Hitung Bini: Ethno-Mathematics in Banjarese Society

Sessi Rewetty Rivilla

, Lathifaturrahmah

and Yusran Fauzi

Mathematics Teaching Study Program, Islamic State University of Antasari, Jalan A. Yani Km. 4,5,

Banjarmasin, Indonesia

Keywords: Hitung Bini, Ethno-mathematics, Arithmetic Operation

Abstract: Banjarese elders who had never attended either formal or non-formal schools have implemented relatively

unique arithmetic operation. The arithmetic operation does not use calculators nor writing tools but can

produce a quick and precise calculation. This kind of arithmetic operation is commonly used in everyday

life and well-known as hitung bini. This study aimed to describe hitung bini as one of ethno-mathematics

found in Banjarese cultures then analyze it from mathematics viewpoints. This study used explorative

method with qualitative approach. The data were collected through observation, interview, and

documentation. The findings of the study obtained that hitung bini operation actually conforms to formal

arithmetic procedures in math which includes place value rules and basic arithmetic operation properties

such as commutative, associative, distributive, identity and inverse.

1. INTRODUCTION

Ethno-mathematics is a culture product which

develops in particular society group and links to

mathematical calculation (D’Ambrosio, 2001; Rosa

& Orey, 2011). A certain culture product in certain

society has its own specialty and distinctive feature

which is different from that of other regions. This is

due to diversity of cultures that develop in each

region.

Indonesia consists of various tribes and ethnic

groups which are rich of culture depending on where

they live. In Kalimantan, especially South

Kalimantan, there is one ethnic group known as

Banjarese. Within Banjarese society, there is a

unique product of culture, an arithmetic operation,

often used in everyday transaction, namely hitung

bini.

Hitung bini has been inherited through

generations and most frequently used now by

Banjarese elders. Hitung bini users are dominantly

women who have never earned formal education.

They recognize no formal mathematical standard

process. Most of them are illiterate. Therefore,

hitung bini operation is simply performed orally by

relying on good memories.

Peculiarly developing among people who never

earned any formal education, hitung bini is worth

analyzing in terms of how the calculation is

performed viewed from formal mathematical

procedures. It is necessary to answer if hitung bini is

relatively fast and accurate in the view of

mathematical operation procedures. This study

performed an analysis of hitung bini as one of ethno-

mathematic product from the viewpoint of

mathematics.

2. LITERATURE REVIEW

2.1 Mathematics

Mathematics is a science that deals with logic which

is arranged consistently and of which the conclusion

is drawn deductively (Salam, 1997). Mathematics is

a branch of science that learns about calculation.

Simple arithmetic operations in math are addition,

subtraction, multiplication, and division on either

integers or rational numbers. These basic arithmetic

operations are most often used in daily life.

Mathematical procedure is one of study objects

in mathematics. It consists of orderly arithmetic

procedures comprising addition, subtraction,

multiplication, and division (Atmaja, 2014). Every

procedure has certain rules or properties. The

following are the properties in addition, subtraction,

multiplication, and division of integers (Bartle &

Sherbert, 2000; Sharma, 1993; Rosen, 1993):

Rivilla, S., Lathifaturrahmah, . and Fauzi, Y.

Hitung Bini: Ethno-Mathematics in Banjarese Society.

DOI: 10.5220/0008518901690174

In Proceedings of the International Conference on Mathematics and Islam (ICMIs 2018), pages 169-174

ISBN: 978-989-758-407-7

169

Mathematics

Mathematical

Modelling

Cultural

Athropology

▪ Number place value;

▪ Closure property of addition, subtraction, and

multiplication;

▪ Commutative property of addition and

multiplication;

▪ Associative property of addition and

multiplication;

▪ Possessing identity for addition and

multiplication operations;

▪ Possessing inverse for addition operation;

▪ Distributive property of addition and

subtraction over multiplication;

▪ Subtraction operation as inverse of addition.

2.2 Ethno-mathematics

Ethno-mathematics was first introduced by Urbiratan

D’ambrosio. He is a mathematician from Brazil.

Ethno-mathematics is a study about math by

discerning the culture where the math emerges and

develops. This study tries to view logic and math

system from the location in which they develop

(D’Ambrosio, 2001; Wahyuni et. al., 2013).

Generally, ethno-mathematics is an

interdisciplinary study comprising cultural

anthropology, mathematics teaching, and

mathematics cognition. Ethno-mathematics is

intersection every of these (sub)disciplines.

Figure 1: Ethno-mathematics definition according to Rossa

and Orey.

