THE TRADITIONAL COUNTING SYSTEM IN THE
ENGA LANGUAGE

Thomas Leme and John Jikap

INTRODUCTION

In any traditional society of Papua New Guinea (P.N.G), people in one way or another used some form of mathematics in most of their daily activities, without realizing the fact that there were some mathematics being involved in anything they did. What they did was normal for them.

Take, for example, the Moka or gift-giving system in the highlands region. During this ceremony the people lined up all their pigs, kina shells and traditional salts and many others and then, after counting them in their own language, gave them away to their relatives or to whomever they intended to give.

In the following pages, we will discuss some of the traditional mathematics used by the Engans in their counting system in terms of the items they used. Unlike all other provinces of P.N.G, Enga province is very unique in its universal language being spoken all through the entire province. As a result there was great impact on the traditional mathematics involved when performing certain activities which involved the four mathematical operations. Mostly, addition, subtraction, multiplication with less involvement of division.

DESCRIPTION OF THE TRADITIONAL MATHEMATICS:

In Enga Province, there are a lot of modern-day mathematical topics involved in any event that the people are engaged with. Although they understand what they actually do, the mathematical concepts are unnoticeable to them. Mathematics is a natural activity for them, and they are not conscious of ‘doing mathematics’. Moreover, there is addition, subtraction, multiplication and division involved which they do not realize. The following tables explain the link or the relationship between the traditional counting system (Enga) and the modern counting system. Some selected counting numbers from both these areas are compiled in the following tables to demonstrate the relationship.

EXPLANATION:

In the traditional Enga language, there never existed any figures when and where unnoticeable mathematics were used. In substitution of the mathematical figures such as 1, 2, 3……. etc, they just used words in their language when they counted certain materials. The counting was purely in terms of concrete materials or items. There was no act of abstract counting (i.e. they counted only real and concrete materials. For example, one pig was counted as “mendai” or two pigs were counted as “lapo” in the Enga language. (see Fig. JJ).

NORMAL:
TRADITIONAL ENGA NORMAL:
MODERN BASE TEN: TRADITIONAL ENGA BASE TEN:
MODERN

Mendai 1 Akalita Mendai 10
Lapo 2 Akalita Lapo 20
Tepo 3 Akalita Tepo 30
Kituma 4 Akalita Kituma 40
Kondape 5 Akalita Kondape 50
Yangisimange 6 Akalita Yangisimange 60
Sakaita 7 Akalita Sakaita 70
Mangelap 8 Akalita Mangelap 80
Tukulap 9 Akalita Tukulap 90
Akalita 10 Aklita Akalita 100
Akalita kisa mendai 11 Akalita Akalita kisa Akalita mendai 110
Akalita kisa lapo 12 Akalita Akalita kisa Akalita Lapo 120
Akalita kisa tepo 13 Akalita Akalita kisa Akalita Tepo 130
………… . etc…………. ……etc….. Akalita Akalita kisa Akalita Kituma 140
Akalita Lalpo 20 Akalita Akalita kisa Akalita Kondape 150
Akalita lapo kisa mendai 21 ………….. etc……………… …….etc……
Akalita lapo kisa lapo 22 Akalita Akalita Lapo 200
…………… . etc……….. ……etc….. Akalita Akalita lapo kisa mendai 201
Akalita Akalita mendae 100 Akalita Akalita lapo kisa lapo 202
………………….. etc…………………… ………etc………
NORMAL KEY NOTES KEY NOTES:
“ Kisa” means addition (+) separated by
Akalita kisa lapo=10+2=12 the word being
Akalita Tepo=10x3=30 involved.
Akalita Akalita kisa Mendai =10x10+1=101 300

Figure = JJ Figure + TK

“Mendai” and “Lapo” by themselves can not act as the traditional counting numbers if there was no pig or concrete materials in general. The pigs are concrete that they allow “mendai” and “Lapo” to be the traditional counting numbers. Comparing this with the modern counting system, the counting numbers 1, 2, 3, ……… etc, are automatically the counting numbers. Even though the numbers (1, 2, 3,………etc) are abstract, people (the modern learners of mathematics) know what the numbers really mean.

LESSON PLAN:

TOPIC: MULTIPLYING 10’S AND 100’S

In teaching the topic: Multiplying tens (10s) and hundreds (100s) of 7A, modern mathematics, we will relate it with the base ten (10) counting system of the traditional Enga language. (refer to fig: TK). However, to begin teaching this topic (multiplying 10s and 100s), we will preview fig: JJ (normal) and identify what the Enga numbers mean and their counting sequential order. This will be further explained with the aid of the normal key notes. After explaining fig: JJ, we will proceed to fig: TK (base 10) This fig: TK will be further explained with the assistance of the base ten key note.

The modern concept of multiplying tens (10s) and hundreds (100s) are as follows:

PRODUCT THINK WRITE/ANSWER
7 x 80-----------? (7 x 8) x 10 --------------? 560
6 x 400 --------? (6 x 4) x 100 -------? 2400
40 x 70 --------? (4 x 7) x 10 x 10 ---------? 2800
90 x 600 ------? (90 x 6) x 10 x 10 ----? 54000

The traditional Enga concept of multiplying tens (10’s) and hundreds (100’s) within the counting system are illustrated as follows. From the table (Fig. JJ and Fig. TK) we can say that:

Akalita mendai = 10 x 1 = 10, Akalita Lapo = 10 x 2 = 20
Akalita Tepo = 10 x 3 = 30, Akalita Kituma = 10 x 4 = 40
Akalita Kondape = 10 x 5 = 50, Akalita Yangisimange = 10 x 6 = 60

HUNDREDS

Akalita Akalita mendai = 10 x 10 x 1 = 100
Akalita Akalita lapo = 10 x 10 x 2 = 200 NB: Akalita Akalita Akalita
Akalita Akalita tepo = 10 x 10 x 3 = 300 mendai = 10 x 10 x 10 x 1 = 100

WORKSHEET

1. Find the products of the following:

a) 10 x 2 = _______________ b) 10 x 3 = _____________________

c) 70 x 4 = _______________ d) 90 x 4 = ______________________

e) 10 x 10 x 1 ________________ f) 100 x 2 = _________________

g) 100 x 5 = _________________ h) 10 x 10 x 10 = ______________

2. Write the above expressions (from question 1) in the Enga language (counting system).

a)_____________________________________________________________

b)_____________________________________________________________

c)_____________________________________________________________

d)_____________________________________________________________

e)_____________________________________________________________

f) _____________________________________________________________

g) ____________________________________________________________

h) ____________________________________________________________

Traditional Counting Systems involve many modern mathematical ideas, particularly the four major mathematical operations as explained above where each and every counting number in traditional counting sequence is a result of each and every counting number by means of addition, subtraction, multiplication and division without realizing them. Therefore, we (LEME Thomas and JIKAP John) would like to make a strong recommendation that different language groups in Papua New Guinea whom modern mathematics is not their language or culture, should first of all learn their own traditional counting system in their own languages in Pre-schools or “Tok Ples Skuls” (community schools) aimed at teaching children how to do some of the basic mathematics in their own languages before they proceed to further their knowledge in other higher institutions.