At its simplest, numeracy is the knowledge, disposition and confidence to use mathematics in day-to-day life. While it is easy to think of mathematics only as complex statistical and algebraic concepts, the fact is children are already using basic mathematics while negotiating the world around them. The following article is on developing number sense and strategies to teach numeracy in early childhood.
Development Of Number Sense In The Ealy Years
Quantifying numbers, making estimates, applying additive and multiplicative techniques, as well as:
- Sharing, ordering and estimating different quantities
- Quantity – develop concepts of more, less, most, least
- Counting, count on
- Trusting the count
Practical Examples include:
- Free and directed play with manipulatives (many different 2D shapes and 3D solids)
- Counting everyday objects and sets, including fingers and toes, family members, toys
- Singing songs and rhymes with a counting sequence to promote ordinal numbers in context, e.g. Five Little Ducks
- Problems like three and two more, with objects or drawings. Watch the video of Hudson (4) adding two more
- Simple takeaway problems with objects (e.g., counters, blocks)
Language To Use:
- More, less, some, few, none, one, two, three, etc.
- Modelling pointing to body parts and saying. “One nose, one. Two eyes, one, two. Two feet, one two. Ten toes, one, two, three,…ten.”
- “Look at those three birds on the wire. How many would be left if one flew away?”
- “Here are three blocks. Could you please count them? Let’s add two more. How many blocks do we have now?”
- “Six peas! Can you put them into pairs/twos? Great, so six is now three twos. Three twos make six. Now we both know that!”
- “What’s the largest number you know?”
Exploring Patterns and Relationships
Incorporating number patterns and applying algebraic reasoning are two ways to explore patterns and relationships, as well as:
- Recognising patterns and continuing them
- How these patterns may be used to predict trends
Practical Examples include:
- Play: Free and directed play with manipulatives to make, copy and/or continue patterns, using colours (pegs, blocks, beads) initially then 2D and 3D shapes
- Clapping patterns for children to copy and create their own
- Put out some counters/blocks. Now add/take away two in the pattern. Watch Hudson (4) continuing a pattern
- Write down every second/fifth/tenth number, going as far as you can. Start with 1/2/other to do that
Language To Use:
- Next, copy, repeat, extend, follow me, pattern
- “Where does this piece of the jigsaw puzzle go?”
- “Look, a pattern! Red, blue, blue … Say it with me. Red, blue, blue, red, blue, blue. Let’s make it longer––red, blue, blue, red, blue, blue …”
- “Follow me clap. (clap a pattern). What comes next in the pattern? Now you make a clapping pattern, and I will follow.”
Using Proportional Reasoning
Working with and understanding decimals, fractions, percentages, ratios, and rates are all part of using proportional reasoning, as well as:
- Dividing quantities, using the ideas of “fair” and “the same” (developing a sense of equality)
- Comparing the relationship between quantities, e.g. “twice as big/half as much”
Practical Examples include:
- Placing baby’s hat on your adult head, saying, “Oh no, your hat is too small for me.”
- Helping to share cooked food onto plates for the family; e.g., smaller and larger portions, ideas about equality and more/less/same/fair. Model the language and ask the child to talk aloud about the portion sizes: “More for Daddy because he’s bigger, less for you because …”. etc. (ratio)
- In the car, talking about going faster or slower (rates)
Language to use:
- Half, quarter, fair, unfair, even, equal, unequal, same, different, more, less
- Asking toddlers, “Can you fit in baby’s bath?”, “No, I’m too big.”
- “My feet are twice as big as your feet.” “Your shoes are half the size of my shoes.”
- “You have eaten half your peas. Eat up the other half.”
- “How will we find half?”
- “What happens when we go up a very steep hill? I think I can, I think I can …”
- “My dog is twice as big as my cat. What are you twice as big as?”
Understanding And Using Geometric Properties And Spatial Reasoning
Understanding and using spatial reasoning and geometrical properties, as well as:
- Interpreting diagrams and visualising 2D shapes and 3D solids
- Naming common shapes and their features
- Sorting shapes
- Responding to locational or directional language.
Practical Examples include:
- Play: Free or structured play with shapes such as Lego, tiles, pattern blocks, jigsaw puzzles, etc.
- Exploring shapes; noticing similarities and differences with shapes, e.g. curves, straight edges, corners
- Reading stories and explicitly using location and directional language through inviting children to point to and identify objects that are ‘beside’, ‘next to’, and ‘on top of’ is beneficial in developing spatial understanding.
Language to use:
- above, below, behind, in front, over, under, on top of, next to, inside, taller, tallest, shorter, shortest, round, straight, curved.
- “Where is your nose? Touch your nose.
- “You are crawling through the tunnel.”
- “Next, we need a thick, red two-by-four. Now place a thin two-by-four on top of it. Excellent!”
- “Teddy is sitting next to the window. Can you sit in front of Teddy?”
Understanding, Estimating and Using Measurement
Understanding, estimating and using measurement includes:
- Measuring objects using direct and indirect comparison, informal units
- Recognising time through identifying and participating in familiar daily events
Practical Examples include:
- Play: Comparing the height of toys or the length of feet, building the tallest tower out of blocks – length
- Volume and Capacity – Explore cooking or filling various containers with water or sand to measure
- Cutting and sharing food and drink of various 2D and 3D shapes and sizes – mass and volume; e.g., Grandpa needs more food because he is bigger. You serve a small serve for yourself because …” (linked to the story of Goldilocks and the three bears)
- Estimating and measuring with informal units, e.g., using body parts and movements such as steps or jumps to measure. Watch Hudson (4) estimate and then count how many steps to the washing machine
- Time – time management, before, after, daily routines. Describing what happens in certain seasons, months, days, or special events (birthday, holiday). Telling the time – lunchtime, bedtime, etc.