In brief, ethno-mathematics can be understood as

inherited culture product that blossoms in certain

society. It is even sometimes not realized by its users

due to the simplicity of its form compared to formal

(formalized) math. As a product of culture, ethno-

mathematics is not equipped with definition, axiom,

lemma, and theorem as formal math.

3. METHODS

This is an explorative study with qualitative

approach. This method was chosen to understand

deeper about hitung bini used in Banjarese society as

well as finding its pattern in the view of

mathematical procedures (arithmetic operation). The

research was conducted in South Kalimantan without

determining particular research location. The

locations were conditional, depending on where the

subjects could be found.

3.1 Research Subject and Object

The research subjects were Banjarese people

living in South Kalimantan who use hitung bini in

their everyday lives. The objects were operation

pattern of hitung bini used in Banjarese society.

3.2 Data and Data Collection

Techniques

There were two kinds of data: main data and

supporting data. The main data consisted of data that

relates to hitung bini operation used in Banjarese

society. The supporting data consisted of description

about research location and respondents’ biodata.

The data were collected through observation and

interview.

▪ The observation was descriptive, focused, and

selective. It was used to investigate the steps

used in hitung bini operation by the users.

▪ The interview was semi-structured by listening

thoroughly and writing along everything said

by the respondents related to hitung bini used

by them.

3.3 Data Analysis Techniques

Data analysis techniques used in this study were (1)

data reduction, (2) data display, and (3) conclusion/

verification. Trustworthiness of the data were

confirmed through the following processes: (1)

credibility test, (2) transferability, (3) dependability,

and (4) confirmability (Sugiyono, 2013; Creswell &

Clark, 2007).

Ethnomathematics

Number 2538

Place value: tens

Place value: ones

Place value: hundreds

Place value: thousands

ICMIs 2018 - International Conference on Mathematics and Islam

170

4. RESULTS AND DISCUSSION

South Kalimantan is a province in Kalimantan

island, precisely in South Kalimatan. Banjarmasin is

the capital city of this province. The latitude and

longitude of South Kalimantan is 10-40 S and 1140-

1170 E. This province has total area 37.530,52 km

Geographically, South Kalimantan is located in the

Southeast of Kalimantan island. It consists of

lowland in the North area and in East Coast and

highland along Meratus mountain. The lowland of

South Kalimantan consists of peat swamp forest

while the highland partially consists of tropical

forest. The natural resources in this province

comprises permanent forest, production forest,

protected forest, convention forest, government

plantation, coal mine, petroleum, silica sand, iron

ore, etc.

South Kalimantan is made of 11 regencies, 2 big

cities, 152 districts, and 2007 sub-districts. The

regencies are Balangan regency, Banjar regency,

Barito Kuala regency, Hulu Sungai Selatan regency,

Hulu Sungai Tengah regency, Hulu Sungai Utara

regency, Kotabaru regency, Tabalong regency,

Tanah Bumbu regency, Tanah Laut regency,

Banjarbaru city, and Banjarmasin city. The majority

of its people is Moslem. The rest of them are Hindu,

Protestant, Catholic, and Buddha. The languages

used by its people are Banjarese and Indonesian.

Regional songs of South Kalimantan Selatan are

Ampar-ampar Pisang and Paris Barantai. Banjarese

traditional house is also well-known as Rumah

Bubungan Tinggi. The following figure is the map of

South Kalimantan.

Figure 2: Map of South Kalimantan

Ethnic groups that can be found in South

Kalimantan are Banjarese, Javanese, Buginese,

Dayaknese, Madurese, Mandarese, Sundanese,

Chinese, Bataknese, Balinese etc. However, the

majority of South Kalimantan people is Banjarese,

which is about 74,34 % of them, comprising three

groups: Banjar Kuala, Banjar Pahuluan, and Banjar

Batang Banyu. Banjar Kuala people are Banjarese

who live in Banjarmasin and Martapura area. Banjar

Pahuluan people are Banjarese who live in the valley

around Nagara river. Banjar Batang Banyu people

are Banjarese who live in the valley of Nagara river.

Banjarese people came from river flow area,

beginning from Bahan river flow, Barito river flow,

Martapura river flow, until Tabanio river flow.

Hitung bini operation pattern performed by

Banjarese people is divided into four operations: (1)

addition, (2) subtraction, (3) multiplication and (4)

division.

4.1 Addition

For addition operation, hitung bini uses several steps.

