History of Number

Evidence from Papua New Guinea and Oceania

  • Kay Owens
  • Glen Lean
  • Patricia Paraide
  • Charly Muke

Part of the History of Mathematics Education book series (HME)

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Kay Owens, Glen Lean, Charly Muke
    Pages 41-60
  3. Kay Owens, Glen Lean
    Pages 61-72
  4. Kay Owens, Glen Lean
    Pages 73-89
  5. Kay Owens, Glen Lean
    Pages 91-111
  6. Kay Owens, Glen Lean
    Pages 113-126
  7. Kay Owens, Glen Lean
    Pages 167-192
  8. Kay Owens, Glen Lean
    Pages 193-222
  9. Patricia Paraide
    Pages 223-242
  10. Back Matter
    Pages 291-461

About this book


This unique volume presents an ecocultural and embodied perspective on understanding numbers and their history in indigenous communities.  The book focuses on research done in Papua New Guinea, and will help educators understand humanity's use of numbers, and their development and change. The authors focus on indigenous mathematics education in the early years and shine light on the unique processes and number systems of non-European styled cultural classrooms. This new perspective for mathematics education challenges educators who have not heard about the history of number outside of Western traditions, and can help them develop a rich cultural competence in their own practice. Featured in this invaluable resource is the data and analysis that chief researcher Glendon Angove Lean collected while living in Papua New Guinea before his death in 1995.

Among the Topics Covered:

- The diversity of counting system cycles, where they were established, and how they may have developed.

- A detailed exploration of number systems other than base 10 systems including: 2-cycle, 5-cycle, 4- and 6-cycle systems, and body-part tally systems.

- Research collected from major studies such as Geoff Smith's study of Morobe's counting systems, Charly Muke's study of counting in the Waghi Valley in the Jiwaka Province, and Patricia Paraide's documentation of the number and measurement knowledge of her Tolai community. 

- The implications of viewing early numeracy, and ways of catering to diversity in mathematics education.

In this volume Kay Owens draws on recent research from diverse fields such as linguistics and archaeology to present their exegesis on the history of number.  Researchers and educators interested in the history of mathematical sciences will find History of Number: Evidence from Papua New Guinea and Oceania to be an invaluable resource.


History of mathematics Numbers and mathematics education Counting systems Mathematics and indigenous cultures Mathematics and non-European classrooms Mathematics and indigenous communities Education and Papua New Guinea

Authors and affiliations

  • Kay Owens
    • 1
  • Glen Lean
  • Patricia Paraide
    • 2
  • Charly Muke
    • 3
  1. 1.Charles Sturt UniversityDubboAustralia
  2. 2.Divine Word UniversityMadangPapua New Guinea
  3. 3.St. Teresa’s CollegeAbergowrieAustralia

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2018
  • Publisher Name Springer, Cham
  • eBook Packages Education Education (R0)
  • Print ISBN 978-3-319-45482-5
  • Online ISBN 978-3-319-45483-2
  • Series Print ISSN 2509-9736
  • Series Online ISSN 2509-9744
  • Buy this book on publisher's site