Raising confident Mathematicians
Mathematics in the early years
As a teacher (with over 10 years’ experience teaching Mathematics) and a mum, I’m often asked about teaching early numeracy effectively. If you are interested in the ‘whys’ feel free to read from the top. If you are time poor then feel free to skip right down to ‘my recommendations in a nut shell’. I have divided my advice into three age brackets; Babies (0-18m), toddlers (18m-2yrs) and pre-schoolers (3-4yrs). Read through all 3 sections as there are lots of ideas that work well across age brackets.
I understand that some parents have no desire to teach their children basic numeracy skills before school age and thats a personal parenting choice. If this is you then this is not the blog for you. You do you :)
If you do get something out of this blog and want to say thanks via caffeine then you can shout me a coffee here.
Why early introduction is important
The importance of early childhood learning and its impact on future development, health and wellbeing is widely acknowledged. However, many parents do not truly understand the significance of early mathematics learning in particular, and the advantages it brings. Did you know that early exposure to foundational numeracy has been shown to provide the critical building blocks for future exploration of mathematical concepts?
Ages 0 to 4 is a time of rapid learning and development. Babies and toddlers learn faster during this period than in any other time in their lives. Have you ever noticed that seemingly without being taught, infants can recognise number, patterns, and shapes? This biological draw towards Mathematics is programmed within us so that we can make sense of our world and connect these concepts with our environment and everyday activities. One of the earliest and most basic examples of this is when we see children playing, sorting or choosing toys according to size, shape, weight or colour. By building on this natural interest in mathematics, parents can help build a love of learning. This is the greatest gift you can give to your little one and the one that will have the biggest impact on their lives!
Not only does numeracy have an important role in future academic success and career pathways, but a strong foundation in numerical understanding allows students to respond to familiar and unfamiliar situations by employing mathematics to make informed decisions and solve problems efficiently (VCAA, 2017). There is also evidence that other areas of development, such as resilience and perseverance, support achievement in numeracy. Numerical proficiency isn’t just about being “good at maths” it’s about helping our children to feel happy and confident in their everyday lives.
The reality is, we all use mathematics to navigate our everyday decisions successfully. Children begin to experience and explore mathematical concepts from birth. With support, they participate in mathematical thinking and use mathematical concepts to organise, record and communicate ideas about the world around them. Understanding and using mathematical concepts, and being numerate, helps children know and describe the world around them and make meaning of these encounters. It is, therefore, an essential skill for successful daily life. Research and practice evidence suggest that mathematics and numeracy skills will support children to be confident and capable learners as they navigate the increasingly complex world we live in.
Parents play a critical role in introducing children to mathematics and encouraging them to be curious and enthusiastic about mathematics. Building children’s confidence in understanding and using mathematics to explore and know the world will benefit everyone. Children benefit from many opportunities to generate and discuss ideas, make plans, exercise skills, engage in sustained shared thinking, generate solutions to problems, reflect and give reasons for their choices. Children who are confident and involved learners have positive dispositions toward learning, experience challenge and success in their learning and are able to contribute positively and effectively to others children’s learning. They develop and use their imagination and curiosity as they build a ‘toolkit’ of skills and processes to support problem solving, hypothesising, experimenting researching and investigating (VEYLDF, 2016).
Parents are the child’s first and most influential teachers and their involvement and engagement is critical for the development of positive attitudes to early learning. In the end, it comes down to parents creating and fostering a favourable attitude towards mathematics as early as possible. Parents have the ability to create a caring and encouraging learning space while supporting their child’s early development. It is imperative that parents are engaged in the nurturing of mathematical skills and positive attitudes in their children’s early years.
The results from the recent Trends in International Mathematics and Science Study (TIMSS) reveal that Australia has slipped to the 28th position in the world mathematics rankings, falling 10 places since 2011. This raises the question, is mathematics a learnt skill or is it just a skill that comes naturally to some?
Studies have recognised that mathematics does not, in fact, stem from natural ability, but is a learnt skill that needs to be nurtured, practised and developed. Creating a positive attitude to early numeracy learning provides the foundation for children to develop a growth mindset in mathematics.
