportunities to recognise patterns and how they can be repeated. While they may not be able to explain these patterns to you, they'll still be able to demonstrate them.

Recognising symbols is a big part of early algebra too. For example, when you put your child's cup or bottle on the bench, they'll probably reach for it, they may start to recognise popular restaurant chains as you drive past them as well. All of this shows an understanding of symbols, and is forming the groundwork for algebraic thinking.

Measurement

Measurement is part of our everyday lives, even though we may not always realise it.

When we drive to work, drop our children off at school or go out on the weekend, we'll constantly be estimating time, distance and speed to make sure we arrive safely and on time. Children do this naturally as well. When infants reach out for an object, or place one in their mouths, they're measuring it, figuring out what fits and what doesn't. This is a really crucial part of development, and even though your child can't tell you about what they're doing, this kind of exploration is really important.

Statistics

Statistics are all about gathering and analysing information, and young children have their own ways of doing this. If you've ever seen your child gather their toys into separate groups, or place matching coloured objects together (like coloured pegs as you're hanging out the washing), they're beginning the earliest form of statistical exploration – gathering data and sharing the information. Classifying objects and separating them into sets allows children to explore the different ways things go together.

When to Worry

There's really no need to worry before your child starts school. While it's wonderful if they can count, recognise the numerals from 1 to 9, and recognise simple geometric shapes before starting school, it's definitely not vital for their future mathematical success.

If you're concerned that your child's not understanding patterns or shapes – for example, when you're reading stories to them and discussing the pictures, when you're out and about looking for shapes, or when talking about the patterns on clothing – it might be worth having their vison and hearing checked. You can talk to your GP or, in New Zealand, your Plunket Nurse about this.

In very rare cases, children can develop dyscalculia – which is a difficulty in understanding and manipulating numbers, or learning facts in mathematics. It can often be linked with attention deficit disorder, and can affect people with a very high intelligence. It's rarely diagnosed in early childhood though, so if you're at all concerned, speak with your GP as soon as you notice an issue.

Mathematical cheat sheet

For very young children, mathematical learning happens naturally and without too much formal thinking. So the best way to teach your child is through lots of adult interaction, play and involvement in daily activities.
There are five main areas of maths – number, geometry, algebra, measurement and statistics – and children will explore all these areas through play and their interactions with you.
There's no need to bombard your child with maths before they start school. Introducing them to simple vocabulary, including counting, numeral recognition and shapes, will give your child a good head start for school and later learning.
There's never a need to worry about your child's mathematical development before they start school. Every child is different, and will learn at their own pace.