- Mass and position – Exploring relationships, e.g. “The big bubble is below the little ones. It might be heaviest”. Lifting shopping bags and talking about which is heaviest, or too heavy to carry.
Language to use:
- Long/longer/longest, short/shorter/shortest, big/bigger/biggest, high/higher/highest, low/lower/lowest, Monday, Tuesday, etc. March, April, etc., summer, autumn
- “Baby had a short nap today. That is why he is tired.”
- “When do you have your nap?” “What do we do after our lunch?”
- “Lifting the shopping bag is hard. It is heavy.”
- “How many jumps is it to the television?”
- “Fill the little bucket, pat it down, and tip it over to make a castle”. “How much sand will you need?
- “What do we always do after your bath? … and then what, … and then?”
- “We need one cup of water next, please”
- “How long is this footprint? Is it longer than your hand span?”
- “How could we measure the…?”
Exploring Chance and Data
Exploring chance and data includes
- Understanding the nature of chance events, including relationships between events
- Interpreting data displays in authentic contexts
Practical Examples include:
- Talking to a baby about what happens next, e.g. “I am warming your bottle and then you will have some milk”
- Exploring predicting events with a very young child dropping a toy from their high chair and you catch and return it to the child quickly several times. Then randomly do not catch it and return it quickly.
- Drawings of family, pets, or anything of interest to young children
- Talking about the chance of rain, informally initially then more formally, e.g., “The weather forecast said there is a chance of rain this morning, and the sky is quite grey, so are you taking your raincoat to kinder? (Yes) Well, that’s sensible.”
- Playing games of chance like bingo, snakes and ladders, and twister, and experiencing that they do not always win
- Follow a simple picture schedule and answer yes or no to related questions, e.g. Do we have story time before lunch?
- Predicting what will happen next in an online game, based on previous experience
Language to use:
- Might, chance, likely, unlikely, certain, always, maybe, win, lose
- “What happens when you push the ball?”
- “Who is picking you up today?”
- “What do you always do before you go to bed?”
- “You rolled four last time. Do you think you will roll four this time?”
- “What is likely going to happen in your game if you do …?”
- “Look, I found a graph of temperatures. Which months are hotter, and which are colder? Why would that be? Yes, that’s right! These months— December and January and February— are the middle of summer, but these—June and July— are always winter months.
Strategies To Teach Numeracy
Relate to their lived experience
Learning happens best when it is integrated into the lived experiences of the learners. So use their daily activities to ask questions about numbers or get them thinking of measurements. Some could be:
How many places do you set for your family supper?
We need a glove for each hand – where is the other one?
Which is the longer pencil – yours or mine?
Ask questions
Children are exceedingly curious by nature and one of the best ways to encourage numeracy is to tap into their wide-ranging interests. So if a child asks if flowers sleep at night, you can use the opportunity to help them count the petals or the colours on a bush. Likewise, use their love for cartoons and toy figures to talk about size and shape which can be eventually used to build spatial and geometrical concepts.
Equip the learning environment
One of the best ways to support numeracy is to keep blocks, rods and other learning aids handy in the learning environment. The more accessible such aids are to children, the easier it will be to engage them in mathematics. So stacking boxes or bowls can be used to introduce concepts like smaller and bigger as well as less and more. Let them find out how many objects of the same size can fit into boxes of different sizes which then you can use to talk about space and volume. Also, a set of blocks can be used to introduce sequence and counting as you go on to explain how numbers work.
Integrate with other topics
Ideally, numeracy should be nurtured as a disposition and way of understanding the world, rather than a stand-alone subject. So while the children are enjoying an art class, ask them to draw different shapes with different coloured crayons. Even when kids are having fun on the playground, ask them to sort different objects like pebbles and leaves in different boxes which then can be used to talk about statistics and even density. Indeed you can use story time to explore probability as your learners use past narratives to predict how many children a king has or how many wishes a character is granted.
Finally, examine your own perceptions of and attitude to mathematics. Studies show that educators who have been deprived of a supportive environment in early mathematical education are likely to pass on some of their anxiety to students. Such educators might find it difficult to come up with engaging ways to support numeracy or relate it to the real world. The good news is that with awareness and conscious effort, the negative effects of past experiences can be worked around so that both educators and students can have an enjoyable, enabling relationship with the very vibrant world of numbers.
Further Reading
Children's Learning Through Numeracy - For the early education context, the EYLF defines numeracy as, “the capacity, confidence and disposition to use mathematics in daily life”. Based on this definition, the following are some significant takeaways.
Preschool Indicators Of Literacy and Numeracy - The following article provides information on What Are The Indicators, the Importance of The Indicators, Learning Processes, Numeracy and Literacy Indicators and more.
Numeracy Activities For Children In Early Childhood - The following provides a list of numeracy activities for children that can be incorporated into an emerging numeracy environment.
Number Worksheets - A variety of free printables that enable children to develop numeracy skills.
Reference:
Numeracy For All Learners, Department Of Education Victoria