Mapping variation in children’s mathematical reasoning: the case of ‘what else belongs?’

Colleen Vale, Wanty Widjaja, Sandra Herbert, Leicha A. Bragg, Esther Yoon Kin Loong

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5 Citations (Scopus)


Explaining appears to dominate primary teachers’ understanding of mathematical reasoning when it is not confused with problem solving. Drawing on previous literature of mathematical reasoning, we generate a view of the critical aspects of reasoning that may assist primary teachers when designing and enacting tasks to elicit and develop mathematical reasoning. The task used in this study of children’s reasoning is a number commonality problem. We analysed written and verbal samples of reasoning gathered from children in grades 3 and 4 from three primary schools in Australia and one elementary school in Canada to map the variation in their reasoning. We found that comparing and contrasting was a critical aspect of forming conjectures when generalising in this context, an action not specified in frameworks for generalising in early algebra. The variance in children’s reasoning elicited through this task also illuminated the difference between explaining and justifying.

Original languageEnglish
Pages (from-to)873-894
Number of pages22
JournalInternational Journal of Science and Mathematics Education
Issue number5
Publication statusPublished - 1 Jun 2017
Externally publishedYes


  • Comparing and contrasting
  • Generalising
  • Justifying
  • Reasoning
  • Variation theory

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