Narrator 1

Welcome to numeracy in early childhood.

We'd like to acknowledge the Aboriginal people who have, for thousands of years, been the custodians of the lands where you are listening to this presentation from and acknowledge their strong continuing connections to lands and waterways across New South Wales. We pay respect to Aboriginal Elders past, present, and emerging and extend that respect to all Aboriginal and Torres Strait Islander people who are participating in this professional learning.

This professional learning has been linked to the Australian Professional Standards for Teachers. It addresses standard 2.5.2. Apply knowledge and understanding of effective teaching strategies to support students' literacy and numeracy development.

In this session, learners will develop an understanding of number, patterning, measurement and space concepts developed in early childhood and how children explore them. Learners will also apply their understandings of numeracy concepts to foster learning.

Numeracy

Narrator 2

Numeracy is defined in the Early Years Learning Framework as the capacity, confidence and disposition to you use mathematics in daily life. Children bring new mathematical understandings through engaging with problem-solving. It is essential that the mathematical ideas with which young children interact are relevant and meaningful in the context of their current lives. Educators require a rich mathematical vocabulary to accurately describe and explain children's mathematical ideas and to support numeracy development.

Numeracy emphasises the context, purpose, and usefulness of a particular approach in solving problems in everyday life and the flexible, negotiable and meaningful applications of mathematical concepts. McMillan states that often the terms, mathematics and numeracy, are positioned as separate from one another. In early childhood, however, numeracy and mathematics can be viewed as interconnected, with each building upon and informing the other. When we think of mathematics, we think of it as a formal abstract system involving rules and requirements for accuracy and precision. However, we also apply mathematical concepts in situations arising from our everyday activities, such as preparing a meal and arranging furniture, and numeracy perspective appreciates and values informal context for the application of mathematical concepts or processes.

Geist states that as educators, we should think of children as competent mathematicians and confident and competent learners in numeracy. It can also be helpful to reflect upon our own experience. In order to facilitate young children's mathematical development, it is important for educators to have a thorough mathematical content knowledge and confidence in using that knowledge.

As educators, our experiences, dispositions and understanding of numeracy and mathematics can have a profound impact on how we engage children in numeracy and mathematics learning. What memories do you have about learning mathematics? How may this affect your confidence to teach mathematics? Reflecting on your own practice is also discussed in the fostering positive dispositions across literacy and numeracy in early childhood professional learning that is available on the Early Learning website. Through ongoing learning and reflective practice, educators can deepen their conceptual understanding of numeracy and mathematics and be responsive in facilitating this learning in their setting. McDonald states that educators need deep conceptual knowledge and skills to identify and build upon the numeracy in children's everyday experiences in play.

With that in mind, we will focus on the interconnected concepts that are foundational to building strong numeracy skills. These are, number, making meaning from numbers and the complexity of the interconnected components of quantity, language, and symbols. Patterning, where something, an object or an event has an element that repeats over and over. Measurement, this is a concept which can be divided into 2 different types of attributes, geometric and physical. And space, which can also be thought of in 2 ways, the relationship between objects and an understanding of the properties of things. There are strong links between all these concepts, so while we'll talk about them individually, these concepts need to develop simultaneously. Crucial to this conceptual development is educators taking an active role by building mathematical vocabulary and providing numeracy-rich environments.

Number

We will now look at the concept of number.

Some of the aspects of number to be developed in early childhood include, that objects are counted using one-to-one correspondence, numerals can be sequenced, the last number said when counting a group tells you how many are in the group, counting the same collection again will give the same result, the ability to say how many objects are in a group without counting, this is called subitising, and that there are different ways of representing the same number. Number is far more complex than just counting. Let's look a little more into what's involved in the concept of number in early childhood.

Making meaningful numbers is a complex skill in which children need to develop a depth of understanding in order to support flexibility. The ideas introduced in the "magic triangle" can support children to build this depth of understanding. The "magic triangle" consists of the connective components of quantity, language, and symbol. We are going to look at a video explaining this idea.

Narrator 3

What is involved in making meaning from numbers? It's quite a complex skill, and there's lots of different bits of information that we need to be able to process. One is the language, so the words that we say, hear, read, and write. Like, for example, 6. This is something that we can make meaning from and use to convey meaning. We also need to have knowledge of symbols and the things that we use to represent the words that we say, hear, read and write, so here I have the symbol for 6, and that is still the symbol for 6, even though it's bigger, or in a different colour, or written in a different font. And as we get older that we learn that we can actually use other symbols to represent a symbol that we don't know yet, or a quantity that we don't know yet. Like, for example, X can be used to represent 6, or a question mark can be used to represent 6, or even sometimes a box. But we also need to have the capacity to imagine what that quantity looks like.