To perform addition 7250 + 2300, for example, the

respondent did the following steps:

▪ 7250 was transformed into 7000, 200, and 50

while 2300 was transformed into 2000 and 300

▪ 7000 plus 2000 equals 9000

▪ 200 plus 300 equals 500

▪ Then 9000 plus 500 plus 50 equals 9550

Referring to formal (formalized) math, hitung

bini operation above can be elaborated as follows:

▪ Addition 7250 + 2300 was performed based

on place value (Kallai & Tzelgov, 2012;

MacDonald et al., 2018; Sharma, 1993;

Hamdani et. al., 2009)

(7000 + 200 + 50) + (2000 + 300 + 0)

(1)

▪ Using associative property, the operation was

performed as the following (Trench, 2013;

Bartle & Sherbert, 2000; Royden, 1988;

Rosen, 1993)

(7000 + 200) + (50 + 2000) + (300 + 0)

(2)

▪ Using commutative property, the operation

was performed as the following (Trench, 2013;

Bartle & Sherbert, 2000; Royden, 1988;

Rosen, 1993)

(7000 + 200) + (2000 + 50) + (300 + 0)

(3)

Hitung Bini: Ethno-Mathematics in Banjarese Society

171

▪ Using associative property, the operation was

performed as the following (Trench, 2013;

Bartle & Sherbert, 2000; Royden, 1988;

Rosen, 1993)

7000 + (200 + 2000) + (50 + 300) + 0

(4)

▪ Using commutative property, the operation

was performed as the following (Trench, 2013;

Bartle & Sherbert, 2000; Royden, 1988;

Rosen, 1993)

7000 + (2000 + 200) + (300 + 50) + 0

(5)

▪ Using associative property, the operation was

performed as the following (Trench, 2013;

Bartle & Sherbert, 2000; Royden, 1988;

Rosen, 1993)

(7000 + 2000) + (200 + 300) + (50 + 0)

(6)

▪ Using identity property, the operation was

performed as the following (Trench, 2013;

Bartle & Sherbert, 2000; Royden, 1988;

Rosen, 1993)

(7000 + 2000) + (200 + 300) + 50

(7)

▪ Using addition operation order, the following

result was obtained (Kallai & Tzelgov, 2012;

MacDonald et al., 2018; Sharma, 1993;

Hamdani et. al., 2009)

9000 + 500 + 50

(8)

▪ Using addition operation order, the ultimate

result below was obtained (Kallai & Tzelgov,

2012; MacDonald et al., 2018; Sharma, 1993;

Hamdani et. al., 2009)

9550

(9)

4.2 Subtraction

To do the subtraction, hitung bini has two versions

of arithmetic operations. In version 1, in solving

5500 – 2700, for example, hitung bini used the

following steps:

▪ 5500 was transformed into 5000 and 500

▪ 5000 minus 2700 equals 2300

▪ Then 2300 plus 500 equals 2800

Meanwhile, for version II, to solve 5500 – 2700,

hitung bini used the following steps:

▪ 5500 was transformed into 5000 and 500.

Then 2700 was transformed into 2000 and 700

▪ 5000 minus 2000 equals 3000

▪ 500 minus 700 equals negative 200

▪ Then 3000 minus 200 equals 2800

Referring to formal (formalized) math, hitung

bini operation above can be elaborated as follows:

▪ Subtraction 5500 – 2300 was altered using

subtraction order as additive inverse (Trench,

2013; Bartle & Sherbert, 2000; Royden, 1988;

Rosen, 1993)

5500 + (–2700)

(10)

▪ Referring to place value, the arithmetic

problem was solved as follows (Kallai &

Tzelgov, 2012; MacDonald et al., 2018;

Sharma, 1993; Hamdani et. al., 2009)

(5000 + 500) + (– (2000 + 700))

(11)

▪ Using distributive property and order property,

the following result was obtained (Trench,

2013; Bartle & Sherbert, 2000; Royden, 1988;

Rosen, 1993)

(5000 + 500) + ((–2000) + (–700))

(12)

▪ Using associative property, the operation was

performed as the following (Trench, 2013;

Bartle & Sherbert, 2000; Royden, 1988;

Rosen, 1993)

5000 + (500 + (–2000)) + (–700)

(13)

▪ Using commutative property, the operation

was performed as the following (Trench, 2013;

Bartle & Sherbert, 2000; Royden, 1988;

Rosen, 1993)

5000 + ((–2000) + 500) + (–700)

(14)

▪ Using associative property, the operation was

performed as the following (Trench, 2013;

Bartle & Sherbert, 2000; Royden, 1988;

Rosen, 1993)

(5000 + (–2000)) + (500 + (–700))

(15)

▪ Using subtraction order as additive inverse, the

operation was performed like this (Trench,

2013; Bartle & Sherbert, 2000; Royden, 1988;

Rosen, 1993)

ICMIs 2018 - International Conference on Mathematics and Islam

172

(5000 – 2000) + (500 – 700)