How to explore the world of maths with your child

Try to add mathematical vocabulary to your everyday experiences. It can be as simple as counting, asking ‘How many?', ‘How much?', and pointing out shapes and numbers as you go about daily tasks together. Let this happen naturally though, you want your child to experience maths in a fun and engaging way.
Read stories that have mathematical ideas in them. These can include counting books, as well as children's tales. We've listed some of our favourites below.
Sing songs like Six Little Ducks, Ten Green Bottles, Twinkle Twinkle Little Star, Wheels on the Bus and Baa Baa Black Sheep with your child. Songs with lots of counting, rhythm (repeated refrains and choruses), and shapes in them like these will help your child learn naturally.
Encourage your child to explore something like the peg bucket or the pot cupboard. Placing objects in order from smallest to largest (and vice versa), or in coloured groups can help develop your child's understanding of measurement and statistics. Just remember that activities like this are all about exploration – so there's no right or wrong way to do it.
Give your child a variety of everyday objects to explore in their own way. You can describe the shapes and sizes to them if it fits in with their play.
Allow your baby to put safe objects in their mouth – your kitchen is full of different textures and sizes that are perfect, things like wooden spoons, measuring cups and whisks. This will encourage your child to explore classification as they discover what things are, and what they're not.
Place toys and other things that your baby loves just out of their reach. This will encourage them to stretch and reach, and can stimulate their understanding of distance and space.
Play music and dance with your child – its great exercise for you, and hearing rhythm and moving to music will help them understand pattern.
Encourage your child to help you with cooking. Measuring, mixing and rolling ingredients for simple cookies can create a shared experience with lots of maths. Talk about how much of each ingredient is going in, and how you read a recipe. You should try to choose simple, quick recipes, and always watch out for safety here.
Go for a walk with your child, and if they'd like to, collect some leaves, twigs or other natural resources. These can be sorted into groups by shape, size or type, and can also be counted.
Give your child some simple blocks to build with. They don't need to be expensive, and even safe offcuts from building can be useful. Blocks give children plenty of opportunities to sort, stack, count, and create – and the clean-up is a maths experience too.
Find numbers in the environment. A number search is a great way to keep a young child focussed on a car trip or while food shopping.
Water, water, water! We all know how much children love to play with water – either in the bath, or with a bucket and hose outdoors on a warm day. It's a great way to explore useful language – like full, empty, nearly full, half – and also promotes problem-solving and lots of open-ended mathematical play. Give your child lots of clean, recycled bottles and containers so they can tip, fill, empty, transport, pour and explore volume
Celebrate family birthdays together. This may seem like something you'd do anyway, but counting the candles before you blow them out is a quick, simple and exciting way to think about numbers.
Talk about fractions. Simple things like sharing – "Half for you, and half for me" – helps your child understand that one whole is made up of two halves. You can make this more complex as your child grows: "There are three people so we need thirds, three pieces of the cake".
Ask your child "how many?" in a variety of contexts, and accept their mistakes when they happen. The act of calculating an answer is more important than getting it right.
Play simple card or board games with young children – even "Snap" helps with matching and numeral recognition.
Discuss time with your child using cues. For example, "After lunch we'll go to the supermarket", or "In two sleeps it will be your birthday".
Plan to go to the beach or local park, and talk to your child about what you might need to take with you. Planning events together will give your child a sense of ownership and excitement, and encourage them to think about time and space. While you're there, collect leaves or create sandcastles – talk about the shapes you see, and look for sets or groups of objects.
Jigsaws are a great way to introduce children to the idea shape and space, as well as encouraging problem-solving.
Big numbers are exciting! Young children love hundreds, thousands, millions and beyond, so try to think of fun and creative ways to explore big numbers.
Climbing trees gives children an opportunity to learn about measurement and comparison (big and small), as well as an understanding of height, as they reach for branches or stretch over roots.
Playing with bikes, trikes, carts and wheelbarrows is a great way for your child to learn about distance, weight, directional and positional language, and provides lots of opportunity to problem-solve.
Painting is another fun way for young children to learn about colour, pattern, space (filling up the page) and directional language.
Playing with blocks, lego or other construction materials will help your child develop an understanding of shape, space, and measurement, as well as wonderful problem-solving and critical thinking skills. For example, "What's the best shape and size for the zoo I'm building?"
Remember, maths is everywhere. All you have to do is find it, and create fun ways to explore it with your child.

Deeper reading

Books to enjoy with your child:

Smee, N. (2003). Five Wriggly Babies. London, United Kingdom: Campbell.

Aiono-Iosefa, S. (2004). Two Cans of Corned Beef and a Manulele in a Mango Tree. New Zealand: Penguin

Briggs, R. (1989). Jim and the Beanstalk. United States of America: Puffin

Hewetson, S. (1999). Dare you go over the Hill? Golden books.

Grossman, B. (2008). My Little Sister Ate One Hare. Paw Prints Books.

Bradman, T. (1993). A Bad Week for the Three Bears. Random House Publishers.

Clement, R. (1991). Counting on Frank. New York: Gareth Stevens Books.

Hissey, J. (1994). Ruff. London: Hutchinson Children's Books.

Moore, I. (1991). Six Dinner Sid. California, U.S.A.: Aladdin.

Dodd, L. (2001). Slinky Malinki Catflaps. New York, New York: Gareth Stevens Publishing.

Dodd, L. (1983). Hairy MacLary from Donalsons Dairy. Keystone picture books.

Gilderdale, B. & Gilderdale, A. (1993). The Little Yellow Digger. New Zealand: Scholastic.

Websites:

www.nzmaths.co.nz

http://connectwith.earlyyears.aamt.edu.au/

http://oldweb.naeyc.org/about/positions/psmath.asp

http://nrich.maths.org/early-years

Further reading for you:

Dehaene, S. (2011). Number Sense. How the Mind Creates Mathematics. New York, U.S.A.: Oxford University Press.

Pound, L. (2006). Supporting Mathematical Development in the Early Years. New York: Open University Press.

Perry, B., MacDonald, A., & Gervasoni, A. (Eds.). (2015). Mathematics and Transition to School. Singapore: Springer.