Nancy Emert

Introduction

Mathematics is known well before formal education was introduced into the country. Our ancestors use mathematics in their every day lives in doing one thing or another. The type of mathematics they use is termed as ethnomathematics or simply cultural mathematics. In which, basically it means mathematics practiced, used, etc through culture.

Since mathematics is used traditionally in our culture, there are cultural language names for several mathematical terms that are used. For example, the counting system, measurements, patterns and designs, and games and puzzles and so on. In this report we will briefly look at how cultural language is used to name or describe the counting system, measurements, patterns and designs, and games and puzzles. In which a questionnaire was done on two of my students in the school where I did my practical – Tarangau Primary School. One is from Simbu Province – Kundiawa district and the other Eastern Highlands Province – Bena district. We will look at the summary of the findings and discuss briefly on Bishop’s, fundamental activities.

I Summary of the student from Simbu Province. Kaupa’s first language is his mother tongue. He speaks Kuman language. His sub-district is Kundiawa and said he can speak three languages. Since he spends most of his life in town he does not know much of his culture. Here’s just a summary on what he has given on the questionnaire attached.

a) Counting System

Kaupa’s counting system is more or less based on body parts. One and two has a distinct name each which do not refer to any body parts. three would be described as one and two, four two and two and five would refer to one side hand. Six would refer to one side hand and one, seven would refer to one side hand and two and so on. Ten would refer to both hands. Eleven would refer to both hands and one and the pattern follows on till fifteen would refer to both side hands and one side leg and twenty would refer to both sides hands and legs. Twenty-five would refer to one person’s both legs and hands and another person’s one side hand. So forty would refer to two persons both hands and legs, and the pattern goes on.

b) Equivalent words or phrases in Kaupa’s language:
i) Fractions:
His cultural group do not use fraction except for half. In his culture fractions are used during pig ceremony, marriage ceremony and compensation payments. During these times food and money are shared so half is sometimes used.
ii) Negative numbers:
Kaupa’s culture do not have negative numbers.
iii) Zero
Yes, zero is significant in his culture.
iv) Counting days and weeks.
Days, week, month and year are counted. For example, one week is referred to as one Sunday (Wakau Swara).

c) Measurement
Measurements of size of the garden is by just looking at the size, but the perimeter of garden or house or length and width are done using rope and sticks. This distance between two villages can be found by comparing it with the distance of two known villages.

Calendar is kept by watching the position of the sun and time their shadow or listening to animals, birds, insects etc.

d) Patterns and designs
Patterns and designs are made on house wall, bilums, belts, armbands, hats, etc.

e) Games and puzzles

Kaupa is not too sure about traditional games and puzzle so he didn’t give any example.

II. Summary of the student from Eastern Highlands Province. Negi’s first language is mother tongue (Bena) and her language group is Bena, comes from the sub-district of lower Bena and can speak three languages. She also spent most of her life in town and does not know most of her culture.

a) Counting System
Negis counting system is only partly based on body parts. One and two have a distinct name each. Like Kumau, three refers to one and two, five refers to one side hand, ten both side hand. Fifteen would refer to both side hands and one side leg, which is all like Kuman language. But twenty refers to one stick and one hundred refer to one bilum.

b) Equivalent words or phrases in Negi’s language.
Fractions are ignored except for half. Half is used especially in sharing of food. Negative numbers are also used, for example when some has gone. One more step than required, in which the numbers are counted in reverse. There is also a term for zero. Counting of days and weeks do occur example is given in the questionnaire attached.

b) Measurement
The size of the garden is known by just looking at the land area; perimeter of garden, house, length and width are all done by using ropes and sticks. She has no idea about how to find distance between two villages. Calendar is kept through viewing the position of sunrise and marking seasons. Time is known through shadow and birds.

c) Patterns or designs.
Traditional patterns or designs are done through weaving pitpit or bamboo walls, making bilums, kundu, etc. Some possible patterns or designs are shown in the questionnaire attached.

e) Games and puzzles
Counting is done when timing how long something is done especially when someone is diving. Measuring is done how far some one swam is measured. Time is measured during hide and seek, i.e. calculating how long someone hid. She has no idea about chance.

Basically, this is just the summary of what I gathered from the questionnaire during practical teaching. Papua New Guinea has diverse cultural background. Although some cultural aspects of the two students are the same, we also see some unique differences. And more importantly, we see that there is an obvious link between formal mathematics and out of school mathematics, by which, I mean mathematics in used in some form which are also related. According to the findings we see that the main area of mathematics – counting and measurement – are involved in the country’s culture where we practice it without realizing it.

