Early numeracy practice guide – full publication

This means making the most of moments throughout the day to support learners’ skills and interest in numeracy.

• Find opportunities to use and reinforce maths vocabulary, including quantitative terms such as ‘more than’, ‘fewer’, ‘less’ and spatial terms such as ‘first’, ‘below’, ‘higher up’. Stories can provide an opportunity to incorporate maths talk into the day (for example, ‘is the rabbit in front of or behind the tree?’, ‘how many pigs are there?’)^1,2.
• Experiment with opportunities to support learners’ numeracy skills during everyday routines³. Sorting and counting foods, solving puzzles that involve a sequence of steps, or searching for and creating patterns in nature are all opportunities to lay the foundations for numeracy.
• Notice learners’ use of numeracy in their play and use this as an opportunity to explore and talk to children about maths and extend their learning⁴. For example, if learners are comparing sizes of objects, provide instruments they can use to measure. Joining in learners’ imaginative play can be a wonderful opportunity to explore mathematical ideas and practice problem solving, as you pose complex questions to stretch learners’ thinking.
• Provide objects and materials that set the stage for numeracy learning, for example blocks, puzzles, mud kitchens and loose parts that can be used for sorting and classifying⁵. Notice when learners play with these materials and use this as an opportunity to extend their learning.

^{1 Purpura et al., 2017. 2 Klibanoff et al., 2006 3 Ginsberg et al., 2008 4 Ginsburg et al., 2008. 5 Ginsburg et al., 2008.}

Plan play-based activities that allow you to extend on children’s learning, either in groups or in individual interactions with children.

• Plan teacher-led activities where numeracy is the goal and which focus on a specific maths skill or set of related skills (such as, comparing, ordering and estimating)⁶. For example, putting blocks in muffin tins or sharing blocks between dolls helps children to learn skills of matching and comparing. Make activities fun and playful to help develop positive dispositions towards numeracy from a young age.
• Help to bring maths ideas to life through use of physical play and objects⁷. Create patterns through movements or dance, challenge children to follow simple maps on a treasure hunt or make shapes with blocks⁸. Make the link between the objects or physical activity and the maths idea they are learning.
• Dedicate time each week for purposeful numeracy experiences⁹. For example, in small groups engage learners in a new numeracy experience lasting 20-30 minutes and repeat it at least twice a week, introducing a new numeracy experience each week. This could include reading books with mathematical concepts, exploring patterning or focussing on shapes in art making.

^{6 Clements and Sarama, 2011. 7 Laski et al., 2015. 8 Clements and Sarama, 2011. 9 Wang et al., 2016.}

Build your understanding of early numeracy development and how to support children’s learning.

• Understand how children develop early maths skills, including the typical developmental trajectories of these skills from infancy through to school (for example, the typical stages in learning to count) to help you scaffold learners’ numeracy development effectively^10,11.
• Know how to assess what learners currently know and what they do not know about a particular maths concept¹². This can be done through observation and formative assessment, asking learners to explain or posing open-ended questions (‘how did you know that?’), and working with learners to problem solve.
• Learn effective techniques to extend learners’ current level of understanding and help them learn the skills and ideas needed to achieve the next level of thinking on a particular maths concept¹³. For example, for learners who can name small sets of objects with ease ‘there are three balls!’, challenge their mathematical thinking by asking them to give you the right number of balls for each child in the group.
• Engage in critical reflection with your team on your own knowledge and confidence as numeracy educators¹⁴. Some early childhood educators and teachers may have limited preparation or confidence in numeracy, so support each other to enjoy exploring numeracy in your day-to-day practice.

^{10 Clements and Sarama, 2011. 11 MacDonald and Murphy, 2019. 12 Doig et al., 2003. 13 Doig et al., 2003. 14 Linder and Simpson, 2018.}

Arnold DH, Fisher PH, Doctoroff GL and Dobbs J (2002) ‘accelerating math development in Head Start classrooms’, Journal of Educational Psychology, 94(4):762-770.