This is where we talk about things like 6 in a 10 frame where I can see 6, but I can see inside of that space that 6 is composed of 5 and one, or that it's 4 less than 10. Here I can see 6 as 2 and 4 more. Here I can see 6 as 2 3s. And here I see 6 almost as if it's the dice pattern. Here I can see 6 as 2 3s, where in my heart it's 3 2s. Here I can see 6 as 6 sides of a hexagon. And I can also see 6 as one less than 7. I also need to be able to think about 6 in terms of its magnitude, that 6 is smaller than 10, and it's also smaller or fewer than 16, but I can also see 6 represented here because I can see 6 ones inside of 16, where I have one 10 and 6 more. And also, I can see 6 as the distance between 10 and 16. And so in order to be able to have this awareness of what a quantity looks like, it's not just enough for me to be able to make these representations, but eventually when I know a number, these are things that I can visualise in my mind's eye, and that you can ask me to tell you about all the things I know about 6, and I can talk about all the different ways that I imagine it. I can also talk about its language, and I can talk about the symbols that we use.

Now, when we're developing this knowledge of number, we're building some really critical relationships, 6 of them, actually. The first 2 are that I can go from the quantity and from the quantity represent that quantity using symbols, and that I can also represent that quantity using language. I also need to be able to go from the symbol and then think about the symbol and match it to a quantity and the symbol to language, and, yes, you guessed it, I also need to be able to go from the language, the words that we say, hear, read, and write, and then connect that to a representation of the quantity and also a symbolic representation. And when kids are able to move and navigate through all of these different ways of representing quantities, that's when we talk about them having the 'magic triangle'. You know, it's a colloquial way that we refer to it as.

Narrator 2

The idea of the 'magic triangle' can be directly related to the Early Years Learning Framework. In learning outcome number 5, children begin to be aware of the relationship between oral, written, and visual representation. As in the points of the magic triangle, where language, the words we say and hear, link with symbol, the symbols we use to replace the words we say and hear, and quantity, what it looks like in real life.

Some of the ways children explore number in early childhood is when they use mathematical language, such as more, less, how many, when they relate numbers to their every day, such as, I'm 4, I have 10 fingers, when they play games with a dice or dominoes, sing counting songs, begin to count objects in a sequence, explore different ways of representing numbers, and compare groups. The Early Years Learning Framework relates to number when children are demonstrating an increasing understanding of measurement and number using vocabulary to describe size, length, volume, capacity, and names for numbers. Or when they use language to communicate thinking about quantities to describe attributes of objects and collections and to explain mathematical ideas.

Educators promote the learning of number when they set up provocations to talk about, use, and explore number and counting, when they provide opportunities for children to explore quantity, symbol and language of number, when they intentionally provide resources, such as loose parts, that children can use flexibly to explore number, when they use song, stories and physical activity to incorporate number, for example, counting when skipping, when they respond to children's spontaneous learning outdoors and indoors, making links to number, when they model the use of mathematical language, such as numeral, symbol, or digit, when they engage in sustained shared thinking to scaffold and extended number thinking.

The Early Years Learning Framework mentions educators recognizing mathematical understandings that children bring to learning and building on these in ways that are relevant to each child, and providing resources that encourage children to represent their thinking, or for learning outcome 5, when educators engage children in discussion about symbol systems, or include real-life resources to promote children's use of mathematical language.

It's now time to pause the video and complete this reflection, thinking about what strategies and resources you currently use to support and extend children's learning of number, and how else could you support and extend children's learning of number in your context. When thinking of your examples, consider how interactions, experiences and flexible learning environments promote number investigation, and also ensure that your program is culturally responsive, inclusive, and differentiated for diverse learners.

Patterning

Narrator 1

We will now explore the concept of patterning. Much of mathematics is about patterns, and mathematics is about searching for, describing, generalizing and justifying these patterns. Patterns have regularities that we can perceive visually, auditorily and somatically through tactile or action-based sensations. Patterns are a sequence of 2 or more items that repeat themselves. To understand patterning, children need to understand similarities and differences between objects and events. Patterns occur in everyday life, in nature and human made forms. Patterning helps children learn sequencing and to make predictions, leading to mathematical skills of logic and structure in algebra.

Patterns are all around us. If something has an element that repeats over and over and over, it is a pattern. Children explore patterning when they recognize and highlight repeated elements of patterns, when they copy and extend on patterns using a variety of materials and resources, when they create patterns from their own ideas, showing clearly repeated elements of a pattern, when they talk about patterns they can see in the environment or daily routine, when they use musical instruments to create patterns, and when they paint their own patterns and examine patterns in art.

In the Early Years Learning Framework, learning outcome 4, children are confident and involved learners. Children create and use representations to organise, record, and communicate mathematical ideas and concepts. Learning outcome 5, children are effective communicators. Children notice and predict the patterns of regular routines and the passing of time. Children begin to recognise patterns and relationships and the connections between them. Children begin to sort, organize and compare collections of events and attributes of objects and materials.

