Numeracy for all learners

Numeracy is the knowledge, skills, behaviours and dispositions that students need in order to use mathematics in a wide range of situations. It involves recognising and understanding the role of mathematics in the world and having the dispositions and capacities to use mathematical knowledge and skills purposefully.  (Literacy and numeracy strategy version 2).

Number, measurement and geometry, statistics and probability are common aspects of most people’s mathematical experience in everyday personal, study and work situations. Equally important are the essential roles that algebra, functions and relations, logic, mathematical structure and working mathematically play in people’s understanding of the natural and human worlds, and the interaction between them.

Why numeracy is important

A child's first years are a time of rapid learning and development. Babies and toddlers can recognise number, patterns, and shapes. They use maths concepts to make sense of their world and connect these concepts with their environment and everyday activities. For example, when playing, children may sort or choose toys according to size, shape, weight or colour.

While much of the teaching of concepts and skills to support numeracy happens in the mathematics learning area, it is strengthened as students take part in activities that connect their learning in the mathematics classroom within the context of other curriculum areas.

As they move through their years of schooling, students are exposed to mathematical:

• understanding
• fluency
• problem solving
• reasoning.

These capabilities allow 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.

Mathematics gives students access to important mathematical ideas, knowledge and skills. Numeracy connects this learning with their personal and work lives.

Numeracy has an increasingly important role in enabling and sustaining cultural, social, economic and technological advances.

Numeracy development

For an overview of numeracy development see mapping the numeracy focus areas. Resources in the guide are organised by levels:

Numeracy across the curriculum

Being numerate involves more than mastering basic mathematics. Numeracy involves connecting the mathematics that students learn at school with the out-of-school situations that require the skills of problem solving, critical judgement, and sense-making related to applied contexts.

Conceptual framework

Learning activities presented draw upon the conceptual framework of Goos, Geiger, and Dole (2014; also discussed in Goos, Geiger, Dole, Forgasz, and Bennison, 2019). In this framework, numeracy is conceptualised as comprising four elements and an orientation:

Element 1: Attention to real-life contexts (citizenship, work, and personal and social life)

Element 2: Application of mathematical knowledge (problem solving, estimation, concepts, and skills)

Element 3: Use of tools (representational, physical, and digital)

Element 4: The promotion of positive dispositions towards the use of mathematics to solve problems encountered in day-to-day life (confidence, flexibility, initiative, and risk)

Orientation: A critical orientation to interpreting mathematical results and making evidence-based judgements

The resources highlight what numeracy is with respect to each learning area, and outline why it is important to develop students' numeracy capabilities within the learning area. Guidance is provided for teachers on the following:

• how to embed numeracy in their learning area
• how to assess numeracy learning
• how to deal with challenges and dilemmas using strategies recommended by experts.

The activities are described in terms of subject-specific learning intentions and content descriptors. The numeracy content and skills are highlighted and explained, with particular focus on how the numeracy links enhance the learning area's specific concepts. Direct links to the Victorian Curriculum: Mathematics highlight the connections between the activity and the students' previously developed mathematical skills and understandings. The VCAA have detailed information regarding the numeracy demands of the Victorian Curriculum on the Numeracy page of the website.

Early childhood numeracy and mathematics resource

Mathematics is everywhere

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 global community of the 21st century.

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)

Families and educators play a critical role in introducing children to mathematics and encouraging them to be curious and enthusiastic about mathematics. From a very young age, adults invite children to use mathematics to understand and participate in their world.

Would you like another piece of toast?
We need to find the other shoe – we need one for each foot!
How old are you today – three – happy birthday!
How many plates do we need?
We live at number 36.

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, and experience challenge and success in their learning.

Numeracy in early childhood

Numeracy is the capacity, confidence and disposition to use mathematics in daily life. Children bring new mathematical understandings through engaging in problem-solving. The mathematical ideas with which young children interact must be relevant and meaningful in the context of their current lives. Spatial sense, structure and pattern, number, measurement, data argumentation, connections and exploring the world mathematically are the powerful mathematical ideas children need to become numerate (EYLF p. 38).

