What’s in a box? Maths!

Who has given a gift to a young child only to see the child play and enjoy the box the gift came in more than the gift? DR AUDREY COOKE and ASSOCIATE PROFESSOR JENNY JAY observe young children playing with a cardboard box and notice the mathematical learning taking place. They also share ways for educators to provide mathematical learning opportunities.

Who has given a gift to a young child only to see the child play and enjoy the box the gift came in more than the gift? Currently, we are engaged in research investigating what mathematics 10- to 24- month-old infants demonstrate as they explore and interact with their learning centre environment. We used a 360-degree camera to record a learning centre room. We watched the recordings and saw and heard everything going on. Each time we viewed the recordings we focused on a different child and observed their mathematical experiences and actions. The children we watched were mostly preverbal—and were using non-verbal gestures to communicate with others. They also frequently used sounds to represent words and actions as part of their oral language development. A preverbal child would most likely understand adults’ verbalisations.

In the 1980s, Alan Bishop presented six mathematical activities he believed were evident across cultures (Bishop, 1988, 1991). His mathematical activities related to much older children and were defined as counting, locating, measuring, designing, playing, and explaining. For this study, we had to rethink these categories when applying them to very young, preverbal children.

We were excited to see the children use these mathematical activities as they explored their environment. The children explored and engaged with a large cardboard box that had been placed in the room. With the benefit of watching and re-watching the video capturing these explorations, and using Bishop’s six mathematical activities, we identified and interpreted the children’s actions and related them to mathematical thinking.

We observed a toddler crawling to the box that was on its side on the floor. The flaps outside the box were partially closed, leaving a small opening. The toddler balanced herself and then pushed a flap out of the way with one of her hands. She crawled through the opening towards the back of the box and sat outwards from the box’s opening.  When she was settled, she stretched her arms and tipped from side-to-side to touch the sides of the box.  She sat in the box swinging the flaps open and closed for a short time before crawling out.

In this short encounter, what were the maths activities we saw this toddler do? ‘Counting’ was involved when the child used one hand to move one box flap; ‘locating’ was involved when she positioned her body in space; ‘measuring’ was involved when she moved because she was too far away or moved the box flaps as the space was too small to crawl through and she was estimating the space as she stretched from side-to-side; ‘designing’ was involved when she manipulated the box to crawl into it; ‘playing’ was involved when she rehearsed actions until she knew what would likely happen when she pushed the flap with her hand; and ‘explaining’ was involved when she knew to balance herself before using her hand to move the flap out of the way.

The role of the educator is crucial in early mathematics learning. Educators need knowledge of the elements involved in mathematical thinking that can be stimulated in everyday behaviours and actions of very young children. Observing what each child engages with and planning for mathematical thinking opportunities within a stimulating environment are important aspects of early mathematical learning (Björklund & Pramling, 2017).

Providing mathematical rich opportunities include:

  • setting up a rotation of objects with various attributes—the same and different in size, shape, colour and weight for exploration
  • creating play spaces that challenge the children both physically and mentally—small spaces; just within reach spaces; hidden objects to be discovered
  • setting up objects that can be put into and tipped out of containers—pegs, gumnuts, pine cones, rocks or dominoes
  • setting up interesting activities—a large box, a sheet over a chair—and leaving children to explore and interact in their own time
  • selecting objects children can move, such as small cartons to create spaces of their own choosing
  • pouring activities—both wet and dry. Any safe medium will be engaging—ping pong balls, sand, water, rice, cornflour or wet mud.


Bishop, A. J. (1988). Mathematics education in its cultural context. Educational Studies in Mathematics, 19(2), 179–191. doi: 10.1007/BF00751231

Bishop, A. (1991). Mathematical enculturation: A cultural perspective on mathematics education, 6, Springer Science & Business Media. doi: 10.1007/978-94-009-2657-8

Björklund, C. & Pramling, N. (2017). Discerning and supporting the development of mathematical fundamentals in early years. In S. Phillipson, P. Sullivan, & A. Gervasoni (Eds.). Engaging Families as Children’s First Mathematics Educators: International Perspectives (pp. 65–80). Singapore: Springer. doi: 10.1007/978-981-10-2553_5

Main author:

Dr Audrey Cooke is a Senior Lecturer in Mathematics Education in the School of Education at Curtin University. She is passionate about mathematics and mathematics education and is interested in how people interact and engage with mathematics, particularly pre-service teachers and very young children. Her research includes disposition towards and engagement with mathematics, development of the skills of noticing mathematics, use of ICT in education, and how the actions of very young children might demonstrate mathematical thinking. Audrey contributes to mathematics education through her work with pre-service teachers, her research, and through papers and presentations, both nationally and internationally.

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5 thoughts on “What’s in a box? Maths!”

    Maryann Zammit says:

    Loved reading this article, great resource information

    donna beckett says:

    very interesting

    Hien Thi Tran says:

    Is help me develop acknowledge

    sarah ross says:

    thank you

    Debbie Bayley says:

    Very interesting

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