This single study reports the findings of a 6-week intervention program implemented by teachers in Head Start classrooms in the United States. Head Start classrooms cater for infants, toddlers and preschool-aged children. The program examined aimed to incorporate numeracy into the regular classroom routines of children aged 3-5 years. It involved teacher-led numeracy activities that were designed to be fun for children and able to be adapted by teachers to suit their own style. Activities used a range of approaches (for instance, books, music, games, discussions and group projects) and targeted the skills of counting, recognising and writing numbers, one-to-one correspondence, comparison, change operations and understanding numbers and quantity. Children who received the intervention had improved early numeracy skills compared to the control group and showed an increased interest in maths. Teachers also reported an increase in their own enjoyment and skill in implementing numeracy activities.

Clements DH, Sarama, J, Spitler ME, Lange AA and Wolfe CB (2011) ‘Mathematics learned by young children in an intervention based on learning trajectories: A large-scale cluster randomized trial’, Journal for Research in Mathematics Education, 42(2):127-166.

This study reports findings from a trial evaluating the effectiveness of the Building Blocks maths curriculum, which is a research-based curriculum designed to improve maths education of preschool children (ages 2 to 4). Teachers completed professional development to increase their understanding of children’s early maths learning progressions, how to assess children’s level of understanding using formative assessment and activities they can use to help move children through these progressions. Teachers then implemented the curriculum which uses a range of teacher-led activities (for instance, whole group, small group, computer-based and ‘throughout the day’) that help children use and extend their mathematical thinking during everyday activities. This trial occurred in preschools serving low-income families in the United States. Findings show that children who received the curriculum learned more maths than children who didn’t receive the intervention.

Clements DH and Sarama J (2011) ‘Early childhood mathematics intervention’, Science, 333(6045):968-970.

This review paper summarises evidence showing that research-based interventions designed to promote mathematical learning for children aged 3 to 5 years can have strong positive effects on children’s learning outcomes. It highlights that the foundational numeracy skills children develop in the early years are key to school success. Unfortunately for many children, particularly those from low-resource communities, their early maths learning potential is not realised. The paper outlines several research-based early numeracy interventions and findings supporting their effectiveness in helping young children learn maths, including skills in number, space, geometry, measurement and mathematical thinking. 

Doig B, McRae B and Rowe K (2003) ‘A Good Start to numeracy: Effective numeracy strategies from research and practice in early childhood’, Australian Council for Educational Research.

This literature review provides an overview of research related to numeracy in early childhood (birth to 8 years). The authors identify a range of effective strategies and practices for educators and parents to promote children’s early numeracy. Effective strategies of early childhood educators and teachers include starting from what the child knows and can do, planning for numeracy learning and using assessment techniques to gather evidence of children’s development. 

Ginsburg HP, Lee JS and Boyd JS (2008) ‘Mathematics education for young children: What is it and how to promote it?’, Social Policy Report, 22(1):1-24.

A literature review of evidence related to effective mathematics education for young children aged 3 to 5 years. From their review of the evidence, the authors present some suggestions to improve and support educators and teachers to promote early numeracy.  The authors review research relevant to three central topics:

• young children’s maths abilities
• the content and components of early childhood mathematics education
• early childhood educators’ readiness to teach mathematics.

Klibanoff RS, Levine SC, Huttenlocher J, Vasilyeva M and Hedges LV (2006). ‘Preschool children's mathematical knowledge: The effect of teacher 'math talk'’, Developmental Psychology, 42(1):59-69.

This study examined the relationship between early childhood teachers’ use of maths talk and growth in children’s maths skills. There are many opportunities in preschool classrooms and during daily routines to engage children in maths talk and discussion. Findings from this study show large differences in the amount of maths related talk provided by early childhood teachers. More maths related talk provided by teachers was associated with greater gains in children’s maths skills over a year. Findings suggest that early childhood teachers and educators may be able to foster young children’s early numeracy skills by increasing their maths talk.

