TRADITIONAL MATHEMATICS IN THE BOGIA & BUIN LANGUAGES:

Volumes, Capacities and Quantities.

Alings A. (Bogia) Madang. Shabre H. (Bogia) Madang. Franklyn J. (Buin) N.S.P

Introduction

The idea of Mathematics has always been part of every human civilization throughout the world. In everyday life man has always depended on some sort of mathematics. Man had to count things, estimate distances, tell time and measure weights and volumes using some sort of primitive standard units. Likewise, Papua New Guinea had and still has its unique counting systems. Of the diverse cultures in PNG, this paper focuses mainly on three different linguistic groups, namely the “Buin Language” of North Solomons Province and the “Kire” and “Warran” Languages of the Bogia in the Madang Province. In these three languages, people have always measured things using the “Comparison Method”. Especially when measuring volumes, capacities and quantities.

The objective of this presentation is to help students to interpret traditional methods of measuring volumes, capacities and quantities. All this is measured mainly by comparing one quantity to another and not counting the individual items as is the case in the Western mathematics. We will be mainly talking about measuring the number of items in terms of comparing two different quantities. it is just like in the English Language where “metaphors” are used to describe something else. It is rather ambiguous where one word is used to describe two things when used.

The reason why people have not used the actual counting system to count was that in many of our languages, the counting systems are not appropriate when measuring or counting large quantities. This is because many counting systems are restricted only to either a base 2 or 5. For example; in the Kire language of the Bogia District in the Madang Province the counting system is in base 2, thus making it difficult to count and describe items which go beyond 2. Therefore one cannot count items in large quantities. Even if it is possible to have a counting system that goes beyond 2, one has to go through the hardships of using a great number of objects to measure, using the comparison method. Moreover the decoder of the message may be totally confused by the time the encoder finishes.

Therefore to make life easier, the people have always used the “Comparison Method” involving a great skill of estimation whereby one quantity is compared to a standard unit of measurement. For instance, in the “Warran Language” of the Bogia District in the Madang Province, people used and still use one full sago bag as a standard unit of measurement to measure volumes, capacities and quantities of different items. For example: if one is to count in order to find out the number of fish caught, he/she will always count them using the sago bag as a standard unit. That is, if it is a full bag of fish then it is the same as saying one full bag of sago. Furthermore, if it is a half bag of fish he/she is actually referring and comparing to a half bag of sago and so on.

Description

The traditional mathematics cannot be seen in isolation from Western Mathematics. There are certainly some notable relationships which exist between the traditional and modern mathematics. Though one might say that traditional mathematics is different because it uses other objects (using the comparison method) to measures volumes, capacities and quantities of different items, really they are similar. They are similar in that they use the ideas of ¾, ½ and ¼. when the measurements are taken.

Suppose that in our example someone is counting the number of fish caught. He/she is actually comparing the amount of fish in regard to either a full bag, ¾ of a bag, half a bag, or a quarter bag of sago. In addition, this traditional mathematics also involves the “Estimation Area” of Western math’s.

Furthermore, a standard unit of measurement is the basis of all measurements both in the traditional and Western mathematics. In the traditional mathematics, one full sago bag is often referred to as the standard unit of measurement. Likewise, also in Western mathematics different standard units of measurement are used. For example, volumes are measured in “litres” (the accepted standard unit for measuring volumes). In many ways traditional mathematics especially in the above mentioned cultures is often neat and it is easy to measure large quantities, volumes and capacities using the comparison method. However one slight difference is that traditional mathematics uses very limited standard units of measurement, whereas in western mathematics a good variety of standard units of measurements are used. For example the unit of “litres” is used t measure volumes of liquids and the unit of “grams” is used to measure mass. In our traditional math’s, the only unit of measurement is the use of the “sago bag”, which can refer rather ambiguously to capacity or mass. This unit is accepted throughout the entire area of Madang Province. So when this standard unit is used everyone else understands it. This particular unit of measurement is still respected and upheld today despite the influence of Western mathematics. For example, in the market one might buy kaukau in terms of a fraction of a bag of sago. This standard unit is not perfectly standardized. There are two disciplines involved in using this standard unit. One, in counting the number of items and two in weighing, that is finding out the exact number of items and how heavy these items are. For instance, if one is to find out how many fish there are in the bag he/she is actually referring to a fraction of the sago bag. That is he/she is referring to fish caught in terms of a quarter, half, three quarters and a whole bag of sago. Similarly, if one is talking about kaukau he/she is referring to the weight of kaukau in regard to the weight of sago bag using the same units of measurement. That is they would not be interested in the amount of kaukau in the bag, but only in the weight of kaukau as compared to the weight of a sago bag.

Ethnomathematics
Topic: Volumes, Capacities & Quantities
Worksheet

Do the following Exercise.

(1) What is the word for “full” in the language?______________________
(2) If I say I caught a “leng” of fish, how many is that? _______________
(3) One “full” pot of water would be ___________ L?
(4) If Fred says he fetched a “liktum” of water, how many litres is that?
(5) Fred’s three children: Ben, Jill and Molly fetched this amount of water respectively; ‘simkun’, ‘duwase’ & ‘leng’. How many litres did they fetch altogether?
(6) Intepret these into western fractions and add.

(a) liktum kaklo leng = ______________________________________
(b) duwase kaklo duwase = __________________________________
(c) simkun kaklo leng = _____________________________________

Equivalent Fractions
Quantities
Simkun = “full” approx. (30) items.
Duwase = (3/4) x 30 = approx. 22 items.
Liktum = (1/2) x 30 = approx. 15 items.
Leng = (1/4) x 30 = approx. 7 items.

Liquid Volume (L)
Simkun = “full” approx. 5L
Duwase = (3/4) x 5L = approx. 3L
Liktum = (1/2) x 5L = approx. 2L
Leng = (1/4) x 5L = approx. 1L.

Note: kaklo = and or +

Conclusion

To conclude, because most of our people are uneducated, the method of measurement using “comparison” is still widely used today. Nevertheless, this method is gradually dying out because of the influence of Western mathematics. This is because the present generation is so used to Western mathematics. The fact that it is much more convenient and appropriate to the modern technological age, our traditional mathematics lies dormant. Furthermore, despite the fact that it is a big inappropriate to use traditional math’s in the modern day world, it would not be a bad idea to encourage students learning mathematics to think about mathematics in their language. After all students first think of mathematics in their own language when they try to solve mathematics problems. Therefore, traditional mathematics must not be done away with completely.