Learning Experiences for Papua New Guinea on Counting and Arithmetic Strategies

Papua New Guinea has a rich variety of languages and counting systems. These counting systems have been analysed for the cycles that they use, that is the way that the set of counting words are used to form larger numbers. For example, in many languages 6 is hand and one or 5 + 1, 7 is hand and two or 5 + 2. In many of these languages the word for twenty is man or two hands and two feet. These systems are usually digit tally systems because the digits of the hands and feet are used for keeping track of the numbers.

This means that many vernacular counting systems are helpful for students in elementary and primary school learning to add and subtract efficiently because they have a culture that is already rich in natural number combinations.

A number of learning experiences will illustrate how these may be useful. If another counting system has a similar pattern to the one described then it may be useful for that language too.

The information on the counting systems was collated and analysed by Glendon Lean. His thesis and appendices are held at the Papua New Guinea University of Technology and University of Goroka. They can also be found on a website set up from the University of Goroka. The Glen Lean Ethnomathematics Centre has put all the counting systems into a database and many language can be found by searching. Details are given of each language. Much of this data was collected from old records dating back to first contact and from University students and some teachers during the 1970s and 1980s.

Selected Counting Systems

The following counting systems are selected because they represent a range of commonly used systems. A teacher needs to work out what combination of words form new counting words in the vernacular. It might match one of the following. The language may also be found in the counting system database where an analysis is given.

Language	Counting System Features	Special Features
Roro	Cycle of 10 system	6=3x2, 7=3x2+1, 8=4x2; 9=4x2+1
Buin, Uisai	Cycle of 10, 100; classifiers	7 is 3 before 10, 8 is 2 before 10, 9 is 1 before 10
Goroka	Cycles of 2, 5
Hagen	Cycles of 4, 8