Mathematics in Culture: Analysis of Mathematical Elements in Buna Woven Fabric - UNNES JOURNAL

Kreano 12 (1) (2021) : 75-84

 KREANO
 J u r n a l M a t e m a t i k a K r e a t i f- I n o v a t i f
 http://journal.unnes.ac.id/nju/index.php/kreano

 Mathematics in Culture: Analysis of Mathematical Elements in Buna
 Woven Fabric

 Meryani Lakapu1, Irmina Veronika Uskono2, Yohanes Ovaritus Jagom3, Wilfridus Beda
 Nuba Dosinaeng4, Samuel Igo Leton5, Kristoforus Djawa Djong6

 1,2,3,4,5,6Pendidikan
 Matematika FKIP Universitas Katolik Widya Mandira
 Corresponding Author: meryanilakapu@unwira.ac.id1, irminauskono@unwira.ac.id2,
 jagom2020@unwira.ac.id3, wilfridusdosinaeng@unwira.ac.id4,
 letonsamuel@unwira.ac.id5, kristodjawadjong@unwira.ac.id 6

 History Article
 Received: November, 2020 Accepted: May, 2021 Published: June, 2021

 Abstract
 The purpose of this research is to analyze in depth the mathematical values contained in
 the buna woven fabric. The method used is a qualitative method with an ethnographic
 design because it will explain one of the cultural artifacts of the people of NTT, in this case
 the buna woven fabric. The results obtained are the motifs on the buna woven cloth that
 analyzed containing geometric and arithmetic concepts. From the analyzed quadrilateral
 characteristics, the quadrilateral found in the buna woven fabric is a rhombus. In addition,
 values or mathematical concepts on woven fabrics that can be taught to junior high
 school students include finding the formula for the area and perimeter of a rhombus using
 a triangle approach; calculate the area and circumference of a rhombus; arithmetic and
 geometric sequences and calculating the number of rhombic models on buna woven fab-
 rics.

 Abstrak
 Tujuan dari penelitian ini adalah untuk menganalisis secara mendalam nilai-nilai matemat-
 ika yang terdapat pada kain tenun buna. Metode yang digunakan adalah metode kualitatif
 dengan desain etnografi, karena akan menjelaskan mengenai salah satu artefak budaya
 masyarakat NTT, dalam hal ini kain tenun buna. Hasil yang diperoleh adalah motif pada
 kain tenun buna yang dianalisis memuat konsep-konsep geometri dan aritmatika. Dari sifat-
 sifat segiempat yang dianalisis maka dapat diketahui bahwa bangun datar segiempat yang
 terdapat pada kain tenun buna adalah belah ketupat. Selain itu nilai-nilai atau konsep-
 konsep matematika pada kain tenun buna yang dapat diajarkan pada siswa SMP antara
 lain: menemukan rumus luas dan keliling belah ketupat menggunakan pendekatan segitiga;
 menghitung luas dan keliling belah ketupat; barisan aritmatika dan geometri serta menghi-
 tung banyaknya model belah ketupat pada kain tenun buna

 Keywords: buna, culture, mathematics

INTRODUCTION cultural elements in the learning process
 (Li, 2019). In these days and age, imple-
Daily life is closely related to culture. Cul- menting cultural elements into the class-
ture could be a medium to help teach room learning process is imperative for
mathematical concepts by introducing

© 2021, Kreano, Jurnal Matematika Kreatif-Inovatif. UNNES
p-ISSN: 2086-2334; e-ISSN: 2442-4218

