Creative MathematicsPatterns, relationships and play

Young children build maths through hands on play with patterns relationships shape space measurement and data.

Introduction

Mathematics in the early years is far more than just counting numbers. It involves identifying patterns, understanding relationships, and making sense of the world through shape and space. Knaus and Roberts (2017) distinguish between mathematics as a knowledge domain of symbols and abstraction, and numeracy which is the capacity to use mathematics in daily life. For young children, effective mathematical learning happens through hands-on play. It occurs naturally when they pour water to learn about volume or when they sort leaves to learn about classification.

Theories and Perspectives

Early mathematics is grounded in Piaget’s theory of cognitive development, specifically logico-mathematical knowledge. Piaget argued that children construct understanding by handling objects and observing the relationships between them. We also consider the distinction between rote counting, which is memorizing number names, and rational counting, which is understanding one-to-one correspondence as outlined by Howard and Mayesky (2022). Vygotsky’s theory is also relevant here, as educators use mathematical language to scaffold children’s understanding during play.

Resources, Materials & Mathematical Tools

A rich mathematics environment focuses on open ended manipulatives and tools available in play.

Loose Parts

  • Buttons, shells, bottle tops for sorting and counting
  • Collections for matching and classifying
  • Patterning trays and simple ten frames

Block Corner & Measure

  • Blocks for geometry, balance and spatial reasoning
  • Measuring tapes, scales, number lines
  • Dramatic play shop with pricing and weighing

Water & Sand Tables

  • Concrete experiences with volume and capacity
  • Funnels, cups and clear containers for pouring
  • Estimation and counting during play

Age-Appropriate Learning Experiences

0 - 2 Years (Size, Quantity & Sensory)

Nesting Cups

For infants, a set of nesting cups or stacking boxes provides an early introduction to size. An educator can sit with the child and demonstrate how the smaller cups fit inside the larger ones, encouraging the child to experiment with fitting them together. Adapted from Howard and Mayesky (2022) regarding seriation, this helps develop spatial awareness and an early understanding of size relationships linking to EYLF Outcome 4.2 where children develop skills in inquiry and experimentation.

Howard & Mayesky, 2022, EYLF Outcome 4.2

Sensory Bag Patterns

Educators can create sensory counting bags by taping sealed zip-lock bags to the floor containing gel and buttons. This allows infants to squish the bags to move the items, and educators can count “one, two” as the child touches the buttons. Adapted from Knaus and Roberts (2017) regarding sensory exploration, this provides sensory stimulation and early exposure to quantity linking to EYLF Outcome 5.1 where children interact verbally and non-verbally.

Knaus & Roberts, 2017, EYLF Outcome 5.1

2 - 3 Years (Classification & Correspondence)

Sorting Button Colours

Toddlers enjoy organising their world. Using a large tray of mixed coloured buttons and small bowls, educators can ask children to put all the red buttons in one bowl and blue ones in another. This practices classification and matching based on a single attribute. Adapted from Howard and Mayesky (2022) regarding classification, this links to EYLF Outcome 5.4 where children begin to understand how symbols and pattern systems work.

Howard & Mayesky, 2022, EYLF Outcome 5.4

One to One Correspondence

Meal times provide a practical opportunity for maths. During morning tea, a child can help set the table by placing one cup for every chair or one cracker for every plate. This helps develop rational counting skills through real-world one-to-one correspondence. Adapted from Knaus and Roberts (2017) this links to EYLF Outcome 3.2 where children take increasing responsibility for their own wellbeing.

Knaus & Roberts, 2017, EYLF Outcome 3.2

3 - 5 Years (Estimation & Geometry)

Water Volume Experiment

At the water trough, educators can provide a large clear bottle and a small cup. By asking children to guess how many small cups it will take to fill the big bottle, they practice estimation. Having them count aloud as they pour tests their prediction. Adapted from Howard and Mayesky (2022) regarding capacity, this links to EYLF Outcome 4.2 where children hypothesise, research and investigate.

Howard & Mayesky, 2022, EYLF Outcome 4.2

Shape Hunt

See enactment video

To take maths outdoors, give children a card with a picture of a shape like a triangle and ask them to find things in the playground that match it. They might find a triangular leaf or a sign. This helps them recognise geometric shapes in the real world. Adapted from Howard and Mayesky (2022) regarding geometry, this supports EYLF Outcome 5.4 where children understand pattern systems.

Howard & Mayesky, 2022, EYLF Outcome 5.4

6 - 8 Years (Data & Measurement)

The Graphing Project

Older children can engage in data collection by voting on a topic like their favourite fruit. They can use the data to create a large bar graph on the wall and discuss which column is the tallest and what that means. Adapted from Howard and Mayesky (2022) regarding data representation, this links to the Australian Curriculum for Mathematics where students create displays of data using lists and graphs.

ACARA Mathematics, Howard & Mayesky, 2022

Measurement with Feet

To understand standard units, children can first measure the length of the room using their own feet by walking heel-to-toe. Comparing why some children got a higher number because they have smaller feet and some got a lower number helps them understand the need for standard units. Adapted from Knaus and Roberts (2017) this links to the Australian Curriculum for Mathematics regarding measuring with informal units.

ACARA Mathematics, Knaus & Roberts, 2017

See full references on the References page.