What are ‘children’s mathematical graphics’?

We originated this term to describe children's own choice of marks that they use to explore their mathematical thinking on paper (and with other media). They use a range of visual representations that may include scribbles, drawings, writing, iconic marks, invented (personal) symbols and standard symbols. Children use marks on paper (and other media) to represent, think about and communicate languages and meaning and to form specific symbols of those languages including the written language of mathematics: see for example Gallery 1. Vygotsky referred to written symbols as ‘symbolic’ or ‘cultural tools’) - and van Oers describes mathematics as a subject as ‘really a matter of problem solving with symbolic tools’ (van Oers, 2001a, p. 63).

Since Martin Hughes’s (1986) publication Children and Number: Difficulties in Learning Mathematics there has been a small but growing interest in what has variously been termed ‘emergent mathematics’, ‘mathematical literacy’; ‘mathematics with reason’ and what we term mathematical graphics.

Our work on children’s mathematical graphics grew from our experiences as teachers of young children as we supported their early, emergent or developmental writing (known as 'process writing' in New Zealand). A keen desire to answer the question: ‘what is it you believe you must do deliberately to support children’s mathematical understanding’ (Gulliver, 1992) continues to guide our research.