76 Lakapu, M et al. Mathematics in Culture: Analysis of Mathematical Elements in Buna Woven …

preserving culture by handing them to woven fabrics is largely unknown. How-
the student of the nation (Labudasari & ever, multiple oral sources depict Timor’s
Rochmah, 2019). Cultural practices facili- traditional woven fabrics being used to
tate the implementation of mathematical protect from the elements. It is remem-
concepts. These are called ethnomathe- bered vividly still to this day by the com-
matics. Ethnomathematics gives rise to munity’s female member that Timor’s
cultural practices capable of motivating cultural heritage is weaving, which are
students to learn mathematics (Fajriyah, observable in Timor’s people life cycle.
2018). The following is a visual represen- Buna, sotis/ lotis/ songket, and futus
tation of the relationship between local are types of woven fabric from Timor is-
culture and mathematics. The intersec- land. This study uses buna as their object
tion between local culture and mathe- of study for their utilization of geomet-
matics is usually referred to as local cul- rical concepts. Buna weave originates
ture-based mathematics. from Timor Tengah Utara regency, spe-
 cifically the palace area. According to
 Tas'au, the types of motifs imprinted on
 buna woven fabric are geometric motifs.
 Each motif represents different tribes in-
 habit the royal territory within the cus-
 tomary structure of the sonafmaubes
 (Maubesi Kingdom) community (Uskono
 et al., 2020)
 People of Indonesia in general (es-
 pecially Timorese) have implemented
 mathematics in their daily activities, par-
 Figure 1: Local Culture Based Mathematical Con-
cept [Author’s Analysis is Based on (Supriadi et al., ticularly when choosing a combination of
 2018)] color, dots, lines, and shapes to create
 patterns on to their woven fabric and ba-
There are two forms of learning activities tik characteristic. This is in line with the
in a local culture based mathematically, opinion that through observation of the
which are mathematical activities and Jogjan batik motif, students are able to
ethnomathematical forms. Mathematical identify its shape, area, circumference
activities consist of the abstraction of dai- (Rudyanto, 2019). A study (Hartoyo,
ly life activities into mathematics and 2013) states that although the communi-
vice versa, as a classification activity, ties do not have a good understanding of
counting, measuring, creating a pattern, mathematics, they can apply mathemati-
and more. While ethnomathematical cal concept (geometry) into their woven
form is all kinds of mathematical activi- fabric’s motif and weaves. In general, Ti-
ties practiced or developed within certain mor people are aware of mathematics in
communities (Sudirman; Rosyadi; Les- an abstract way, in which mathematics is
tari, 2016). only considered a science that can only
 Woven fabrics are a cultural herit- be used to solve problems in class. For
age and clothing of the Indonesian peo- instance, several cultural activities out-
ple ever since ancient times developed as side the classroom, such as building a
an improvement to using grass and bark lopo (Timor traditional house), are never
as clothing (Saputra, 2019). considered to contain any mathematical
 The origin of Timor’s traditional elements. The community's understand-

Kreano, 12(1) (2021): 75 – 84  77

ing of building a cone-shaped lopo is only due to its geometrical elements that can
based on cultural values. Hence, the be analyzed. Next, a preliminary survey
measurement is inconsistent, not in ac- was conducted to determine the topic of
cordance with the actual cone model. In this study. The research team conducted
this case, lopois not built with a fixed the preliminary survey by observing mul-
mathematical calculation that leads to tiple types of buna woven fabrics that
differences from one lopo to another may have a geometrical concept. The re-
(e.g., the width of the outer circle, inner sults of the survey were used to deter-
circle, etc.). In other words, the mathe- mine the topic of this study, which is the
matical measurements are not consid- geometry of buna woven fabric. This
ered in detail; thus, several elements are study collected data by interview (un-
not in their actual size. In conclusion, structured) and measuring the fabrics.
mathematical concepts are not fully ap- The data collected from interviews and
plied in traditional architecture because measurement was then analyzed to ob-
the traditional community emphasizes tain a detailed description of buna woven
more on cultural values and aesthetics fabric by describing and classifying the
elements (Lapenangga et al., 2020). geometrical concept on buna woven fab-
 According to the statement above, ric. Finally, translating and writing the
the research team is interested in analyz- mathematical concept into written text.
ing mathematical aspects that can be In general, the steps of this study can be
found in buna woven fabric's motif and seen in the Figure 2.
their relation to geometry and arithme-
tic’s. The purpose of this buna woven fab-
ric research is to identify relationships
between culture and mathematics so
that it may be better understood, pre-
venting the students from seeing their
culture as something 'foreign' and shift-
ing the community's perception of math-
ematics to be more accurate. In addition,
mathematics applications can be opti-
mized in the community and students'
daily activities, that they may benefit
from their mathematical studies. Another
objective of the study is for students to
know, maintain, and preserve the local
cultures around the community (Rewatus
et al., 2020)

METHODOLOGY

This is a qualitative study with an ethno-
graphic design to explain one of East
Nusa Tenggara’s cultural artifacts, in this
case, buna. The initial step of this re-
search was choosing the study object. Figure 2: Research Flowchart (Author’s Analysis,
The chosen object is buna woven fabric 2020)

78 Lakapu, M et al. Mathematics in Culture: Analysis of Mathematical Elements in Buna Woven …

This study's limitation is that it only uses
one type of woven fabric as the object of
the study. There is no other object that
can be used as a comparison.

