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ETHNOMATEMATICS EKSPLORATION AND BE CONNECTED WITH MATHEMATIC CONCEPT’S IN AMANUBAN

Alfonsa Maria Abi1), Zaenuri Mastur2), Hardi Suyitno3)

1) STKIP So’e

1)Mathematics Education, Postgraduate Program, Semarang State University

1)email: fonsa_fan@yahoo.com

ABSTRACT

Humans are creatures of culture, living in a cultural environment, and helped create the culture.

Cultural integration in learning of mathematics be said to be ethnomathematics. Cultural raised

depending on where and to whom mathematics is taught. Assuming that ethnomathematics raised

already known and can assist students in learning mathematics. The goals in this research is

explore and connect ethnomathematics forms at Amanuban community in South Central Timor,

focus to activities and artifacts with mathematical concepts. This research is a descriptive

qualitative ethnographic method using triangulation techniques such as observation, interviews,

and documentation. Data analysis it became two phase that is Miles & Huberman model for

exploration phase and Glaser & Strauss for analysis connected phase. Results of study revealed

that the form ethnomathematics community have a close relationship with mathematical concepts,

especially in field of geometry and algebra. Appointed field geometry is a square, rectangle,

rhombus, regular hexagon, circle, hexagonal prisms, cubes, blocks, cylinder, hexagonal pyramid,

cone, and spheres. Concept’s from ethnomathematics forms can be integrated in learning at the

elementary school level and high school.

Keywords - ethnomatematics, culture of Amanuban, mathematic concept’s.

Introduction

Hiebert & Capenter (1992) reminds all

parties that the teaching of mathematics in

schools and mathematics are found in the

child's daily life is very different. Therefore,

learning of mathematics is necessary a

charge or bridge between the world of

mathematics in everyday based on the local

culture with school mathematics. So,

ethnomathematics is mathematics with

cultural element.

Cultural raised depending on where and to

whom mathematics is taught. Assuming that

ethnomathematics raised are well known

and can assist students to learn mathematics.

Seeing the cultural wealth of Indonesia, a lot

of culture that can be explored and linked

with mathematical concepts can even be

implemented on learning. This has been

revealed by previous researchers. Hartoyo

(2012) reveal the value ethnomathematics

in West Kalimantan border area with

Malaysia precisely Sanggau area inhabited

by the Dayak clan. Hartoyo explore the

value that exists in the Dayak culture and

implement in teaching mathematics. The

material be addapted in accordance with the

characteristics of each object.

Question in this research is how

ethnomathematics forms that exist in

people's culture Amanuban clan district of

South Central Timor and how the

relationship ethnomathematics forms in the

culture of the clan with mathematical

concepts. The goals of research is explore of

ethnomathematics forms that exist in the

culture of clan Amanuban people and

analyze the relationship between

ethnomathematics forms accordance with

mathematical concepts.

Theoretical Review

William (1985) reveals the culture is a

medium used by humans to solve the

problems. Because these systems are

adaptive, then its quite steady and

unchanged. Unless the reference conditions

adaptation or a human view of the changed

52

conditions. Culture describe a characteristic

of a nation. As happens in education,

innovation with involving cultural diversity

that we have, becomes a unique learning.

Innovation in education is growing in

accordance with the needs of curriculum,

schools and student. Ibrahim (1988) said that

the innovation usually comes from the

willingness of the school organize to

response for utilities in society and any

attempt used the school for problem solving

in society. The advances in technology now

very fast and this gives contribution in

developing educational technology and

learning, especially in mathematics. But it

should be known that the technology is not

only associated with the tool and means all

powerful. Isjoni, et al (2008) explains that

the educational technology view about the

learning process as a problem that must be

dealt with rationally and scientifically.

Application of the use of technology would

be better if it is not to forget the existing

culture in the everyday environment of

student that culture that exists in society. In

addition to maintaining the culture of the

community, students were helped to

recognize and appreciate their own culture.

Cultural integration in the learning of

mathematics called ethnomathematics.

Etymologically, the word comes from the

ethnomathematics ethno and mathematics.

Ethno means ethnic and matematic means

mathematics. According to Gerdes (1994),

ethnomathematics is mathematics applied by

certain cultural groups, labor groups /

farmers, children of a certain class of

society, the professional classes, and so on.

This means ethnomathematics not just talk

about ethnicity or clan. Hiebert & Capenter

(1992) reminds all parties that the teaching

of mathematics in schools and mathematics

are found in the daily life student is very

different. Therefore, learning of

mathematics is necessary a charge or bridge

between the world of mathematics in

everyday based on the local culture with

school mathematics. Cultural raised

depending on where and to whom

mathematics is taught. Assuming that

ethnomathematics raised are well known and

can assist students in learning mathematics.

Seeing the cultural wealth of Indonesia,

many culture that can be explored and

connected with mathematical concepts can

even be implemented on learning. This has

been revealed by previous researchers.

