History of Number

This unique volume presents an ecocultural and embodied perspective on understanding numbers and their history in indigenous communities.  The book focuses on research carried out in Papua New Guinea and Oceania, 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 and a new vision of foundational number concepts such as large numbers, groups, and systems. Featured in this invaluable resource are some data and analyses that chief researcher Glendon Angove Lean collected while living in Papua New Guinea before his death in 1995.

Among the topicscovered:

• 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 and Sue Holzknechts studies of Morobe Province's multiple counting systems, Charly Muke's study of counting in the Wahgi 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 in the light of this books research, 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 reachingback ten thousand years ago.  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.

Kay Owens chose a lecturing position at Charles Sturt University in Dubbo in the School of Teacher Education in 2003 after serving for 15 years at the University of Western Sydney where she was a Senior Lecturer. During that period she gained her PhD in mathematics education on young children engaged in spatial problem solving. She has a long career internationally with 15 years in Papua New Guinea where she held a lectureship in mathematics at the PNG University of Technology and a Head of Department position at Balob Teachers College. She was also selected for a Swedish lecturer exchange to Gothenburg University for the enhancement of tertiary education in that country and for a Masters Course at the Inter-University Institute in Macau. Kay has continued her research working with colleagues in Papua New Guinea and Sweden with a focus on ethnomathematics (mathematics, language and culture) and space, geometry and measurement education. Her international projects have been funded byUSA National Science Foundation, AusAid and her universities competitive grants while her local and state projects have had funding from state and federal governments and non-government agencies and her universities.

Patricia Paraide is an associate professor in Education Research at Divine Word University. She received her PhD at Deakin University in 2009. She has published a number of papers on education in Papua New Guinea, including mathematics education, and has presented at several conferences internationally. Her expertise and interests include language and linguistics, literacy across the lifespan, and education and indigenous knowledge.

An Overview of the Studies, Papua New Guinea, Oceania, Languages and Migrations.- The Languages Studied by Lean and his Analysis of Counting Systems.- 2-Cycle Systems Including Some Digit Tally Systems.- Body-Part Tally Systems.- 5-Cycle Systems.- 10-Cycle Systems.- 4- and 6-Cycle Systems.- Number and Counting in Context Including Classifications.- Testing the Diffusion Theory.- Towards a Prehistory of Number.- Indigenous and Western Knowledge.- Integration of Indigenous Knowledge in Formal Learning Environments.- Rewriting the History of Number from Papua New Guinea and Oceania Evidence.