My recommendations in a nutshell-
Research shows that early (before school age) introduction to basic numeracy concepts is important to future success
Studies show having strong mathematics skills help improve decision making, problem solving, resilience and perseverance across all aspects of life
Many mathematics concepts are built into us biologically and building on this from a young age can prove advantageous
Foster a love of learning mathematics from a young age to avoid an anxious “I can’t do it” attitude in the school years
The most important early mathematics skills to teach your child are-
Rote counting (saying the numbers in order)
One to one counting (being able to count a group of objects by pointing to each one)
Number (symbol) recognition
Comparing and ordering (size- taller/sorter & biggest to smallest, weight- heavier/lighter, amount- more/less)
2D Shape recognition (counting edges & corners- square, rectangle, circle, triangles, oval)
Patterns (start with basic XYXYXYXY AND XYZXYZ patterns)
Pre-measurement (measuring object lengths with objects like sticks, stones or steps. Measuring out ingredients in a recipe)
Addition and subtraction using real world phrasing e.g. We have 3 bananas left in the fruit bowl, if you eat one how many will we have? If we go to the shops and by 4 more, how many will we have?
Other important skills-
2D Shape recognition (counting edges & corners- hexagon, pentagon, kite, rhombus (avoid calling a kite or rhombus a diamond, differentiate the two from the start), trapezium)
3D shape recognition (counting faces, edges & vertices- cube, rectangular prism, sphere, then move onto triangular prism, pyramid, cylinder)
Basic analogue clock time (o’clock)
Directions (including left & right)
More complex patterns e.g. YYZYYZY or YYXYYZYYXYYZ
Addition and subtraction using manipulatives (like fingers, blocks, shells etc).
Comparing and ordering (value- greater/less than)
Fractions (introduce basic language like half, quarter etc)
Money
Babies: tips for building numeracy skills
Your baby loves hearing your voice and enjoys stories and songs with repetition, rhyme and numbers. Some things you might already be doing or could start doing with your baby to build numeracy skills include:
reading stories with numbers – for example, ‘Goldilocks and the three bears’
playing counting and sorting games
singing number songs and rhymes e.g. 5 little ducks, 6 cheeky monkeys, 3 speckled frogs
changing your tone of voice to describe concepts – for example, a deep, loud voice to describe something big, or a soft, squeaky voice to describe something little.
Ideas for talking
everyday activities – for example, ‘Let’s put half of the bird seed here and half over there’ or ‘Let’s find matching socks’
the environment – for example, ‘Look at the little bird over there’ or ‘That’s a tall tree’
food – for example, ‘Let’s have two pieces of banana’ or ‘How many cups do we need?’
time – for example, ‘7 pm, time for bed’
shapes and patterns – for example, ‘Let’s look for all the triangles’.
Point out and name the one digit numbers you see, like the numbers on mailboxes, buses and road signs.
It’s best if you can make these everyday numeracy activities and experiences playful and relaxed so that they’re fun for your child.
Ideas for play
Lining up toys
Putting balls or pom poms into different sized cups
Stacking blocks
Hiding a set number of toys under coloured scarves (say ‘can you find the 3 toys’ etc)
Include mathematic toys into your toy rotations. Our favourite ones can be found in my baby best buys guide.
Toddlers: tips for building numeracy skills
Talking, everyday activities, play and reading help your child develop communication, imagination and other skills for understanding maths concepts. Here are some ideas.
Ideas for talking
Use maths 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 one and two digit numbers you see, like the numbers on 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.
Write numbers on the sides of a large block (similar to a dice), during nappy change times have your child play with it and ask them what numbers they can see. Later ask them to find numbers themselves.
Find numbers on licence plates in the car park or on letterboxes
When you’re out and about, encourage your child to describe or compare shapes of leaves, colours of flowers or sizes of birds.
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 outside games like ‘I spy’ (for numbers around the neighbourhood/shops) or hopscotch (ask your child to jump/hop on certain numbers)
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.
Help your child to arrange their toys in order from shortest to tallest.
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.
Get a giant dice and take turns throwing it then saying the number.
Ordering number magnets or foam numbers in the bath/shower
Use a spray bottle to spray off numbers on a chalk board as they are called
Count pegs as they’re pegged to a box
Write numbers on a page and match the correct number of stickers (1 digit numbers)
Build different height towers with same sized blocks (or duplo), count the blocks
Include mathematic toys into your toy rotations. Our favourite ones can be found in our toddler best buys guide.
