CMNetwork E-bulletin: April/May 2017

    © Copyright M. Worthington & E. Carruthers 2012

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Occasionally a picture-story book will trigger some mathematical explorations, in this instance, counting and addition. The teacher had read the story ‘One is a Snail, Ten is a Crab’ (2006) by Pulley Sayre, A., Sayre, J. and Cecil, R. The children were very excited by this and wanted to find creatures to calculate their own chosen total.

Shimae decided to ‘find out what 100 is’. She wrote the number ‘100’ and as she progressed, counted the legs of each creature she drew. After a while she said that so much counting was difficult, and an adult counted with her, Shimae noting the total she counted each time. When she reached 100 she wrote ‘6 spidr 3 insec 1 pursn a well (whale) 1 pig.’.

Other children explored different quantities, allowing them all to differentiate according to the number they felt able to deal with. Harrison (not shown) had chosen to work out which creatures to select so that their feet would total 11. He began by explaining, ‘I don’t know how to draw spiders, so I’m just going to do the legs.’ Next he drew two additional legs, saying ‘one person’, and then counted them all: ‘One, two, three, four… ten’. Now I just need one more – it’s a snail. There! That’s eleven altogether.’
The children used a range of ways of representing, such as Jamie’s written response below:

Jamie also chose ‘100’, ‘because that’s massive!’ He wrote ‘9 peeple’ and then used his fingers to count in twos, writing ‘1 optpus 2 spiders, admitting ‘This is getting hard now. I know! I can write it down each time and count on!’ When he neared his total he added ‘9 spiders’, then crossed it out and wrote ‘8’, explaining ‘Nine makes too many legs – so I had to take one off to make the right amount.’

Children love to challenge themselves, and analysing thousands of children’s examples we have never found a child who planned to work on something that was too easy: they either match what they do to their understanding, or stretch themselves to go beyond what they have previously done.

Taxonomy:

  • Written number and quantities: representing quantities that are counted

  • Calculations: children's own methods: counting continuously; separating sets

Gallery 7: The emergence of graphic symbols and texts in pretend play

Gallery 8: Children's graphic symbols and texts in self-initiated contexts.

Resources

Most Recent publications:

Worthington, M. and Van Oers, B. (2016) Pretend Play and the cultural foundations of mathematics. European Early Childhood Education Research Journal 24 (1). 51-66.

Worthington, M. and Van Oers, B. (2015) Children’s social literacies: Meaning making and the emergence of graphical signs and texts in pretence. Journal of Early Childhood Literacy 16(1), 1-29.

Carruthers, E. (2015). Listening to children's mathematics in school. In B. Perry., A. Gervasoni and A. MacDonald. Eds. Mathematics and Transition to School - International Perspectives. Sydney, Australia: Springer.

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