RESULTS AND DISCUSSION

Below are patterns of woven fabric that
are used as the object of this study.
This buna woven fabric originates from
the North Central Timor Regency of the
East Nusa Tenggara province.
 Figure 5: Buna Woven Fabric Modeling
 (Author’s Analysis, 2020)

 The modeling in Figure 5 shows that the
 four shapes are quadrilateral because
 each of them has four sides and four ver-
 tices. A further detailed analysis was then
 conducted regarding the rectangular
 shapes on buna woven fabrics, especially
 in the red square.

 The following were the properties of the
 rectangular shapes.

 Property 1: All sides have equal length.

 According to measurement results,
 length of = = = = 8 

 Figure 3: Buna Woven Fabric (Doc. Author, 2020)

The following is a motif found in buna
woven fabric that can be geometrically
modeled:

 Figure 4: BunaWoven Fabric Figure 6: Buna Woven Fabric Modeling
 (Author’s Doc, 2020) (Author’s Analysis, 2020)

Kreano, 12(1) (2021): 75 – 84  79

Property 2: Both diagonals are axes of Property 3: Two vertices next to each
symmetry other are equal to °

 Figure 7: Buna Woven Fabric Modeling
 (Author’s Analysis, 2020)
 Figure 9: Buna Woven Fabric Modeling
 (Author’s Analysis, 2020)
Analysis of Figure 7
 Based on the measurement taken:
If folded at AC then point A is located at
 ∠ + ∠ = 180° ;
point A, point C is located at point C and
 ∠ + ∠ = 180° ;
point B is located at point D; there-
 ∠ + ∠ = 180° ; and
fore, AC is an axe of symmetry.
 ∠ + ∠ = 180° .

 The angle of each vertex can be divided
 equally by their diagonals.

 Figure 8: Buna Woven Fabric Modeling
 (Author’s Analysis, 2020)

Analysis of Figure 8 Figure 10. Buna Woven Fabric Modeling (Author’s
 Analysis, 2020)
If folded at BD, then point B is located at
point B, point D is located at point D and Based on measurement taken: ∠ 1 =
point C is located at point A; there- ∠ 2 = 53,645° ; ∠ 1 = ∠ 2 = 36,355° ;
fore, BD is an axe of symmetry. ∠ 1 = ∠ 2 = 53,645° ; ∠ 1 = ∠ 2 =
 36,355° .

80 Lakapu, M et al. Mathematics in Culture: Analysis of Mathematical Elements in Buna Woven …

Property 4: The diagonals are perpen- Topic 1: Determining the formula of ar-
dicular to each other and divide both ea and perimeter of a rhombus using a
diagonals into two lines of equal length. triangular approach.

 Figure 12: Buna Woven Fabric Modeling (Au-
 thor’s Analysis, 2020)

 Figure 11: Buna Woven Fabric Modeling
 (Author’s Analysis, 2020)

It can be analyzed that: (a) The intersec-
tion of and shows that is per-
pendicular to ( ⊥ ); (b) The di- Figure 13: Buna Woven Fabric Modeling (Au-
agonal is divided by the diagonal thor’s Analysis, 2020)
into two lines of equal length, =
 = 6,2 ; and (c) Diagonal is di- Area of Rhombus 
vided by the diagonal into two lines of = Area ∆ + Area ∆ 
equal length, = = 5 . 1 1 1 1
 = ( × 2 × 1 ) + ( × 2 × 1 )
 2 2 2 2
 The analyzed properties are the 1 1
 = ( × 1 × 2 ) + ( × 1 × 2 )
properties of a rhombus. Some of the 4 4
 2 1
theories used to analyze this shape's = × 1 × 2 = × 1 × 2
property are measurements, axes of 4 2
symmetry, and angles. (Siswoyo, 2011;
Ilham, 2015; and Rohayati, S., Karno, W.,
& Chomariyah, 2017)
 In addition to the findings above,
the mathematical aspect of buna woven
fabric can be used in the primary school
classroom activity. This finding can be
used as a source of study by students to
learn the sub-topics below:

