Analyzing Aceh Cultural Heritage: Mathematical Tools and Language Use

Acehnese people have many culturallyunique mathematical treasures, such as for measuring size and volume. Some of which are different from the ones used in other parts of Indonesia and some have been rarely used and even unknown by today’s generation. However, research on the measuring scales in Aceh is scant. This study was carried out to understand the Acehnese people’s prevailing measuring scales used. These scales are ethnomathematics parts of the Aceh culture. The research was conducted in six districts. Snowball sampling was employed through which people who are knowledgeable on Aceh culture were selected for interview. It shows that the volume scaling units of ethnomathematics in the culture of Aceh society are kay, aree, naleh, gateng, gunca, and kuyan. 1 kuyan = 10 gunca; 1 gunca = 10 naleh; 1 naleh = 16 aree; 1 aree = 4 kay. The size and volume of the kay, aree, naleh, gateng scales vary in each district.Moreover, the language used for scales and meanings slightly varies, such as naleh that is used for measuring volume or size only in some districts of Aceh and for both volume and size in other parts of the province.


A. Introduction
Indonesia is a big country that is rich with diverse cultures. Aceh as an Indonesian westernpart province is also rich with cultural artifacts and symbols. Of which were and are used for counting, weighing, and measuring. The wealth of cultural artifacts in Indonesia should be explored to understand and preserve them. More importantly, the cultural artifacts can be used for learning materials as well as learning methods at schools.
In Indonesia, it has also been emphasized in the currently implemented curriculum, Kurikulum 2013, to explore and use cultural artifacts for teaching and learning resources . However, cultural artifacts in Aceh are less explored to be used as learning resources at schools. Consequently, young generations in Aceh are not aware of their ancestral, cultural heritage used for counting or measuring.
Despite the limited use as Pais (2011) argued, using cultural-based products for teaching can result in creative and meaningful teaching and learning. This is reasonable because cultural-based teaching and learning can create contextual learning, which is strongly connected to cultural community and are therefore interesting for students whose cultural products are used. In teaching mathematics, for instance, locally used measuring units can also be used, which is ethnomathematics. As Furito (2014) suggests that ethnomathematics can be used for learning resources, let alone that students of multi-cultures occupy many schools today.
Ethnomathematics is a mathematical principle used by a certain cultural group, such as children of particular class society (D'Ambrosio, 1985;Gardes, 1994). Historically, society relies on mathematics to support its lives. Ethnomathematics is bound up with history, as can be understood from the mathematical history of Mesolithic, Babylonian, ancient Egypt, and the medieval invention of Calculus. Ethnomathematics criteria can be exemplified by symbols, artifacts, values, ordinances. And mathematicians can use ethnomathematics as inspirations.
There are a plethora of studies on ethnomathematics in many ethnics in the globe (e.g., Abdullah, 2017;Furito, 2014;Nusantara, 2016;Risdiyanti & Prahmana, 2017;Kucuk, 2014;Muhtadi, 2017;Pais, 2013;Palhares, 2012;Yusuf, Saidu & Halliru, 2010). All these studies suggest that exploring ethnomathematics is beneficial in understanding the meanings behind the use of mathematical thoughts in a variety of cultures and how different people in a culture solve their daily problems using mathematical tools.
Abdullah (2017) Risdiyanti and Prahmana (2017) in their research on several motifs of Yogyakarta batik clothes found that the concept of mathematics, mainly geometry, is used in crafting batik.
Kucuk (2014) researched ethnomathematics in terms of the motifs on carpets and rugs made in Anatoly, Turkey. It was found that many mathematical symbols were used in the motifs with certain meanings for the people of Anatoly in the 13 century. Geometrical shapes were widely utilized in architectural works of art and hand-knotted. Palhares (2012) after researching the ethnomathematics in Portugal concludes that "there is mathematical thinking behind many people's actions and discourse and even behind all the different kind of products of human activity.All these findings suggest that ethnomathematics in every culture plays important role in people's activities. Therefore, it is crucial to understand the meanings and mathematical thoughts behind their activities and how they can be used to support mathematics education.
In an Acehnese culture as well, many ethnomathematics treasures were and are still used in daily activities. However, ethnomathematics treasures in Aceh culture have received little attention from researchers.
As such, some of the tools have been unknown, especially by the young generations. Therefore, it is very important to explore and preserve the ethnomathematics treasures in Aceh. This research focuses on exploring and uncovering the meanings of the ethnomathematics that exist in Aceh society, especially in Pidie, Pidie Jaya, Bireuen, and Aceh Utara districts.

