Young children use a range of visual representations that may include scribbles, drawings, writing, iconic marks, invented (personal) symbols and standard symbols. They use their own mathematical representations to help them think about and communicate meaning and to explore specific symbols and calculations: see for example Gallery 1. Vygotsky referred to written symbols as ‘symbolic’ or ‘cultural tools’) and mathematics as a subject has been described as ‘really a matter of problem solving with symbolic tools’ (van Oers, 2001, 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’ or 'mathematical marks' that we term children’s mathematical graphics.

Our work on children’s mathematical graphics grew from our many years' experiences as teachers of young children and has led to extensive research with children, parents, teachers and practitioners - in homes, nursery and schools across the 0 - 8 year age range.