Educators promote learning of patterning when they demonstrate and discuss how to make patterns in play, when they identify and discuss patterns in natural and human made structures, when they provide resources, such as loose parts, to support patterning, when they use mathematical language to describe patterns, when they make patterns in music, when they notice and point out patterns in rhyme, when they create movement patterns. In the Early Years Learning Framework, learning outcome 4, children are confident and involved learners. Educators recognize mathematical understandings that children bring to learning and build on these in ways that are relevant to each child. Learning outcome 5, children are effective communicators.

Educators provide children with access to a wide range of everyday materials that they can use to create patterns and to sort, categorize, order and compare. It is time to reflect on patterning. What strategies and resources do you use to support and extend children's learning of patterning in your context? How else could you support and extend children's learning of patterning in your context? When writing examples, consider how interactions, experiences and flexible learning environments promote patterning investigation. Consider how your program is culturally responsive, inclusive, and differentiated for diverse learners.

Pause the video to complete this reflection.

Measurement

We will now look at the concept of measurement.

Understanding of measurement begins developing for children very early, and they enter preschool with prior knowledge of measurement, although they may not be able to quantify or measure them accurately. Objects and events have attributes that can be measured. Measurement involves assigning a numerical value to spatial qualities of an object or events. Measurement can be used to compare objects and events. Formal and informal tools can be used to measure objects and events. There are strong links between number, geometry, and measurement, so concepts need to be developed simultaneously. Children need to use the interconnected skills of number recognition, understand the final number is the count, and other concepts to investigate measurement.

Measurement concepts include attributes that are either geometric or physical. Length is related to the geometric construct of lines. Length refers to the attributes, while other terms like height, width, or depth are specific to particular context. Area is the 2-dimensional measure that describes the region enclosed by a plain figure. Volume refers to the space occupied by a 3-dimensional figure. Capacity refers to the same 3-dimensional attribute, but specifically to measure how much will fit in the volume of space. Mass and weight are often confused.

Mass is a measure of the amount of matter, so the term weighing something is actually measuring its mass. Weight is the force that gravity exerts on an object. Time cannot be measured using tangible experiences like the other attributes. Time can only be perceived through changes in natural occurrences, such as day and night, seasons, or movement of a clock hand, or changing numerals on a digital clock. Time is one of the most difficult measurement concepts for children to understand. Money embodies the units that measure the value of an item. It is important that children understand and can identify the attribute that they are going to measure. This involves developing an awareness of the attribute and adopting any new associated language.

Children explore geometric attributes of measurement when they use natural materials to measure, for example, length and height, when they experiment with scales, rulers and measuring tape, when they fill the area of shapes with blocks and other materials, when they compare the heights of groups, such as children, toys or natural items, when they use resources such as water, rice, and marbles to experiment with volume, when they describe and order objects according to attributes of weight, volume, length, and height, when they explore the relationships between quantities, shorter, heavier, same, different, equal.

In the Early Years Learning Framework, learning outcome 4, children are confident and involved learners. Children create and use representations to organise, record, and communicate mathematical ideas and concepts. Learning outcome 5, children are effective communicators. Children demonstrate an increasing understanding of measurement and number using vocabulary to describe size, length, volume, capacity, and names of numbers.

Educators promote learning of geometric attributes of measurement when they provide real-life experiences to explore measurement, when they use play experiences to provide repeated practice of measurement skills, when they use measurement in flexible and appropriate ways, when they model question and use mathematical language, when they provide comparisons, when they ask questions, which of these is longer, which is taller, which is wider?

In the Early Years Learning Framework, learning outcome 4, children are confident and involved learners. Educators recognize mathematical understandings that children bring to learning and build on these in ways that are relevant to each child. Educators listen carefully to children's attempts to hypothesise and expand on their thinking through conversation and questioning.

Children explore physical attributes of measurement when they talk about changes in temperature, weather forecast, and seasons, when they experiment hefting items and comparing weight, when they attribute money value to an item and pay for items in role-play or excursion scenarios, when they discuss money value of items from the supermarket on an excursion or in a catalogue, when they explore timelines and daily routines, when they experiment with clocks and timers to investigate the lapse of time.

In the Early Years Learning Framework, learning outcome 4, children are confident and involve learners. Children use the processes of play, reflection and investigation to solve problems. Learning outcome 5, children are effective communicators. Children use language to communicate thinking about quantities to describe attributes of objects and collections, and to explain mathematical ideas.