Hartoyo (2012) reveal the value

ethnomathematics in West Kalimantan

border area with Malaysia precisely Sanggau

area inhabited by the Dayak tribe. Uloko and

Imoko (2007) mentions about the success of

Japanese nationals and Chinese in the

learning of mathematics because they use

ethnomathematics in learning math. This

implementation has been done by Gerdes

(1994), Lipka and Irhke (2009), Sirate

(2012), and Tendeling (2013). Not only that,

the development of learning tools nuanced

ethnomathematics also been developed

conducted by teachers and has been tested

solely to improve performance and ability of

student in learning mathematics. Sirate

(2012) concluded that the application of

ethnomathematics as a means to motivate

and stimulate they student, can overcome

boredom and give a new feel to the learning

of mathematics. Because ethnomathematics

already known by student so in invites

students to identify and associate part of the

culture they already know in a matter of

mathematics with guidance will be easier

with provided of teacher.

Research Methods

This research is a descriptive qualitative

with ethnographic method using

triangulation techniques. Descriptive

qualitative study aimed to portray and

describe in more detail with the intention of

explaining, explaining and addressing the

research. By learning as much as possible an

individual, a group, or an event, researchers

aim to provide a complete view and depth of

the subject under study. The research was

conducted in the clan areas Amanuban

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sizeable majority in the South Central Timor

was that Amanuban West districts,

Batuputih district, Oenino district and

Central Amanuban district. Cultures were

explored in the form of activities and

artifacts Amanuban clan society.

Data analysis phase consists of two phases:

exploration and analysis phase

ethnomathematics form in relationships with

mathematical concepts. Exploration phase

analysis using the method from Miles &

Huberman, while the analysis phase

relationships using constant comparison

method. At the end of each stage will be the

validation of the results obtained. Validation

for the first phase carried out by community

and traditional leaders, while the second

phase of validation performed by math

teachers at each school level both primary

and secondary schools.

Result and Discussion

1) Result of Study

Research carried out has identified various

forms ethnomathematics in the area of

research and integrate the learning of

mathematics in basic education (primary)

and secondary (junior and senior high

school) in the form of a case, as shown

below.

2) Measurement Unit

Explorated of measurement unit in

Amanuban culture is a time unit, unit of

length and speed unit. Units of time

indicated in the farming society activity, a

unit of length exposed to the weaving

society and speed unit on traditional games

is faela and Huila beba.

3) Integer Operation

Kuti kelereng, tiup karet and kayu do'i game

help someone learn about the operation

mainly on integer numbers. Rules in the

kayu do'i game namely:

a. Short wood thrown and if it is not able to

arrest the opponent then the player has

the right to calculate the distance of a

wood fall short to the hole with a

distance of 1 (one) point per expanse of

wood

b. Short wooden back beaten and thrown as

far as possible without hindrance from

the opponent

c. The amount of decisive blow timber fall

short distance to the hole which is

calculated using the long timber on the

condition that one stretch of the long

wooden multiplied by the number of

blows before.

Integer consists of the set of negative

integers {..., -3, -2, -1}, zero {0}, and the set

of positive integers {1, 2, 3, ...}. In a

division operation, the remainder of the

results of the so-called fractions. This

fraction represents the ratio. Yields of

society usually packaged before it is stored

in the granary. Usually crops are mainly

corn lace-and grouped according to size to

make it look presentable when packing

(Figure 3). Each one bond (ais fes) contains

eight (8) ears of corn, one horse (bikaes es)

contain corn belt 20, which means 20 x 8

grains, and 10 horses (tuke mese) containing

10 x (20 x 8) grains.

Figure 1. Huila Beba

Figure 2. Kayu Do’i

54

4) Circle

Drum, floor of the house and brown sugar

which is owned by the tribal community

Amanuban related to the broad concept of a

circle (see Figure 4).

One element that is circular arcs can be

found in the kil noni or comb silver owned

by the community. While the length of

tangent circles concept can be found on the

headband (pilu). See Figure 5.

5) 2D Shape

Mats (nahe) is bedding and cushion are

commonly used as a substitute seat for

public use rectangular (see Figure 6). In

society, usage and mat illustrates that man

(whoever is he) has the same dignity. The

mats are stored in a manner resembling

rolled cylinder. While nyiru (tupa) has a

relationship with the concept of regular

hexagons. For motive buna on society and

woven wicker motif on the results of

rhombus.

6) Polyhedron

Types of sikidoka were most played the

Amanuban community is sikidoka bendera,

sikidoka salib and sikidoka 8 (see Figure 7).

In (b), sikidoka sketch be depicted

connected with nets cube.

(a) Drum (b) Floor of the House (c) Brown Sugar

Figure 4. Circle in Ethnomathematics

(a) Kil Noni

(b) Pilu

Figure 5. Element of Circle

Figure 3. Jagung ais fes

55

(a) Nahe

(b) Tupa

(c) Buna Motive

Figure 6. Parallelogram

(a) sikidoka bendera (b) sikidoka salib (c) sikidoka 8

Figure 7. Sikidoka Sketch

Oko Mama (tempat sirih) has an bases

shaped cuboid with a pattern such as were

contained in the weave (see Figure 8). While

Oko used related to the hexagonal prism.