Linder SM and Simpson A (2018) ‘Towards an understanding of early childhood mathematics education: A systematic review of the literature focusing on practicing and prospective teachers’, Contemporary Issues in Early Childhood, 19(3):274-296.

A systematic review of research across all areas of early childhood mathematics, relating to prospective and practising teachers in early childhood. Findings show that early childhood teachers seem to lack foundational maths content knowledge, and this should be a priority for teacher preparation and professional development. Research suggests that early childhood teachers struggle with the enactment of early numeracy practices particularly when there is an over-reliance on textbooks which do not provide effective strategies for teaching. Findings also suggest that professional development has positive results for teachers early childhood maths knowledge, beliefs and attitudes.

Laski EV, Jor’dan JR, Daoust C and Murray AK (2015) ‘What makes mathematics manipulatives effective? Lessons from cognitive science and Montessori education’, SAGE Open, April-June 2015:1-8.

This paper reviews research related to the use of manipulatives in early childhood mathematics education (ages 3 to 6 years). The paper offers concrete examples of the use of manipulatives from Montessori instruction. The authors identify four main principles for effective strategies that ensure manipulatives promote maths learning:

• use a manipulative consistently over a long period of time
• begin with highly transparent concrete representations and move to more abstract representations over time
• avoid manipulatives that resemble everyday objects or have distracting features
• explain to children the relationship between the manipulatives and the maths concept being taught.

MacDonald A and Murphy S (2019) ‘Mathematics education for children under four years of age: A systematic review of the literature’, Early Years: An International Journal of Research and Development, 1-18.

This systematic review synthesises evidence concerning maths education for children under four years of age. Findings suggest that educators’ knowledge, attitudes and strategies play a critical role in shaping the mathematical learning opportunities available to children, however there is uncertainty among educators about how to support young children’s maths learning. There is evidence for the importance of relational and interactional elements of early maths education, highlighting the importance of play, talk and shared exploration in maths practice for children under four.

Purpura DJ, Napoli AR, Wehrspann EA and Gold ZS (2017) ‘Causal connections between mathematical language and mathematical knowledge: A dialogic reading intervention’, Journal of Research on Educational Effectiveness, 10(1):116-137.

This study reports the findings of a dialogic reading story book intervention aimed at increasing children’s exposure to quantitative and spatial mathematical language. This was conducted in preschool settings in the United States, which caters to children aged 2 to 4. Educators read books with children and provided questions, prompts and discussion about the mathematical content of the books to scaffold children’s mathematical language. The findings show that children who participated in the intervention demonstrated improvements in both their maths language and maths knowledge.

The following illustrations of practice focus primarily on children in their pre-Primary school year.

Australian Institute of Teaching and School Leadership (AITSL) – Curriculum and pedagogy in the early years

This resource provides an example of a teacher using ‘concrete manipulatives’ to help students develop their numeracy skills.

This video shows a teacher in Western Australia delivering a numeracy lesson to her pre-primary and Year 1 students. The video shows students working at mixed-ability learning stations to achieve individual student goals in early numeracy. The learning station activity was designed to help students with counting, trading and place value. Blocks, playdough and measuring tools were all used to make the numeracy concepts tangible for the students.

Australian Institute of Teaching and School Leadership (AITSL) – Problem solving in the block corner

This resource provides an example of a teacher developing students’ numeracy skills and engaging in formative assessment.

This video shows a teacher in Victoria working with 3 and 4-year-old children. The video shows how the teacher understands how to monitor children’s learning to tailor the learning program to meet the social, emotional, and cognitive needs of each learner. She focuses on students developing their early numeracy skills, providing them with language such as 'in front of', 'behind' and 'next to'. Block building is used to increase students understanding of mathematical concepts by planning and building structures. During class activities, the teacher also supports the development of self-regulation through modelling and discussing negotiation and collaboration strategies, so that the children can work together to build their structures. The teacher’s formative assessment strategies are also highlighted, which involve  ongoing communication with families, taking running records, collecting work in portfolios and developing learning stories.