Dynamic imagery in children's representations of number

An exploratory study of 77 high ability Grade 5 and 6 children investigated links between their understanding of the numeration system and their representations of the counting sequence 1-100. Analysis of children's explanations, and pictorial and notational recordings of the numbers 1-100 revealed three dimensions of external representation-pictorial, ikonic, or notational characteristics-thus providing evidence of creative structural development of the number system, and evidence for the static or dynamic nature of the internal representation. Our observations indicated that children used a wide variety of internal images of which about 30% were dynamic internal representations. Children with a high level of understanding of the numeration system showed evidence of both structure and dynamic imagery in their representations.