Mathematically rich interactions in early childhood

A large pile of Lego sits on the table, and you watch as young children are actively engaged in creating vehicles. Moments of quick chatter are followed by a quick run around the room to test their latest vehicle, then intense concentration as they try to find the next perfect piece.

‘You need two bad guys, ’cause there is two of us.’ (one-to-one correspondence).

‘This one is big enough for two.’ (classification, spatial awareness).

‘This one is faster than the police car, so it’s great.’ (measurement).

‘Mine can go up, down and around really fast.’ (spatial awareness, measurement).

‘No, no, no, it has to go faster, too fast to see it. Then the goodies won’t see it.’ (measurement).

Walking to the lunch table you overhear children chatting about their food. The discussion on sandwich shapes and apple sizes is interrupted by a new child joining the table.

‘My sandwich is in two rectangles.’ (geometry, fractions).

‘I’ve got one, two, three, four squares.’ (counting, geometry).

‘I got the last seat, no room for anyone else now.’ (fractions).

‘I’ve got small triangles.’ (measurement, geometry).

‘I’m nearly finished; I’ve just got half an apple to go.’ (fractions).

Wandering outside, you notice some delicious cakes in the sandpit kitchen. The containers are filled to various levels as the children decide on the yummiest ingredients.

‘First you add all the ingredients, then you stir, then it can go in the oven.’ (sequencing).

‘My favourite is the chocolate one. Is that yours too?’ (classification).

‘I need more strawberries to fill this cup.’ (measurement, fractions).

As demonstrated in these scenarios, children are constantly engaged in mathematically rich experiences.
Dewey (1938, p. 27) explains the important aspects in any experience—‘an immediate aspect of agreeableness or disagreeableness, and there is its influence upon later experiences.’

Play-based mathematics covers these aspects as children are having fun and gaining confidence as they build a strong mathematical foundation (Perry, 2000; Van Oers & Duijkers, 2012). Through play and discussion, these children have covered various mathematical concepts: classification is the matching or sorting of objects or ideas by chosen characteristics, these objects can then be counted, compared, or sequenced; spatial awareness and geometry include an understanding of shapes and boundaries that can be rotated or transformed; and measurement, including the use of fractions, is where children are exploring the size, weight or volume of objects.

By being aware of these mathematically rich experiences, parents and educators are able to support opportunities to explore these concepts and scaffold mathematical language, helping to build the strong mathematical foundation all children are entitled to.


Kathy Swinkels
PhD Candidate, Deakin University


Dewey, J. (1938). Experience and education (1997 ed.). New York, NY: Kappa Delta Pi.

Perry, B. (2000). Early childhood numeracy. Canberra, ACT: Department of Education, Training and Youth Affairs (DETYA) and Australian Association of Mathematics Teachers (AAMT).

Van Oers, B., & Duijkers, D. (2012). Teaching in a play-based curriculum: Theory, practice and evidence of developmental education for young children. Journal of Curriculum Studies, iFirst, 1–24. doi: 10.1080/00220272.2011.637182

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Mathematically rich interactions in early childhood by Kathy Swinkels was featured in Every Child Vol. 19 No. 3—Celebrating 75 years of ECA. Click here and purchase your copy today!