Mathematics Education Research Journal

, Volume 13, Issue 1, pp 47–71 | Cite as

The work of Glendon Lean on the counting systems of Papua New Guinea and Oceania

  • Kay Owens


Glendon Lean collated data on nearly 900 counting systems of Papua New Guinea, Oceania, and Irian Jaya (West Papua). Lean’s data came from a questionnaire completed by students and talks with village elders. He read old documents written in English, German, and Dutch. He made comparisons between older and new accounts of the counting systems and compared neighbouring counting systems from both Austronesian and non-Austronesian languages. His work drew attention to the rich diversity of the systems and suggested that systems based on body parts and cyclic systems developed spontaneously. Digit tally systems were also relatively common. Lean’s thesis on spontaneous developments of these ancient cultures challenged traditional theories describing the spread of number systems from Middle East cultures.


Counting System Counting Word Number Word Cycle System Operative Pattern 
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© Mathematics Education Research Group of Australasia Inc. 2001

Authors and Affiliations

  • Kay Owens
    • 1
  1. 1.Faculty of EducationUniversity of Western SydneyCampbelltown

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