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Children’s Mathematical Graphics (CMG)

What are Children’s Mathematical Graphics?

     Children’s Mathematical Graphics is the term we originated to describe the marks, signs and symbols that children freely (and often spontaneously) choose to use to communicate their mathematical thinking. Our use of the word graphics ren use in their very earliest marks for 'drawing' (e.g., includes scribbles, lines, dots, drawings, tally marks, crosses, ticks, arrows, occasional drawings, children’s early (emergent) writing, and invented and standard abstract mathematical symbols. These marks signs and symbols originate in their earliest and in their very earliest marks for 'drawing' (e.g., Lancaster, 2003; 2014). We have included the word Children's to emphasise the significance of the children's role and agency in their mathematics.

    Children's mathematical graphics are remarkable, and relentlessly intriguing!


Close the gap!

We developed Children's Mathematical Graphics to help young children come to understand the formal system of mathematics, through at first using their own, intuitive ways of representing their mathematical thinking, including their own signs and symbols. In order to 'close the gap' of which Martin Hughes (1986) wrote, children need many opportunities to communicate through graphicacy in their own ways. Hughes urged teachers to "build on children's own strategies" and to "respect children's invented symbolism' (pp.176/177), and these are at the heart of Children's Mathematical Graphics.


Note: Children’s mathematical signs and representations are variously termed external representations; inscriptions; notations; cultural, psychological or symbolic tools; emergent models; schematisations; visual signs, and (from Worthington & Carruthers, 2003), Children’s Mathematical Graphics. All of the of the examples we have gathered arose freely, naturally and spontaneously, without any adult guiding or telling a child what to do.


    Hughes, M. (1986). Children and Number: Difficulties in learning mathematics. Basil Blackwell.


    Lancaster, L. (2003). Moving into literacy: How it all begins. In N. Hall, J. Larson & J. Marsh (Eds.).

    Handbook of Early Childhood Literacy. Sage.


    Lancaster, L. (2005). The emergence of suymbolic principles: The distributions of mind in early sign

    making. Biosemiotics, 7(1), 19-47.


    Worthington, M. & Carruthers, E. (2003). Children's Mathematics: Making Marks, Making Meanings.

    (1st ed.). Paul Chapman.