Screen time
· Leap frog numberland (Netflix)
· Reading eggs Mathseeds (app)
Pre-schooler: tips for building numeracy skills
Talking, everyday activities, play and reading help your child develop communication, imagination and other skills for understanding maths concepts. Here are some ideas.
Ideas for talking
Use maths concepts to describe what you and your child are seeing and doing together. For example, ‘We have 2 apples in the fruit bowl but we need 5, how many more do we need to get from the shops? (write a list and take this to the shops with your child, allow them to help you unpack the groceries when you return and use it as an opportunity to teach addition e.g. we had 2 yoghurt pouches and bought 6 more, how many do we have now?’
When you’re preparing food, talk about what you’re doing. For example, ‘I’m cutting this orange into quarters, how many pieces are there?’ or ‘we have 8 grapes to share, how many can we have each? (note- encourage the child to share them out in a variety of ways e.g. 4+4, 2+6, 8+0 etc)
Point out and name the two and three digit numbers you see, like the numbers on mailboxes, buses and road signs.
When you’re out for a walk or driving in your car allow your child to direct your movement using right/left language. Encourage this language when putting on shoes, brushing teeth etc.
When you notice it is a standard hour time like 8 o’clock, take the opportunity to ask your child what time it is (focusing on number that the small hand is pointing to).
Ideas for everyday activities
Find numbers on licence plates in the car park or on price tags or signs at the shops.
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 house and the next.
Use a growth chart or marks on a wall to measure your child’s growing height, and describe to your child what you’re doing.
Involve your child in cooking. Your child can help you to follow the recipe by counting, measuring, adding and estimating ingredients.
Ideas for play
Go for a nature walk and let your child gather a mix of leaves, sticks, pebbles and other natural items. Use them to measure the length of objects around your home.
Count the ducks at the local lake, or flowers in the garden
Continue to sing songs and read books with repeating, rhyming or rhythmic numbers. This will help your child understand patterns. Encourage your child to explore the mathematical nature of songs such as 5 little ducks by giving them story stones or laminated pictures to play with independently.
Play simple board games, card games and puzzles with shapes and numbers, like ‘Snap’, matching pairs, dominoes, connect 4, pop the pig, snakes and ladders
Play outside games like skittles (counting how many are knocked down and how many are left- link to adding/subtracting) and ‘What’s the time Mr Wolf’.
Use a peg board, light bright, stickers or playdough to create patterns for your child to finish
Play shops or restaurants and pay using play money.
Build towers out of different 3D shaped blocks and take the time to name each piece, count the faces, edges and corners
Tracing numbers
Write numbers on a page and match the correct number of stickers (2 digit numbers)
Include mathematic toys into your toy rotations. Our favourite ones can be found in our pre-schooler best buys guide.
Screen time
· Jack Hartman let’s get fit count to 100 (YouTube)
· Numberblocks (abc iview)
· Reading eggs Mathseeds (app)
All ages- Ideas for books and reading
Here are some books that feature numbers, counting, shapes and sizes. Click the title to show you where you can buy it.
At the beach I see by Kamsani Bin Salleh
Counting kisses by Karen Katz
One woolly wombat by Kerry Argent
Soup day by Melissa Iwai
Ten little dinosaurs by Mike Brownlow
Ten little fingers and ten little toes by Mem Fox
Ten little ladybugs by Melanie Gerth
The very hungry caterpillar by Eric Carle
We all sleep by Ezekiel Kwaymullina
After more ideas?
For additional ideas click the below links. These resources are organised in Levels rather than ages as they have been designed for a range of children (from remote aboriginal communities to inner city kids) and their abilities (which are dependent on genetics, birth order, health, level of support and a range of other factors). I have given a rough guide of ages to help guide you.
B to Level 2 (children aged 0-2yrs)
Levels 3 to 8 (children ages 18m-8yrs)
Levels 9 to 10 (children ages 6-10yrs)
Teaching Numeracy- how I did it
Bearing in mind that every child is different, this is how I taught numeracy (understanding numbers) to Maisie.
At 16 months we started rote counting, that is saying the numbers aloud, in order. We would count out aloud while driving in the car. Starting from with 0-6 first then moving onto at around 18m. By 2 years she could rote count to 100.
At 18 months Maisie would play with a wooden block with numbers on it while I changed her nappy. She would say “what’s that?” and I would tell her what each number said. Within a week or two she was able to tell me what each number (1-6) was. This was the beginning of her letter recognition journey.
