Linda Lawrence

Introduction

This research write up will basically be on the questionnaire on the indigenous mathematical knowledge. The research has been carried out to find the six fundamental activities which are common to all cultures and which terms the basis of all mathematical ideas. The write up will include the counting system for two language groups. One language group is from the Southern Highlands Province and the other language group is from the Simbu Province. The write up will also include the type of measurement and the instruments used. It also includes the patterns and designs created in the different places. Nothing much will be mentioned on games and puzzles.

The research will conclude with the finding of common fundamental activities carried out in both societies.

1. Background information

The questionnaire form was given to two students from the Program doing grade ten (10). One of the students was from Pangia in the Southern Highlands which is 9 male and the other one was from Chuave in the Simbu Province. The one from Simbu was a daughter of a senior mathematics teacher at Mt. Hagen. The student gave the questionnaire to her father so the father filled the questionnaire. As mentioned, the mathematics teacher is from Chuave district in the Simbu Province. He is from a language group called “Kepai”. He mentioned that he can speak four (4) different languages including his traditional or cultural language (Kepai). He also speaks his mother’s language which is the Asaro language in Goroka. The third and the fourth languages are ‘tok pidgin’ and ‘English’ language. The questions in the questionnaire were answered according to Kepai language which is his father’s language.

The other informans was from Pangia as mentioned and he speaks Wiru language. Wiru language is his mother tongue and he indicated that he speaks only three (3) languages. The first language was his mother tongue and his second language was ‘tok pidgin’. His third language was the language for learning which is the English language. He said that his parents are from nearby villages and they speak the same language (Wiru language).

2. Counting System

The counting systems are totally different from each other. The counting system from the Kepai language group in the Chuave district has an interesting counting system. Their counting system had same number patterns and the relationship between the numbers was very clear. The words that represent the numbers in the counting system were only two words that had some pattern in the counting. The two words that were used are ‘tran’ which stands for number one(1) and the other word is ‘swo’ which represents number two(2).

The only word that is different or does not follow any pattern is the name that represents number five. There is a word that connects the two basic words is ‘era’. Era does not represent any number but it is the word ‘and’ that connects the two words to form other numbers. For example, the number three (3) reads as ‘two and one’ which is ‘swo era tran’ in Kepai language group.

From the counting system, I saw that ‘tran’ represent one which is an odd number and ‘swo’ represent two which is an even number. It is therefore in the counting system, there is no tran (one) to represent even numbers. It only consist of ‘swo’ which is the even number. For example the number six(6) is (swo era)3 [editor’s comment: this is a colloquial way of writing repeated three times] meaning there are 3 lots of 2’s which adds up to 6. For the even odd numbers, they contain tran (1) that makes the number odd. For example the number 9 is 4 lots of 2 and one(1).

Because the Kepai language group does not have specific words for each number, they repeat the two words so the name became longer and longer. For example, the number 4 is (swo era) and twenty two is (swo era). When they came to large numbers which is thirty and onwards, the Kepai language group use the fingers and toes of person. When they came to thirty, they use a finger to represent number 2 and number thirty reads a person’s both hands and one feet [editor’s comment: double 5 represented by each hand and the foot or 3x10].

When they came to very large numbers like one hundred or two hundred, they represent one single finger as forty. For instance, one hundred is calculated as a persons hand which is twenty (in reference to one finger represents 2) plus two finger (in reference to one finger represent forty) [editor’s comment: this is 20 plus 2x40]. It is not very clear to understand using fingers but we see that when counting tens, they use the whole hand containing five (5) fingers. When they go to the larger numbers they use individual toes and fingers. The Kepai language group themselves understand whether it is a smaller or larger numbers.

Apart from the questionnaire if there is a base number and he or the informant mentioned that when they go to larger numbers, they use forty (40) as their base number. For example, when the old people at these time, they count and put their money in the bundle of forty.

The second informant is from Pangia as mentioned and Wiru is his language group. The counting system for Kepai group is totally different from the Wiru language group. The Wiru language group use their body parts to represent the numbers in the counting system. They count from the finger where the small man finger is one. In these kind of counting system, patterns cannot be clearly seen. Because the body parts have different names, the number also have their own different names. A copy of the sketch of the number system is attached at the back. From the Wiru language, a base unit cannot be found, that does not mean that they do not practice one fundamental activity which is the counting. The counting itself takes place.

3. Equivalent words or phrases

As modern mathematics, traditional activities also have similar or equivalent word phrases on Fraction and zero but nothing for the negative numbers. The Kepai language group use the word share which is equivalent to fraction. In these language, group, the measure of the quantity is not much recognized when activities on special occasions the word fraction is used when sharing of foods and other stuff. In these same language groups, they refer zero to something they do not have or when things are finished. They also have their cultural terms to describe or to name the days.

For the Wiru language group, they refer ‘half’ as fractions. In their cultural terms, they do not really mean the half of a whole thing. They refer any fraction of a thing as half. When occasions such as pig killing, they use fractions when sharing the pork. When things are shared, they do not refer to as a small proportion of the food compared to the others, they will only say they got half. In these case, the word half does not mean half of a thing, it will represent any fraction of the thing e.g sharing of pork. The word zero is also referred to as there is nothing or when something is finished.

4. Measurement

In the cultural context, there is nothing on measurement but the time keeping and the measurement of length. Measurement is another fundamental activity in the cultural societies where sticks and ropes are used for measuring an object or even measuring the perimeter of a garden. When a perimeter of a garden is found, they refer it as an area and not the space [distance] around that area.

The both language groups (Wiru and Kepai) have the same sort of calendar to keep time. Moon is very common in most of the areas where it is used for many activities like planting new garden. Shadow is also used in keeping time for a day, where morning and afternoon can be seen clearly from the shadow. Mountains and rivers can be counted as distance, even though they are not so accurate in their measurement. In the cultural context, every measurement is done through approximation and not accurate.

5. Patterns and Designs

Design is also one at the six fundamental activities in the society. Similar things are constructed in both Chuave and Pangia area but their designs differ. For example, a man in Chuave can make an armlet but its design will be different from someone from Pangia. Their carving may be different.

In patterns and designs, the cultural knowledge is very perfect. People make sure that all the patterns are even and have geometric shapes.

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