 Figure 14: Buna Woven Fabric Model-
 ing (Author’s Analysis, 2020)

Kreano, 12(1) (2021): 75 – 84  81

Perimeter of Rhombus Topic 3. Arithmetic and Geometric se-
= Total length of all its sides quence: forming pattern from the
= + + + rhombus model.
= + + + = 4 

Topic 2. Calculating the Area and Pe-
rimeter of Rhombus

 Figure 17: Buna Woven Fabric
 (Doc. Author, 2020)

 Figure 15. Buna Woven Fabric
 (Doc. Author, 2020)

 Figure 18: Buna Woven Fabric Modeling (Au-
 thor’s Analysis, 2020)

 The measurement result of the rhombus
 model of buna woven fabric (Figure 18)
 shows that 1 ≅ 1 ≅ 1 ≅ 1 ; 2 ≅
 2 ≅ 2 ≅ 2 ; 3 ≅ 3 ≅ 3 ≅
 Figure 16: Buna Woven Fabric Modeling
 3 and 4 ≅ 4 ≅ 4 ≅ 4
 (Author’s Analysis, 2020)
 Because each sided opposite to
Area of Rhombus each other has equal length and angle,
 1 1 the area and perimeter of the rhombus
= 2 × 1 × 2 = 2 × 10 × 12,4 = 62
 can be written as:

Perimeter of Rhombus 1 = 1 = 1 = 1 = 8;
= 4 = 4 × 8 = 32 2 = 2 = 2 = 2 = 16;
 1 = 1 = 1 = 1 = 24;
 1 = 1 = 1 = 1 = 32

82 Lakapu, M et al. Mathematics in Culture: Analysis of Mathematical Elements in Buna Woven …

The perimeter of rhombus 1, 2, 3, and the four rhombi (1, 2, 3, 4)which is more
4 can be written as an arithmetic and ge- than 80 (because the weaving pro-
ometric sequence as follows: cess of buna requires the weaver to do a
 tying process).
Topic 4. Limited Arithmetic Sequence

 = 8, 16, 24, 32 Topic 6. Calculating the amount of
Difference: = 8 rhombus model in buna woven fabric
First term: = 8
Pattern: From the rhombus model in Figure 18,
 = + ( − 1) there are 17 rhombi in its entirety. The
 = 8 + ( − 1)8 following is a list of rhombi in figure18:
 = 8 + 8 − 8
 = 8 1 , 1 , 1 , 1 , 2 , 2 , 2 , 2 , 3 , 3 , 3 ,
 With = 1, 2, 3, … 3 , 4 , 4 , 4 , 4 and rhombuses
 formed from multiple rhombuses
Numbers of terms of is: 4 , 4 , 4 , 4
 
 = 2 ( + ) = 2 ( + 8 )
 4
 The following are the preparation steps
 4 = 2 (8 + 8(4)) = 80. and process of traditional weaving, in this
 case using manual weaving tools: Firstly,
 the tread (abas) are prepared using the
Topic 5. Limited Geometric Series needed color and are rolled (naunu) (into
 each color) until it is round, then the
 = 8, 16, 24, 32 treads are arranged (nonot) in the weav-
Ratio: = 2 ing tools according to the desired design,
First term: = 8 then using a weaving wood called atis, ut,
Pattern: sia, nekan are arranged so that the pre-
 = −1 pared treads are ready to weave into a
 = 8 × 2 −1 woven fabric using senu, mona,
 niun (other weaving tools). According to
 = 23 × 2 −1 the buna's motif, what has become a
 = 23+ −1 characteristic while weaving a buna wo-
 ven fabric is its tying tread (na’bun). For
 = 2 +2
 instance, if the buna motif that is woven
With = 1, 2, 3, … is shaped like a rhombus, as shown in
Numbers of terms of is: Figure 3, the weaver needs to count the
 amount of tread that needs to be tied to
 = ( −1)
 achieve the desired result.
 −1
 = 8( −1) In this study, the researcher also
 2−1 compared the size of multiple rectangu-
 = 8(2 − 1) lar shapes of buna woven fabric used as
 4 = 8(24 − 1) the object of this study. The following is
 4 = 80 an example of rectangular shape model
 that was compared:
 The numbers of term of ( 4 =
80) shows that the thread used to make

