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History of Number: Evidence from Papua New Guinea and Oceania

Kay Owens, Glen Lean, Patricia Paraide, and Charly Muke
Publication Date: 
Number of Pages: 
History of Mathematics Education
[Reviewed by
Tom Schulte
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Having previously reviewed Visuospatial Reasoning, I was intrigued to learn more about the insights gleaned through years of study done with the varied indigenous peoples of Oceania. This volume focuses on the development of counting systems from body-part tallying (by fingers, toes, etc.) to more abstract application. The studies here approach variously the diffusion, categorization, and modern-day survival of the systems studied.

In searching for the wellspring of these tally methods, the studies find indigenous roots. That is, they looks back over the millennia and do not find echoes of the Middle East — no distillation of proto-Indo-European numerals, etc. This makes the Upper Paleolithic to Mesolithic roots probed here as fascinating as Mayan and other independent cultures. Interaction among the island societies also resulted in sexagesimal features in many systems, apparently without it being a Babylonian or Greek inheritance. Comparisons are also made to African and Native American systems.

In sum, these conclusions here directly dispute the diffusion theory and the genealogy of counting systems promoted by Abraham Seidenberg since the early 1960s. (Seidenberg argued that counting was diffused from one center.) Not only does the research here find counting systems uninfluenced by the Middle Eastern systems, it finds that they predate them. It was while Seidenberg’s work was itself diffusing that Glen Lean was surveying tribes of Papua New Guinea (PNG). Much of the content here derives from Lean’s original research among the dense linguistic landscape of 850 distinct languages. The island area represents a sixth of the languages spoken on earth and Lean assayed this vein for twenty-two years.

Presented here is a detailed exploration of the varieties of number systems other than base 10 systems, such as the 2-, 5-, “thumb-less” 4- and 6-cycle systems enmeshed with body-part tallying. There is also an interesting consideration of the apparently mythical “one, two, many” system-less enumeration surmised to exist since at least the Nineteenth Century. Many of the systems surveyed still survive.

Lower primary school teachers of PNG adapt their methods to the tribal understandings as they surface in the classroom. Some of these methods are detailed here, for example in teaching multiplication tables. The authors argue that understanding the indigenous methods can lead to pedagogical improvements:

Teachers have to be made aware of similarities in the mathematics that is present in the two knowledge systems… Indigenous mathematical knowledge is actually used in the peoples’ lives and teachers must be trained to link this to the type of mathematics taught in the formal learning environment.

In reviewing this copy, I more than once checked to see if it were a pre-publication galley copy of some sort. It is not. What prompted this is the numerous illustrations that are crudely rendered, blurry, or containing distracting defects. It is as if rough draft placeholder images made it to final printing. This is an oversight that I have not seen in any other Springer title.

Tom Schulte tallies packing boxes and rolls of tape as he relocates from Michigan to Louisiana.

See the table of contents in the publisher's webpage.