The emergence of multiplicative thinking in children's solutions to paper folding tasks

Susan B. Empson, Erin Turner

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Although children partition by repeatedly halving easily and spontaneously as early as the age of 4, multiplicative thinking is difficult and develops over a long period in school. Given the apparently multiplicative character of repeated halving and doubling, it is natural to ask what role they might play in the development of multiplicative thinking. We investigated this question by examining children's solutions to folding tasks, which involved predicting the number of equal parts created by a succession of given folds and determining a sequence of folds to create a given number of equal parts. Analyzing a combination of cross-sectional data and case studies from standardized clinical interviews, we found that children were most successful at coordinating folding sequences with multiplicative thinking when they used a conceptualization of doubling based upon recursion. This conceptualization tended to generate more sophisticated solutions.

Original languageEnglish (US)
Pages (from-to)46-56
Number of pages11
JournalJournal of Mathematical Behavior
Issue number1
StatePublished - 2006


  • Folding
  • Multiplication
  • Multiplicative thinking
  • Partitioning
  • Problem solving
  • Repeated halving

ASJC Scopus subject areas

  • Education
  • Applied Psychology
  • Applied Mathematics


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