COUNTING TO TEN IN THREE COUNTING SYSTEMS

Eileen Kassman, Gabriel Ninkama and Ishmael Nombe

INTRODUCTION

This ethnomathematics lesson on counting systems is a combination of the Wuvulu (East Sepik Province), Motu (Central Province), and Unggai (Eastern Highlands Province) counting systems. Strictly speaking, the cultural aspect of mathematics in these three areas differs. However the treatment of the topic will be limited to ideas which are related, provided that mathematics education in this aspect should be relevant to the goals and aspiration of students wherever they may be. It is therefore our understanding that mathematics is not culture free. Since counting will be done in three different languages we have to ask certain questions as educators. Firstly how does the language of instruction affect the meeting of individual needs? Do students develop their general mental processes better in their own language?

The answer to this question has usually been a resounding and an unquestioning “yes” as being evident in the report of a 1951 UNESCO conference on vernacular languages in education. Therefore we are hoping that the level in which we present this topic to the students does not conflict with their values of teaching the counting system in their culture, furthermore they should have at least have an understanding of the way counting is done in these three places and cultures. Moreover the students should try to relate this to their own counting systems if possible in terms of the base (e.g. base 5 or 10 etc…) regardless of the languages which interpret the numbers.

DESCRIPTIONS

1. The Wuvulu counting system.

Numerical value Tokples name
1 eai
2 guai
3 olumanu
4 obao
5 eaipana
6 eaipani ma eai
7 eaipani ma guai
8 eiapani ma olumanu
9 eaipani ma obao
10 hefua

Note: The word ‘pana’ (number 5) represents one hand therefore every number that succeeds 5 is oe hand and that number. e.g. The number 6 exceeds 5 by 1 so that means that it is one hand and one. Therefore it is only true to say that the Wuvulu counting system uses base 5 which corresponds to one hand.

2. Motu counting system

In the Motuan culture the counting system is base 10 but every ten has a name of its own. It depends on what you are counting.
For example counting fish, coconuts, and shellmoney is different from counting money, stones, heads and sticks. Below is a table of the Motuan counting system of fish.

Numerical value Motu name
1 ta
2 rua
3 toi
4 hani
5 ima
6 taura toi
7 taura hani
8 taura hanita
9 hitu
10 gwauta (for counting most objects)

But the ‘rabu’ is the word for 10 when counting shell money or coconuts, and ‘ituri’ is the word for 10 when counting fish.

3. Unggai counting system.

Below is the general counting system of Unggai. The base used usually changes after every five count.

Numerical value Tokples name
1 mako
2 lowe
3 loweki mako
4 loweki loweki
5 ade mako
6 ade makoki mako
7 ade makoki lowe
8 ade makoki loweki mako
9 ade makoki loweki loweki
10 ade lowe

The word for 5, ‘ade’, simply means one whole hand. Ade lowe (=10) means ‘two hands’.

Further counting uses feet. For example, the expression for 15 is ‘ade lowe ki ika mako’, meaning ‘two hands and one foot’. 20 can be expressed in two ways: either ‘ade lowe ki ika lowe’ (2 hands and 2 feet), or ‘we mako’ (‘we’ means ‘person’), that is to say, 2 hands and two feet make one whole person.

LESSON PLAN:

OBJECTIVES:

Students should be able to:

1) state in their tokples the numbers 2 and 5,
2) count numbers 1 to 10 using the counting system from the three different areas,
3) identify the base in the counting system and relate it to equivalent numbers.

MATERIALS:

Charts, Flash cards, Worksheets.

INTRODUCTION PERIOD

TEACHING STEPS
PUPIL ACTIVITY
1. Ask students to state in their language the
numbers 2 & 5.
1. Students to state in their language the
numbers 2 & 5.
2. Introduce the topic and define base to the
students.
2. Students are to listen to the teacher.
3. Give examples of base to the students.
(tally, Roman numerals, hands).
3. Students to watch and listen
carefully.
4. Ask students to identify base in their
counting system and give examples. 4. Students to identify base in their
counting system and give examples.

BODY OF LESSON

1. Wuvulu counting systems

- put chart with tokpeles numbers on the board.
- students to look at the chart
- explain the counting systems to the students,
numbers 1 to 10.
- students to listen to the teacher.
- ask students what base is used. - students to answer.
- use flashcards to test students’ memory. - students to respond to the flashcards.

2. Motu counting system.

- make students play jumble game. - students to play jumble game with teacher.

- explain the counting system from 1 to 10
and its uses.
- students to pay attention.
- ask students to identify the base. - students to identify the base.

3. Unggai counting system

- explain the counting system to the students.
- students to pay attention.
- ask students to identify base. - students to identify base.
- ask students to identify if there is a change
of base. - students to identify and state change
of base.

- explain to the students that the base
changes every now and then. - students to pay full attention.

4. Exercises

- Give students exercises concerning the three
tokples.
- students to complete exercises.
- Supervise while students do exercises.
- students to continue exercises.
- correct exercises together with the students. - correct work together with the teacher.

YABIUFA LANGUAGE
1. What are the bases used?
2. How is six expressed in Yabiufa language?

WUVULU LANGUAGE

1. What is the base used?
2. How is six expressed in Yabiufa language?

MOTU LANGUAGE

1. If gwauta = 10, and toi = 3, then what is the number expressed from these two words?
2. How do they express 10 when referring to fish?
3. What is referred to when they say ‘rabu rua’?

4. How do you say 500, if 100 = sinahu ta and 5 = ima?

LESSON CONCLUSION

1. Divide students into three groups - students to move into 3 groups

2. Have a drill game to test their - students to play drill game.
understanding using flash cards.

3. Add scores and give prizes to all the - they will know who wins and
groups. collect their prizes.

CONCLUSION

From the above three languages we can conclude that despite the differences in languages, they are all similar in that they have bases and most of the bases are 5. Different cultures have different ways of counting different things but they still have a general counting system. We can also see that the number 5 in each counting system above refers to the hand so we can also say that when they count in their tokples they usually use their hand to show its value. Although they are different in language they are similar in the way of expressing them using their hands.

Next lesson