When educators consider including mathematics and numeracy in early childhood programs, there is often confusion about the relevance of concepts such as algebra or statistics. Children are active learners, exploring the world and beginning to develop explanations for observed phenomena from a young age. With encouragement, guidance, experience and learning, children further develop their capacity to reflect on their own thinking processes, approaches to learning and using mathematics in their everyday engagement with their world..This resource illustrates the variety of ways that educators, working with children from birth to age five, can support numeracy learning and development.  Presented across three key mathematical concepts; Number and Algebra; Measurement and Geometry; Statistics and Probability (reflective of the Victorian Early Years Learning and Development Framework and the Victorian Curriculum) and organised to consider children's learning from birth to age five; early childhood educators are offered ideas for learning experiences, ways to engage families and opportunities for intentional teaching.

The suggestions included in this resource represent only some recommendations to help educators strengthen and enhance numeracy learning in programs for young children. Educators will have their own ideas that will complement this collection and are encouraged to work with their colleagues, as well as children and families, to expand their ideas and resources. Links to a range of resources are included that offer additional materials for further consideration.

Number and Algebra

Number and Algebra for young children involves exploring mathematical concepts such as patterns, symbols, and relationships. A large part of learning in this area involves using numbers in everyday contexts, counting objects and understanding how the numbers combine and connect to describe the world and help us to make meaning.

Children are engaging with number and algebra when they:

• use mathematical words to describe the world. E.g. ‘lots of’, ‘more than'
• use numbers to count and refer to objects and people in their lives. E.g. 'I'm three years old, 'I have two trucks at home'
• use numbers to solve problems. E.g. ‘I need another glass for the table’
• begin to count objects in a sequence and recognise the way numbers work.

Measurement and Geometry

Measurement and Geometry for young children involves exploring mathematical concepts such as the size, shape, position and dimensions of objects. A large part of learning in this area involves becoming familiar with and using numbers and words to describe objects and know the difference between objects.

Children are engaging with measurement and geometry when they:

• feel different shaped items
• sort objects according to their shape
• draw shapes in their art
• describe the world around them using concepts such as ‘I like the circle one’ or ‘I put my hat in the big basket’ or ’the snake was really long.’

Statistics and Probability

Statistics and Probability for young children involves sorting, understanding and presenting information from groups of objects in order to understand what is happening.

Probability is about understanding the chance of something occurring and making decisions based on that thinking.

Children are engaging with statistics and probability when they:

•  collect and sort ideas or groups of objects into categories
• talk about whether they need to take a coat with them when they go on a walk. E.g. ‘Is it going to rain?’

Early childhood educators' beliefs on mathematical learning

Educators’ own beliefs and attitudes towards mathematics and numeracy have a significant impact on the way these ideas are incorporated into programs for children. Increasing numbers of studies (Anders & Robbach, 2015) (Australian Mathematical Sciences Institute, 2018) have identified that many early childhood educators have had negative mathematics experiences in their schooling and therefore believe they will not be able to support children in this area adequately. It is important for adults to reflect on their anxiety in relation to mathematics and shift their perception towards the potential that mathematics provides to make their lives more meaningful. Many early childhood educators are competent users of mathematical concepts, and their numeracy skills are excellent however, these are not always recognised as a positive and necessary part of their daily lives.

Families

Families play a crucial part in the development of children's mathematics and numeracy learning. As is the case for educators, family members’ own beliefs and attitudes towards mathematics and numeracy influence the way that children feel about engaging with and developing their mathematics and numeracy skills. Since numeracy in the early years is so highly connected to daily life and the way we make meaning of the world, families can provide opportunities to explore mathematics and support children to become confident about their mathematics and numeracy learning.

Educators can encourage families to recognise their role in supporting children’s mathematics and numeracy learning in many ways; from formal communication with families (in a family handbook for example or newsletters) about  how they can support children at home to informal conversations that promote positive attitudes and reinforce responses to children that help build their confidence. When educators maintain a commitment to sharing ideas with families about children’s mathematics and numeracy, learning outcomes are more likely to progress.

Throughout this resource, learning experiences have been identified that are specifically designed for families to try at home. Educators are encouraged to share these ideas with families in their regular communications.

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.

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.