(16)

▪ Using operation order of subtraction, the

operation was performed like this (Kallai &

Tzelgov, 2012; MacDonald et al., 2018;

Sharma, 1993; Hamdani et. al., 2009)

3000 + (–200)

(17)

▪ Using subtraction order as additive inverse, the

operation was performed like this (Trench,

2013; Bartle & Sherbert, 2000; Royden, 1988;

Rosen, 1993)

3000 – 200

(18)

▪ Using operation order of subtraction, the

ultimate result below was obtained (Kallai &

Tzelgov, 2012; MacDonald et al., 2018;

Sharma, 1993; Hamdani et. al., 2009)

2800

(19)

4.3 Multiplication

In solving multiplication problem such as 11000 ×

12, these are the steps conducted in hitung bini

▪ 12 was transformed into 10 and 2

▪ 11000 multiplied by 10 equals 110000

▪ 11000 multiplied by 2 equals 22000

▪ Then 110000 plus 22000 equals 132000

Viewed from formal math, the above hitung bini

operation can be elaborated as follows:

▪ Multiplication 11000 × 12 was altered

referring to place value, such as follows

(Kallai & Tzelgov, 2012; MacDonald et al.,

2018; Sharma, 1993; Hamdani et. al., 2009)

11000 x (10 + 2)

(20)

▪ Using distributive property, the operation was

performed as the following (Trench, 2013;

Bartle & Sherbert, 2000; Royden, 1988;

Rosen, 1993)

(11000 x 10) + (11000 x 2)

(21)

▪ Using multiplication order, the subsequent

result was obtained (Kallai & Tzelgov, 2012;

MacDonald et al., 2018; Sharma, 1993;

Hamdani et. al., 2009)

110000 + 22000

(22)

▪ Using addition order, the following ultimate

result was obtained (Kallai & Tzelgov, 2012;

MacDonald et al., 2018; Sharma, 1993;

Hamdani et. al., 2009)

132000

(23)

4.4 Division

In solving division problem such as 665000 : 2, these

are the steps performed in hitung bini:

▪ 665000 was transformed into 600000, 60000

and 5000

▪ 600000 divided by 2 equals 300000

▪ 60000 divided by 2 equals 30000

▪ 5000 divided by 2 equals 2500

▪ Then 300000 plus 30000 plus 2500 equals

332500

Viewed from formal math, the steps used in

hitung bini can be elaborated as follows:

▪ Division 665000 : 2 was altered into rational

numbers (Kallai & Tzelgov, 2012; MacDonald

et al., 2018; Sharma, 1993; Hamdani et. al.,

2009)

665000

(24)

▪ Using place value, the arithmetic operation

was performed as follows (Kallai & Tzelgov,

2012; MacDonald et al., 2018; Sharma, 1993;

Hamdani et. al., 2009)

600000 + 60000 + 5000

(25)

▪ Using rational number operation, this is the

result obtained (Kallai & Tzelgov, 2012;

MacDonald et al., 2018; Sharma, 1993;

Hamdani et. al., 2009)

600000

60000

5000

(26)

▪ Using the relation between division and

rational number results in the following

(Kallai & Tzelgov, 2012; MacDonald et al.,

2018; Sharma, 1993; Hamdani et. al., 2009)

(60000 : 2) + (60000 : 2) + (5000 : 2)

(27)

▪ Using division order led to the following result

(Kallai & Tzelgov, 2012; MacDonald et al.,

2018; Sharma, 1993; Hamdani et. al., 2009)

Hitung Bini: Ethno-Mathematics in Banjarese Society

173

300000 + 30000 + 2500

(28)

▪ Using addition order, the ultimate result below

was obtained (Kallai & Tzelgov, 2012;

MacDonald et al., 2018; Sharma, 1993;

Hamdani et. al., 2009)

332500

(29)

From the arithmetic operation patterns of hitung

bini, similarity in operation procedures are found

between hitung bini and formal (formalized) math.

This is shown in every step in hitung bini which

always include formal mathematical arithmetic

operation although some parts or formal math

operations were skipped.

Since the beginning, hitung bini tends to use

place value to finish the calculation. It conforms to

formal math’s basic concept that a number can be

arranged according to its place value (Fajariah &

Triatnawati, 2008). In addition, hitung bini also

followed standard arithmetic operation order just like

in formal math.

5 CONCLUSIONS

The results of exploration and study on literatures

pointed out that hitung bini used by Banjarese people

is part of ethno-mathematics. In solving problems,

hitung bini indirectly use formal mathematical

arithmetic operations comprising number place value

and operation properties (such as associative,

commutative, distributive and identity properties and

inverse).

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