Mathematics as a cultural product
From a historical point of view, culture is defined as the legacy of a society's tradition or the whole of human activities. Mathematical activities exist in every human activity (Muhtadi, 2017;Nurhasanah, Kusumah, & Sabandar, 2017;Prahmana, 2012). In the same vein, Orey and Rosa (2008) state that mathematics is a cultural heritage. This is reasonable as people of any tribe usually utilize mathematical tools for counting, predicting, measuring, and evaluating things in their daily life, even though the tools used might be different from one culture to another.
It is for such reasons that mathematics develops in many parts of the world. It grows in the territories of India, America, Arab, China, Europe, Indonesia, and other countries. The growth and development of mathematics occur because of the challenges of life faced by humans in various regions with different cultural backgrounds. Every culture and subculture develops mathematics in their way. Accordingly, mathematics is seen as the result of the human mind in the activities of everyday society. That is why many scholars conclude that mathematics is a cultural product (Sardjiyo & Pannen, 2005), that is the result of abstraction of the human mind, as well as problemsolving tools. It has also been pointed out that mathematics is a form of culture, which is integrated into all aspects of people's lives wherever they are (Bishop, 1994;Sembiring, 2010, as cited in Rachmawati, 2012.

Mathematics and language
Researching language when researching ethnomathematics is indispensable. This is so because mathematics and language are interrelated and interinfluencing. Mathematics is part of language and language and other semiotic signs are products of a culture. This is so because mathematical symbols are used in communicating meanings in human activities in a variety of cultures. According to Orey and Rosa (2008: 30), mathematics is "a language system that has its history, symbols, syntax, grammar, and comes with an enormous variety of representations. It relies on intensive use of different variables, signs for numbers, diagrams, formulas, and algorithms." That mathematics is a language system can be understood from the use of different language for a certain amount of thing in various culture. For instance, "a handful of nuts" in English is expressed in "saboh reugam kacang" in the Acehnese language. When it is said "saboh reugam", the meaning is understood in Aceh society how much it is.

Ethnomathematics
The reviewed works of literature indicate that researchers have different perceptions about who firstly coined "ethnomathematics". While Rohrer and Schubring (2011), the term "ethnomathematics" was firstly introduced by researcher EwaldFettweis in the 1930s, other researchers such as Abdullah (2017) and Kucuk (2014) note that it was a Brazilian mathematician UbiratanD'Ambrosio who introduced "ethnomathematics" in 1960s. According to D'Ambrosio (as cited in Abdullah, 2017), "ethnomathematics" emanates from three Greek roots: Ethno, mathema, and tics. The term "ethno" means the socio-cultural context, including language, jargon, codes of conduct, myths, and symbols. "Mathema" refers to explaining, knowing, understanding, and a variety of related coding, measure, classify, deduce, and modeling. And the suffix "tics" equals technique. Hence, ethnomathematics can be understood as the technique used in a certain culture in measuring, classifying, counting, and the like.
Concerning this, several scholars have attempted to define what they mean by ethnomathematics. D'Ambrosio (1989), for instance, defines it as a mathematics science employed by humans in their own culture.
Concerning this, Kucuk (2014: 172) states that ethnomathematics functions "to explain the relationship between culture and mathematics." Other researchers, Albanese and Perales (2015) point out that ethnomathematics is research focusing on the relationships between mathematics and culture.
Seeing the importance of ethnomathematics, many studies have been rigorously carried out today. According to Kucuk (2014: 171), researching ethnomathematics paves the way for understanding "the nature of mathematics" and "one's self as well as the other people sharing the same planet." However, many of the research studies focused on 'local cultures' (Horsthemke, 2006;Pais, 2011Pais, , 2013Rowlands & Carson, 2002).
This is because ethnomathematics intends to explore the mathematics used by people based on their cultures. Pais (2011) (Putra, 2018). According to Orey and Rosa (2008: 28), "Good mathematical learning occurs with social and cultural interaction through dialogue, language, and through the negotiation of meaning of the symbolic representations between teacher and student".

C. Method
This is by nature explorative qualitative research as it explored a symptom or event (concept or problem) by doing an explanation of the symptoms (Bogdan &Biklen, 1998). It sought to produce descriptive data in the form of a description of ethnomathematics exploration of society in Aceh. The ethnographic approach of empirical and theoretical approach was used to get a description and in-depth analysis of culture based on field research. This approach focuses efforts to discover how people organize their culture in the mind and then use that culture in life, the culture exists in the human mind. The ethnographic task is to discover and describe the organization of the mind. Analysis of the data in this study was by using the framework proposed by Creswell and Guetterman (2019), namely by conducting domain analysis, taxonomic analysis, componential analysis, and theme analysis, with the following steps. Firstly, all data or an overall picture of the phenomenon of experience, or knowledge that had been collected were organized. Then, the data was read in its entirety and marginal notes on data that is considered important were made. The meaning of statements felt by respondents by treating the same statements was found and classified. Furthermore, statements that are irrelevant to topics and questions or statements that are repetitive (overlapping) were omitted, leaving only basic questions and statements