Kreano, 12(1) (2021): 75 – 84  83

 2019); (3) study by (Lapenangga et al.,
 2020)shows that size in mathematics in
 certain cultural elements are not
 acknowledged in detail; thus, some ele-
 ments shift from its initial design because
 of the weaver or the community in gen-
 eral emphasizes cultural aspect more
 than aesthetics; (4) Study by Senita and
 Neno (Senita & Neno, 2018) shows that
Figure 19: Buna Woven Fabric (Doc. Author, 2020) traditional fabric manufacturing (using
 weaving tools) causes some mathemati-
 cal concept to be obscured due to the
 weavers focus on motif they are weaving.
 Further, by understanding the ethno-
 mathematics of Batik will increase the
 student critical thinking (Martyanti and
 Suhartini, 2018; Febriani et al, 2019).

 CLOSING
 Figure 20: Buna Woven Fabric Modeling (Au- Conclusion
 thor’s Analysis, 2020)
 Based on the results of this study, it can
Immediately (without measuring), some be concluded that the motives found
sides correspond to the shape model that in buna woven fabrics have geometric and
shares the same size; however, upon arithmetic concepts. From the rectangu-
measurement using measuring tools, the lar shape properties that were analyzed, it
corresponding sides do not have the can be concluded that the rectangular
same size. For example, perimeter 4 = shape on buna woven fabric is a rhombus.
32,4 , 4 = 32 , 4 = 32,4 dan Such properties are as follows: each side
 4 = 32.This due to the tying of the has equal lengths; both diagonals are axes
tread during the weaving process; there of symmetry; the sum of two angles of
is an unevenness of strength of each neighboring vertices are180°; each angle
strand of the tread. can be divided equally by the diagonal,
 The results of this study, as shown and both diagonal perpendicularly inter-
above, is supported by the previous stud- sect while dividing themselves into two
ies as follows: (1) Previous Study (Har- equal lengths line. In addition, mathemat-
diarti, 2017) shows that within a certain ical elements, or concepts on buna woven
culture, we are able to analyze mathe- fabric that can be taught to middle school
matical concepts that can be used as a student are as follows: determining the
concrete mathematical study material; formula of area and perimeter of a rhom-
(2) Another study (Arwanto, 2017) show bus using the triangular approach; calcu-
that Cirebon’s trusmi batik contains lating area and perimeter of a rhombus;
mathematical elements, including the arithmetic and geometric sequence and
geometrical concepts of symmetry, counting the amount of rhombus model
transformation, and congruency within buna woven fabric.
(Zayyadi, 2018; Disnawati and Nahak,