Dulang (tobe) is used in traditional or other

formal event as a place serving food or

drinks as well as a place to put a scarf or

other belongings to be given addressee as

the award has hexagonal pyramid shape.

7) Geometry Curved Sides

Aluk (pocket / bag) usually containing betel

nut and comes with a shape to present it

called ok tuke and kal ao. Kal ao used as a

lime and relating with cylinder concept.

While in the game piol or gasing relate with

cone concept. Similarly, cassava steamer

(toeb laku) relate with cone concept. While

the ume kbubu, lopo and plates in

community Amanuban connect with

hemispherical concept.

1. Discussion

1) Circle

A circle is a shape with all points the same

distance from its center. A circle is named

by its center. Thus, the circle to the right is

called circle A since its center is at point A.

Some real world examples of a circle are a

wheel, a dinner plate and (the surface of) a

coin. From radius and diameter, can be find

area and circumference of circle.

. circle of Area 2dr ππ ==

rπ2circle of nceCircumfere =

56

(a) Oko Mama (b) Oko (c) Tobe

Figure 8. Cuboid and Prism

(a) Kal Ao dan Ok Tuke (b) Toeb laku (c) Piring

Figure 9. Geometry Curved Sides

Figure 10. Area and Circumference of Circle

Destar or headband has a long connect with

tangent of circle concept. From figure 10,

the lines AB and BC is a tangent of circle

centered at the point O. The length of the

OA = OC = r = radius of the circle. As the

tangents always perpendicular to the radius

of the circle so long tangents AB and BC

can be calculated using the Pythagorean

theorem.

squere of length of the hypotenuse = squere

sum of length

�� ��� ���

�� � �� ���

�� ��� ���

diameter

Jari-jari Titik pusat

57

2) Polygon

Nyiru its irregular hexagons shaped.

Irregular hexagon consisting of six (6)

pieces of equilateral triangles. Thus, the

surface area of the hexagon can be

calculated using the concept of equilateral

triangles (see Figure 12). So,

at

at

3

2

16

triangleof area 6 hexagon irregular of Area

=

×=

×=

3) Prism

Oko in used connected with hexagon prism.

Hexagon prism is 3D shape with identic

bases form hexagon lateral and laterak side

rectangel. From Figure 13, surface area can

be determined by looking for area of nets.

Figure 11. Tangent of Circle

Figure 12. Polygon

( ) ( )

( ) ( )

( )plat

plat

pl

+=

+=

×+×=

+×=

×+×=

6

66

6at3 2

area lateralbases 2

rectangel6hexagon area 2 prism of area Surface

23at

t3at

axis bases prism Volume

=

×=

×=

58

Figure 13. Hexagon Prism

4) Cylinder

The men’s in dress equip themselves aluk

(pocket/bag). These bags usually contain

betel nut and comes with a shape to

present it called ok tuke and kal ao. Ok

tuke and kal ao relate with cylinder

concept. Cylinder is a 3D geometry

formed by two identical parallel circle and

a rectangle were surrounds the circle.

Because the base of cylinder is then used

two identical circles and cylinder lateral

face form is rectangular, we can used

circle concept to find bases area.

So,

Cylinder is in terms of the approach of

prism with polygon side, where n

approaches infinity. That is, if the laterals

axis the prism propagated it forms a

cylinder where only approached bottom

single base, up single base and one

perimeter. Because it the base shape

circle, so the cylinder volume is obtained

by multiplying the area of a circle with a

high the base cylinder.

Conclusions and Recommendations

Results of the analysis concluded that the

mathematical concept has been owned and

lived in society since long away. It is

realized from the ethnomathematics form

in clan Amanuban that contains many

mathematical concepts, especially in the

field of geometry and algebra. Its concept

of geometry is the circle, square,

rectangle, rhombus, cone, pyramid,

prisms, polygons, beams and cubes.

Besides surface area, volume concept can

be analyzed from the forms existing

ethnomathematics .

Figure 14.Cylinder

rt2

tr2

lp

rrectangula=cylinder of face lateral

π

π

=

×=

×=

L

( )trr 2

rt2r2=cylinder of Area2

+=

×

π

ππ

td

t

2

2

4

1

r=cylinder Volume

π

π

=

59

Operation either integer addition,

subtraction, multiplication and division can

be found in the traditional game which is

owned by the community. These games help

people (especially children) in the study of

arithmetic operations. The concept of chance

and arithmetic sequence as well as other

concepts that need to be analyzed in depth.

All forms of ethnomathematics can be

integrated in the learning of mathematics at

primary school level and secondary school.

Keep in mind that while all forms of

ethnomathematics which have been

analyzed in general can be integrated into

learning but if not packed properly it will

hamper the process of learning mathematics.

For that need to be analyzed further and

developed in accordance with the

appropriate context. Ethnomathematics

form of a culture that is owned by a group

requires high precision in exploring and

analyzing it into mathematical concepts. For

that there needs to be further research deeper

in discussing mathematical concepts in a

culture, the development of teaching

materials based ethnomathematics and

measured levels of misconceptions learning.

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