Children's representation and structural development of the counting sequence 1-100

Noel D. Thomas, Joanne T. Mulligan, Gerald A. Goldin

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


In an exploratory study, we interviewed 172 children from Grades K to 6, and an additional 92 high ability children from Grades 3 to 6, seeking to infer aspects of their internal imagistic representations from their drawings and explanations of the numbers 1-100. We interpret our observations with respect to developing theoretical models for mathematical learning and problem solving, based on characteristics of internal systems of representation. Focusing on children's understandings of the conventional base ten system of numeration, we explore how internal representational systems for numbers may change through a period of structural development, to become eventually powerful, autonomous systems.

Original languageAmerican English
Pages (from-to)117-133
Number of pages17
JournalJournal of Mathematical Behavior
Issue number1
StatePublished - 2002

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Education
  • Applied Mathematics


  • Counting sequence
  • Internal representations
  • Visualisation


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