D. Result and Discussion
After analyzing the data, it was found that Acehnese people in their daily life use many kinds of scales to measure or calculate the volume of crops, both in their rice fields and other planting gardens. As well as in buying and selling transactions, they always use measuring tools or volume scales.
Some of the various volumes of tools and units in the Aceh community are explained below.

a. Volume measuring units in Aceh society
The results of field observations and interviews with community leaders show that in their day-to-day transactions, Aceh people use several units in calculating or measuring rice yields. The units start from the smallest unit to the large unit. The small one is mok. Mok is often used in measuring goods or objects such as flour, rice, and others. It is always used when cooking or trading transactions. Next is kay. Kay is a unit larger than mok. Next is aree. Aree is larger than mok and kay. The comparison between mok with aree is, 1 aree equals 6 mok. While the comparison between kay with aree is 1 acre equal to 4 kay.
The next unit is naleeh. A naleeh is a larger unit of mok, kay, and aree. The comparison is 1 naleeh equals 16 aree. The larger unit of naleeh is gunca, a single shoot equal to ten naleh. The highest unit of all the units of sukatan owned by the people of Aceh is Kuyan. One kuyan equals 10 gunca.
Aceh people in their cultural life use units that are inherited in the heredity for measuring volume or ordering. The results of interviews with community leaders in Pidie, Pidie Jaya, Bireuen, and North Aceh reveal thatthe units of scales ranging from the smallest to the largest. The scale units are: mok, kay, aree, naleh, gateng, gunca, and kuyan. Some people still understand this scale, but many young people today do not understand it (the results of interviews with several people -people around 20 years old -in Pidie and Pidie Jaya). The comparison is: 1 kuyan = 10 gunca 1 gunca = 10 naleh 1 naleh = 16 aree 1 aree = 4 kay 1 aree = 6 mok In applying these scales, the Aceh people since the ancients made a measuring instrument or volume that is mok, kay, aree, naleh, and gateng. To measure the size of rice field, for instance, using units applicable to the volume units of aree and naleh, which are associated with the number of rice seedlings required to plant in a patch of rice fields. When measured using a standard unit area, the size of rice filed for one naleh of seeds is approximately 2500 square meters or ¼ ha. But there is also a unit of scale teungeh dua, which is used for rice fields or land area of 1.5 naleh rice seedlings or 24 aree of rice seedlings. (The result of the interview with a community of Pidie and Pidie Jaya district).

b. Volume Measuring Scales in Aceh Society
The people of Aceh, in addition to having the units mentioned previously,

1) Mok
Mok is one of the smallest volume measuring scales in Aceh society. Many people in Aceh use it for daily cooking as rice as the main food for a family there is measured by mok rather than by kilogram. That is why Acehnese people frequently use "Padum boh mok lon taguen bu?" (How many mok I should cook the rice). It is usually made of a used milk can. From the results of the interviews with the respondents in Pidie district, Pidie Jaya, and Aceh Timur, it was found that mok was made of a can of milk the size of 300 ml.

2) Kay
Kay is also a small volume measuring scale used by the people of Aceh. Kay is also homemade and it is not sold in the market. Kay is made of coconut shell or half of the coconut paraboloid or half ball. To determine the volume of a kay, it needs to compare with the volume of aree, which 1 aree equal to 4 kay or 1: 4. It is not known what the diameter and height of the kay are. According to some respondents and observationsin Pidie, Pidie Jaya, and Aceh Utara districts, to make a kay it needs to have a coconut shell, which is cleaned and rubbed its inside and outside parts. The contents of the volume of one aree must have four kay. If the size of a volume of a kay has not reached a quarter of aree, it needs to be reshaped or changed with another coconut shell to fit four kay in one aree.

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The results of observations and interviews with community leaders in the districts of Pidie and Pidie Jaya show thatcreating a kay as mentioned above can be said as a trial and error process. The kay produced must be reliable. From the research in several sub-districts in Pidie, it was found that the size or volume of kay used there varies.From the results of observations and measurements of cultural objectsof akay in Rambayan, for instance, is 7.5 cm in height, its circumference of the top surface 28.5 cm, and its volume 350 ml. Differently, kay in Beureueh, Pidie district, is 7 cm high, its circumference of the top surface 33 cm, and its volume 330ml. Kay in Lala village Meunasah Tuha, Mila, Pidie District, its height is 7.5 cm, its circumference of the top surface 34,5 cm, and its volume 400ml. Kay in Paloh village, Pidie district, its height is 7 cm, its circumference of the top surface 23 cm, and its volume 450 ml. This shows that the measurement tools that exist in today's society vary significantly in volume size. However, of course, this is not good if the tool is used in buying and selling transactions.