Educators promote learning of physical attributes of measurement when they engage children in discussion about symbols and systems, for example, time and money, when they invite children to investigate mass through hefting and using scales, when they discuss the daily routine and passing of time, when they add resources to dramatic play that shows symbols that represent mass of objects, such as grams or kilograms, when exploring how weight and gravity work, such as on a see-saw.

In the Early Years Learning Framework, learning outcome 4, children are confident and involved learners. Educators provide opportunities for children to revisit their ideas and extend their thinking. Educators in10tionally scaffold children's understandings. Educators model mathematical language. Educators join in children's play and model reasoning, predicting and reflecting processes and language. Educators provide resources that encourage children to represent their thinking.

It is time to reflect on measurement. What strategies and resources do you use to support and extend children's learning of measurement in your context? How else could you support and extend children's learning of measurement in your context? When writing examples, consider how to provide opportunities for both geometric and physical attributes of measurement for children to explore. Consider how interactions, experiences, and flexible learning environments promote measurement investigation. Consider how your program is culturally responsive, inclusive, and differentiated for diverse learners.

Pause the recording to complete this reflection.

Space

Narrator 2

The concept of space in early childhood.

Research has shown that young children's spatial, rather than numerical, abilities predict their overall mathematics achievement. Children learn about the relationships between objects, an understanding of the properties of things and the language to talk about these things by experimenting and playing. Development of spatial concepts greatly contributes to the developing visual memory. And several studies have shown that spatial abilities are not innate, but teaching young children spatial skills improves their maths, including their number understanding and general thinking skills.

Children are exploring the relationship between objects when they navigate a play space, watching carefully where their friends are so they do not run into them, when they describe their positions, such as 'I'm on top', 'I climbed under', or 'You are behind', when they participate in obstacle courses, join in movement games, moving around both stationary and moving objects. The Early Years Learning Framework, learning outcome number 3 talks about children using their sensory capabilities and dispositions with increasing integration, skill and purpose to explore and respond to their world. And that children demonstrate spatial awareness and orient themselves, moving around and through their environments confidently and safely.

Educators promote learning of the relationship between objects when they ask children to draw or take photos with objects at different distance, depth, and angles, when they engage and observe simple map creation, for example, at the playground, classroom or community, when they play "I spy" using spatial relation words and phrases such as next to, beneath, on top of, and provide flexible problem-solving activities, such as multi-solution puzzles like tangrams and Tetris. The Early Years Learning Framework outcome number 3 talks about educators planning for and participate in energetic physical activity with children, including dance, drama, movement, and games, and provide a wide range of tools and materials to resource children's fine and gross motor skills.

Children are exploring the properties of things when they group objects according to an attribute, such as 'all the pointy ones together' or 'all the cubes together', when they describe objects in their environment, such as 'my grapes are around', or 'the pineapple is spikey', when they build a tower using wooden blocks, when they complete puzzles of increasing difficulty, and when they notice and work with symmetry. Learning outcome 4 talks about children using their senses to explore natural and built environments, and children beginning to sort, organize, and compare collections and events and attributes of objects and materials.

Educators promote learning the properties of things when they draw attention to objects inside or outside that are shaped like a circle, triangle, rectangle, or square, in different sizes and positions, when they model and encourage the correct use of terms like side, face, edge, curved, corner, or flat, when they provide loose parts to investigate symmetry, for example, designing faces, when they use art to explore and create tessellating patterns, when they prepare sensory bags containing natural and manmade objects. Learning outcome 4 talks about educators recognising mathematical understandings that children bring to learning and building on these in ways that are relevant to each child. And you may have noticed this point repeated in each of the concepts, highlighting the importance. They also provide resources that encourage children to represent their thinking.

Once again, it's time to pause the recording for a reflection. What strategies and resources do you currently use to support and extend children's learning of space in your context? And how else could you support and extend children's learning of space? When writing examples, consider providing opportunities for both relationship between objects and properties of things for children to explore. Think about interactions, experiences, and flexible learning environments to promote space investigation. And ensure your program is culturally responsive, inclusive, and differentiated for diverse learners.

Key messages

The key messages of our session today is that numeracy is the capacity, confidence and disposition to use mathematics in daily life, that in early childhood can be explored through the concepts of number, making meaning from numbers and the interconnected components of quantity, language, and symbols, patterning, where an object or event has an element that repeats over and over and over, measurement, involving geometric and physical attributes, and space, including the relationship between objects and understanding of the properties of things. Also, that talk can build mathematical vocabulary and conceptual knowledge in early childhood, and that rich environments support the development of numeracy. This brings us to the end of our presentation today.

Here are some references. You might like to pause the recording and note down any that you were interested in.

For more information and professional learning and resources, visit the Early Learning website via this link.

Finally, thank you for participating in our session today. Please complete the survey below to provide your feedback, which helps us plan for future learning opportunities. You can use the QR code or the link below.

Thank you.

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