This paper provides an overview of recent studies in mathematical education exploring the relationship between children's representations of number and their conceptual development. Our observations are interpreted with respect to developing theoretical models for mathematical learning and problem solving based on characteristics of representations. Children's external representations are categorised according to three dimensions: (i) the type of imagistic representation identified by pictorial, ikonic and notational recordings; (ii) the level of creative structural development, and (iii) evidence of a static or dynamic nature of the image. In some cases the representations revealed idiosyncratic, highly individualistic images. We draw on our data collected from a number of studies in early number learning: a cross-sectional study of 166 children in grades K-6; a 2-year longitudinal study of children's multiplication and division strategies; and related teaching experiments.
|Title of host publication||Proceedings of the Annual Conference of the Australian Association for Research in Education|
|Place of Publication||Newcastle, Australia|
|Publisher||University of Newcastle|
|Number of pages||15|
|Publication status||Published - 1994|