84 Lakapu, M et al. Mathematics in Culture: Analysis of Mathematical Elements in Buna Woven …

Suggestions in mathematics education. In 5th Interna-
 tional Conference on Education Technology,
Suggestions for future studies are as fol- Management and Humanities Science. (Vol.
 10).
lows: (1) more object of study could be Martyanti, A., & Suhartini, S. (2018).
added or expanded so that more mathe- Etnomatematika: Menumbuhkan Kemam-
matical elements can be; and (2) there is puan Berpikir Kritis Melalui Budaya Dan Ma-
a need for an in-depth interview (struc- tematika. IndoMath: Indonesia Mathematics
tured) to increase the amount of data col- Education, 1(1), 35-41.
 Rewatus, A., Leton, S. I., Fernandez, A. J., & Suci-
lected. ati, M. (2020). Pengembangan Lembar Kerja
 Peserta Didik berbasis Etnomatematika pada
REFERENCES Materi Segitiga dan Segiempat. Jurnal Cen-
 dekia, 04(02), 645–656.
Arwanto. (2017). Eksplorasi Etnomatematika Batik Rohayati, S., Karno, W., & Chomariyah, I. (2017).
 Trusmi Cirebon Untuk Mengungkap Nilai Identifikasi Etnomatematika Pada Masjid
 Filosofi Dan Konsep Matematis. Phenome- Agung Di Yogyakarta. Prosiding. Seminar Na-
 non : Jurnal Pendidikan MIPA, 7(1), 40. sional Pendidikan Matematika, 1–8.
Disnawati, H., & Nahak, S. (2019). Pengembangan Rudyanto, H. E. (2019). Etnomatematika Budaya
 lembar kerja siswa berbasis etnomatematika Jawa : Inovasi Pembelajaran Matematika Di
 tenun timor pada materi pola bilangan. Sekolah Dasar. Jurnal Bidang Pendidikan Da-
 Jurnal Elemen, 5(1), 64-79. sar, 3(2), 25–32.
Fajriyah, E. (2018). Peran Etnomatematika Terkait Saputra, H. (2019). Seni dan Budaya Tenun Ikat
 Konsep Matematika dalam Mendukung Lit- Nusantara. May, 16.
 erasi. 1, 114–119. Senita, P., & Neno, E. S. (2018). Kristalografi Bi-
Febriani, P., Widada, W., & Herawaty, D. (2019). dang Datar Dalam Kain Tenun Masyarakat
 Pengaruh pembelajaran matematika realistik Manggarai. Prosiding Sendika, 50–56.
 berbasis etnomatematika terhadap kemam- https://202.91.10.50/prosiding/index.php/sen
 puan pemahaman konsep matematika siswa dika/article/view/264
 SMA Kota Bengkulu. Jurnal Pendidikan Ma- Siswoyo, B. (2011). Peningkatan Hasil Belajar Si-
 tematika Raflesia, 4(2), 120-135. fat-Sifat Segiempat dengan Pendekatan
Hardiarti, S. (2017). Etnomatematika: Aplikasi STAD (Student Teams Achievement Divi-
 Bangun Datar Segiempat Pada Candi Muaro sions) di Kelas VII-1 SMP Negeri 2 Kutalimba-
 Jambi. Aksioma, 8(2), 99. ru. Kreano: Jurnal Matematika Kreatif-
Hartoyo, A. (2013). Etnomatematika Pada Budaya Inovatif, 2(2), 89–103.
 Masyarakat Dayak Perbatasan Indonesia- Sudirman; Rosyadi; Lestari, W. D. (2016).
 Malaysia. Jurnal Pendidikan Matematika Dan Penggunaan Etnomatematika Padakarya
 IPA, 2(1). Seni Batik Indramayu Dalam Pembelajaran
Ilham. (2015). Penerapan Model Pembelajaran Geometri Transformasi. Pedagogy, 2(1), 74–
 Think Pair Share Untuk Meningkatkan Pem- 85.
 ahaman Siswa Kelas Vii Smpn 3 Palu Pada Supriadi, S., Sunda, E., & Kaganga, A. (2018).
 Materi Belah Ketupat. Elektronik Pendidikan Pembelajaran Etnomatematika Sunda. PED-
 Matematika Tadulako, 2(3), 305–316. AGOGIA, 225–304.
Labudasari, E., & Rochmah, E. (2019). Peran Bu- Uskono, I. V., Lakapu, M., Jagom, Y. O.,
 daya Sekolah Dalam Meningkatkan Karakter Dosinaeng, W. B. N., & Bria, K. (2020). Pen-
 Siswa. March 2018. dekatan Pendidikan Matematika Realistik
Lapenangga, A., Rowa, Y., & Lakapu, M. (2020). berbasis Etnomatematika dan Prestasi Bela-
 Matematika dalam Arsitektur: Konsep jar Matematika Siswa. Journal of Honai Math,
 Susunan Bilangan Real dalam Konstruksi 3(2), 145–156.
 Atap Lopo di Benteng None. ATRIUM, 6(1), Zayyadi, M. (2018). Eksplorasi etnomatematika
 11–22. pada batik madura. Sigma, 2(2), 36-40.
Li, Y. (2019). Mathematics education and mathe-
 matics culture-training mathematics literacy