Investigating young students’ multiplicative thinking: the 12 little ducks problem

Jill Cheeseman, Ann Downton, Anne Roche, Sarah Ferguson

Research output: Contribution to journalArticleResearchpeer-review


Children's multiplicative thinking as the visualization of equal group structures and the enumeration the composite units was the subject of this study. The results were obtained from a small sample of Australian children (n = 18) in their first year of school (mean age 5 years 6 months) who participated in a lesson taught by their classroom teacher. The 12 Little Ducks problem stimulated children to visualize and to draw different ways of making equal groups. Fifteen children (83 %) could identify and create equal groups; eight of these children (44 %) could also quantify the number of groups they formed. These findings show that some young children understand early multiplicative ideas and can visualize equal group situations and communicate about these through their drawings and talk. The study emphasises the value of encouraging mathematical visualization from an early age; using open thought-provoking problems to reveal children's thinking; and promoting drawing as a form of mathematical communication.

Original languageEnglish
Article number100817
Number of pages16
JournalJournal of Mathematical Behavior
Publication statusPublished - Dec 2020


  • Children's drawings
  • Early mathematics
  • Multiplicative reasoning
  • Problem solving
  • Visualization

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