3) Aree
The results of observations in Pidie, Pidie Jaya, and North Aceh found a measuring tool called aree. Aree is one of the measuring scales the people of Aceh have. Aree is a hand-made product by the community for their use and there is also not sold in the market. Aree is made of tubular bamboo.
To make an aree, people only need bamboo, and cut at the base of the aree is the separator of the bamboo is shaped like the original. To determine the volume of the aree, they only measure from a comparison with a kay that has a ratio of 1 aree equals 4 kays or 1: 4. There is no specific provision for the exact height or circumference.

4) Naleeh
The observations carried out in the districts of Pidie, Pidie Jaya, and North Aceh, found a measuring tool called Naleeh.Naleeh is one of the measuring tools owned by the people of Aceh. Naleeh is also a hand-made product by the community themselves, and it is not sold in the market. Naleeh is made of board-shaped beams. To make a naleeh, it needs raw materials from the board, and it is made in the form of blocks. To determine the volume of naleeh, it needs to compare with that aree with a ratio of 1 naleeh equal to 16 aree or 1:16. There is no specific provision for its length, width, height, or circumference.

5) Gateng
The results of observations and interviews with community leaders in Pidie, Pidie Jaya, Bireuen, and North Aceh, found a measuring tool called the Gateng. Gateng is one of the largest measuring tools owned by Aceh society. Gateng is made by the community for their use and also there is no gateng sold in the market. Gateng is made of cut cone-shaped aluminum.
To make a gateng, it needs raw material from zinc or aluminum plate and is shaped in cone-shaped. To determine the volume of the gating, it needs to compare with the ise which has a ratio of 1 gateng equals to 20 aree or 1: 20.
There is no specific provision of its size, either its diameter, its circumference, the circumference of the base or bottom, and its height. After measuring the top and bottom circumference and the height of the Gate, we found the following results. From the research in the Pidie district, it was found that the size of gateng is 37 cm high, its perimeter 97.5 cm, and its bottom is 123 cm. But there is no specific provision concerning its size, except its volume as described above.

Discussion
This study shows that many of the sizing tools used in the community in Aceh Province are not the same size, both in length, width and height, and volume. For the measurement tools to be reused, it is necessary to standardize them so that the size and volume are the same. If the tools are no longer used, they can be used as a cultural heritage of high value. This is similar to Darsa, Sumarlina, and Permana's (2020) argument that all documents resulting from the culture of local wisdom of the community are maintained properly so that the next generation will understand the culture of their ancestors through a learning process (Selasih & Sudarsana, 2018). Documents resulting from the culture are part of ethnomathematics (Rosa & Orey, 2019).
As an Islamic society, Acehnese people highly uphold the values and rules of Islam teachings that necessitate accuracy. The accuracy is also important when allocating must-shared zakat (charities). Zakat issued and shared by the community is divided into two major parts of zakat of agricultural yields and zakat of fitrah (soul). It was found that Aceh people know whether the harvest has reached nisab (limit of wealth that requires to allocate zakat) or not. The people harvest their crops using naleh scale. If the harvest has reached more than six gunca, it is obliged to release zakat as much as 2.5 percent of the harvest for the rain-fed rice field. As for issuing zakat fitrah, the size of zakat in Aceh society is six kays plus two handhelds. Hence, it is clear that the importance of measuring scales in Aceh society. However, the accuracy or reliability of the measuring scales needs to be researched because the way of making is still traditional or by way of trial and error.

E. Conclusion
After having analyzed and discussed the result, several conclusions can be drawn as in the following: The type of ethnomathematics that exists in the Islamic culture of Aceh society is the kind of unit of volume and size. The units of volume, namely: mok, kay, aree, naleh, gateng, gunca, and kuyan. The comparison is: 1 kuyan = 10 gunca; 1 gunca = 10 naleh; 1 naleh = 16 aree; 1 aree = 4 kay; 1 aree = 6 mok.
The existing measuring instruments in the Aceh community are: mok, made from used milk cans; kay, made of coconut shell that has been cleaned. The volume of the tool used still varies from one place to another; aree, made of cleaned bamboo. The volume is equal to 4 kays, but the tool used is still very varied from one place to another; naleh, is divided into two types of Naleh made of cone-shaped zinc whose volume is equal to 16 aces, and some are made of open top-shaped beams with a volume of 16 aces, but still need further investigation of the uniformity of the volume of tools it uses; gateng, which is made of zinc or cone-shaped steel plate cut off with a volume of 20 aces, but still needs further investigation of the uniformity of the volume of tools it uses. However, the size and volume of the sizing tool vary in different areas.
However, language use for scales or measuring units is different in some parts of Aceh. For example, naleh is used for the size of rice field in the Pidie district whereas in some parts of Aceh Utara naleh is for the amount of harvested rice. Naleehis also used as a measure of rice fields and is also used for the volume of harvested rice.