At 18m she started mimicking our counting during real life situations. For example, then handing us balls from a bucket, she would say “one ball, two balls, three balls” as she handed me each one. She began lining up her toys to count them around this age too.
At 20m we were at a park with ducks. We had been to this park many times and often counted the small groups (5 or 6) ducks when feeding them (so they together and relatively still). On this day she decided to count them while they were swimming, which was a challenge. Pointing her little finger out she counted up to 9 (which was accurate). I had no idea she could do this! Never underestimate your little one, they might just surprise you!
At 20m she enjoyed finding and naming numbers on licence plates and letter boxes
Around 22m we started using foam numbers (0-9) in the bath. She would find each number floating about and place it in numerical order around the tub.
At the same age we bought some large plastic dice of various shapes, 6, 9 and 12 sides. We would take turns rolling them and saying the number we saw.
Once she turned 2 Maisie moved onto 2-digit number recognition. We played games where she’d use a spray bottle with water to squirt off chalk numbers, or paint number inside the shower screen.
At 2.5years Maisie enjoyed playing hopscotch. The great thing about this game is you can change the numbers in the boxes to which ever ones you are working on! She also enjoyed using a paint brush to wipe sand away to reveal numbers (sand in a clear dish, a piece of paper with numbers underneath).
Around this age she started loving the show Number blocks on Netflix and all of a sudden was hugely interested in addition and subtraction so we started using the abacus and duplo towers to teach this more explicitly. She also started liking dry erase books at this age.
Around her third birthday Maisie took an interest in the clock and would ask what time it was often. She would then move the hands of her toy clock to match the ‘real time’ (I’d always tell her it was something o’clock at this At 3.5 her fine motor skills improved dramatically and she began being able to have more control. She enjoyed tracing numbers from this age. Both with a whiteboard marker on a dry erase board or with a wet paintbrush over chalk numbers on the blackboard.
Some of Maisie’s favourite maths toys can be found here
References
Human Capital Working Group, Council of Australian Government. (2018). National Numeracy Review Report. Canberra: Commonwealth of Australia.
Jonas, N. (2018). Numeracy practices and numeracy skills among adults. Paris: Organisation for Economic Co-operation and Development.
Shomos, A., & Forbes, M. (2014). Literacy and Numeracy Skills and Labour Market Outcomes in Australia. Canberra: Productivity Commision Staff working paper.
Attard, C. (2020, Jan 21). Mathematics education in Australia: New decade, new opportunities? Retrieved from Engaging Maths: https://engagingmaths.com/2020/01/21/mathematics-education-in-australia-new-decade-new-opportunities/
Buckley, S. (2011). Deconstructing maths anxiety: Helping students to develop a positive attitude towards learning maths. Retrieved from ACER: https://www.acer.org/au/occasional-essays/deconstructing-maths-anxiety-helping-students-to-develop-a-positive-attitud
Church, A., Cohrssen, C., Ishimine, K., & Tayler, C. (2013). Playing with maths: Facilitating the learning in play-based learning. Australasian Journal of Early Childhood Volume 38 Number 1 March 2013, 95-99.
Cohrssen, C. (2018, June 6). Assessing children’s understanding during play-based maths activities. Canberra, ACT, Australia. Retrieved from http://thespoke.earlychildhoodaustralia.org.au/assessing-childrens-understanding-during-play-based-maths-activities/
DEEWR. (2009). Belonging, Being and Becoming: The early years learning framework for Australia. Canberra: Commonwealth of Australia.
Department of Education and Training . (2012). Integrated Teaching and Learning Approaches Practice Principle Guide 6 . Melbourne : Department of Education and Early Childhood Development).
Department of Education and Training. (2016). Victorian Early Years Learning and Development Framework . Melbourne: Department of Education and Training.
Knaus, M. (2016). Maths is All Around You: Developing Mathematical Concepts in Early Years . Blairgowrie: Teaching Solutions .
NAEYC. (2020). Math Talk with Infants and Toddlers. Washington, USA. Retrieved from https://www.naeyc.org/our-work/families/math-talk-infants-and-toddlers
Vogt, F., Hauser, B., Stebler, R., Rechsteiner, K., & Urech, C. (2018). Learning through play – pedagogy and learning outcomes in. EUROPEAN EARLY CHILDHOOD EDUCATION RESEARCH JOURNAL, 589-603.