Bishop’s Fundamental Activities

According to (Bishop; 1990; 59), Bishops, fundamental activities involve six aspects.
1. Counting: The counting system of Papua New Guinea is more or less related to what Bishop describe about counting. It may involve body or finger counting.
2. Locating: Though much information is not gathered on this, we do symbolize other environments with other thing too, especially in my village, comparing distances, size, etc.
3. Measuring: Measuring is one of the fundamentals of building houses in a traditional Papua New Guinean society. And for sizes, it can be compared by just look at the land area for example.
4. Designing. Designing is one of the tradition of PNG. Each Province has its own unique design, which identifies it or distinguishes it from other provinces. Designs are still created in PNG, even today.
5. Playing: Traditionally, the games that people play would be hunting, fishing etc. in which the rules of how to play that same is manipulated well to win or obtain a good outcome.
6. Explaining to me personally, to explain or describe something, the best explanation I would give would be in my own language. Relationships can be better made in language culturally.

Conclusion

Cultural mathematics include all the in-school mathematical concepts. In addition, the natives are more familiar with their cultural mathematics than the foreign. Furthermore, due to the diversity of culture, to understand formal mathematical concept is affected. From the findings, it seems that nearly everything in formal mathematics has a distinct name in language. In which, the name in the language describe the concept more deeply on naming it alone.

Bibliography

1. lecture notes
2. Bishop Alan J. (1990)
Race and Class, 32(2)

Kaupa – Simbu – Kuman language

1. Background information
- What is your first language (Mother tongue)?
Mother tongue
- What is the name of your language group?
Kuman language group.
- Sub –district Kundiawa
- Province: Chimbu
- How many languages can you speak?
Three.

Are the equivalent words or phrases for the following in your language.
Fractions: Yes. (There is a language word for half only).

On what occasions would they use fractions in your culture.
1. Pig ceremony
2. Marriage ceremony
3. Compensation payment.

Negative numbers: No.
On what occasions would they use negative numbers in your culture. There are no negative numbers in this culture.

Zero. Yes

Counting days and weeks:
How do they count days and weeks in your culture? Give example.
1. One week: Wakau swara
2. One month: Ba swara
3. Buga inhhu swara
4. One day: Ande enge swara

3. Measurement
Describe or explain how the following are measured in your culture. Also describe the instruments which may be used in these measuring activities.

Size of a garden: (e.g. area)
This group of people do not measure the size of the garden by using any instrument or so but they determine the size or area of the garden by looking at the size of the garden. i.e. how wide or how tall.

Perimeter of a garden:
Instrument used to measure the perimeter: rope and small sticks. They stand the sticks at the ends of the piece of land and join these ends with the rope tied to them.

Perimeter of the House:
Instrument used: rope and small sticks.
The foundation of the house is done by putting/standing sticks at the corner of the house and then joining these sticks with rope.

Length and Width of house.
Use one rope to measure the length by joining them to the sticks and another rope to measure the width by also joining them to the sticks that are planted to the soil.

Distance between two villages:
There are no special instruments to measure the distance between two villages but the distance between two villages is describe by using the distances of known villages or comparing the distance of two villages which is unknown to someone with the distances of the villages that is known to him.

Keeping calendar
These people kept the calendar by watching the position of the sun as it rises in the east and wind direction.

Time
They tell the time by
a) standing in the sun and looking at their shadows.
b) by listening to animals, birds, reptiles, insects, etc.
e.g.: during the early hours of the morning the chicken crows.

4. Patterns and designs
Give examples of traditional activities which create: Patterns/designs:
- house walls, bilums (bag), belts, arm bends, hat, etc.

If possible give examples of the patterns or designs below.

Examples of patterns which have geometrical shapes.

5. Games and puzzles
Describe the traditional games that children play which involves any of the following.
Counting: -
Time: -
Chance:-
Negi – EHP – Bena language

1. Background information
What is your first language (mother tongue)? Bena
What is the name of the language group? Bena
Sub-district? lower Bena Province: Eastern Highlands
How many languages can you speak? Three.

Are the equivalent words, or phrases for the following in your language?
Fractions: Monekiya-ayawe ( )
On what occasions would they use fractions in your culture?
When they are sharing food, especially cutting of meat or breaking kaukau.

Negative numbers: igrehuto Lihumeki
On what occasion would they use these negative numbers in your culture?
When someone has gone more steps than what was required, he would be told to count/reverse back. (Negative)

Zero: Menii

Counting days and Weeks.
How do they count the days and weeks in your culture? Give examples:
Tomorrow/yesterday. Yago
The day after tomorrow or the day before tomorrow: Ologo
One week: Sale mone
One month: Ikahi mone
One year: Mleke himone

3. Measurement
Describe or explain how the following are measured in your culture. Also describe the instruments which may be used in these measuring activities. Size of a garden (e.g. area). They make the judgment of the area by just looking at the land area.

Perimeter of a garden
Put sticks at the corners of the garden and tie ropes around by the stick.

Perimeter of a house
Use ropes and sticks or count steps around the house.

Length and Width
Length – Yatma’a
Width – Sipi’a
Distance between two villages.
-

Keeping calendar
Sunrise to mark wetseason from dry season.

Time
Shadow or birds

4. Patterns or designs
Give examples of traditional activities which create:
Patterns/designs
Weaving of pitpit or bamboo walls, bilum making, kundus, etc.