An ethnography study on mathematical terminologies within two indigenous Makian languages in North Maluku

. Studies on the exploration of language and mathematical concepts in the traditional culture of the tribes in Indonesia have been widely carried out in the last ten years. These reports can be grouped into two groups. The first group specifically examines the mathematical content used by traditional societies, while the second integrates traditional mathematical ABSTRACT The two indigenous Makian languages, Western Makian ( Makian Luar) and Eastern Makian ( Makian Dalam/Taba), stem from two different language families in North Maluku. The indigenous Makian people are typically ignorant of the riches of values and knowledge reserved in their language and culture, including mathematical content. Therefore, through an ethnography ap-proach, this study identifies mathematical terminologies (natural numbers, fractions, number operations, indefinite quantifiers and adverbs of time) that exist in indigenous Makian languages. Data Collecting was conducted through indepth interviews with indigenous community leaders and some primary literature reviews, then analyzed qualitatively. The mathematical language that has been identified along with the context of its use can be a good entry point and a meaningful material in integrating indigenous languages and cultures in mathematics learning


INTRODUCTION
Mathematics is a product of human culture like other disciplines such as science, social humanities, and language since Mathematics is not a culture-free discipline (Zaslavsky, 1998).All knowledge related to human experience in social life is always through a cultural system that contains norms, values and conventions (Nasir et al., 2008).Symbols, operational processes, and representations of arts and crafts are historically the roots of mathematics (Barton et al., 2006) which is continuously rehearsed even by indigenous communities to ensure their survival (Meaney et al., 2011).A range of activities such as counting, measurement, design, and game are illustrations of mathematizing activities found in most major cultural phenomena (Bishop, 1988).
The existence of a close relationship between mathematics and culture is a sign of the importance of bringing mathematics learning closer to culture itself.Historically, mathematics and its teaching learning process have been an inseparable part of cultural reproduction from generation to generation and have even become a fundamental teaching approach (Acharya et al., 2021;Machaba & Dhlamini, 2021).However, nowadays, mathematics standards that tend to be Eurocentric alienate students from their own culture (Alangui, 2017).Hence, some recommendations for creating culturally relevant mathematics learning experiences have long been voiced with the aim that students can reflect on and appreciate their own culture (Acharya et al., 2021;Aronson & Laughter, 2016;Civil, 2002;D'Ambrosio, 1985;d'Entremont, 2015;NCTM, 1989).Thus, the experience can enable students to implement mathematical operations in their cultural environment (Acharya, 2020).
One of the first actions to simplify the process of providing mathematical experience to students is internalising the formal language of mathematics into the local language.Many studies carried out in the context of broader language revitalisation were conducted on indigenous peoples trying to decipher their native language for teaching and learning mathematics (Kirmura, 2009).The study stimulated the emergence of a paradigm of recognising the linguistic rights of traditional tribal groups who elaborated their language to teach mathematics (Barwell, 2012).However, at the same time, the hierarchical matrix formed since colonial periods tends to encourage resistance to these activities by limiting the use of native languages to only a few domains (excluding mathematics) which will cumulatively lead to extinction (Grosfoguel, 2011;Simons & Lewis, 2011).
Studies on the exploration of language and mathematical concepts in the traditional culture of the tribes in Indonesia have been widely carried out in the last ten years.These reports can be grouped into two groups.The first group specifically examines the mathematical content used by traditional societies, while the second integrates traditional mathematical concepts in school mathematics learning.The study of the mathematical language of indigenous societies is an illustration of research that explores mathematical content in the languages of ethnic groups in Indonesia, such as the mathematical language of the Yogyakarta people (Prahmana, 2020), the Sundanese (Muhtadi et al., 2021), the Yapen people of Pa-pua (Aritonang, 2017) and other ethnic groups in eastern Indonesia such as Maluku and East Nusa Tenggara (Winarti, 2017).
Other mathematical content such as geometry is also one of the cultural mathematical studies such as the concept of geometry in Rumah Kaki Seribu of the Arfak Tribe in Papua (Haryanto et al., 2016), the concept of geometric transformation in Batik (Masrukha & Budiarto,Maki 2021) and the use of mathematical concepts in calculations of Agricultural products (Umbara et al., 2019).In addition, the assimilation of traditional mathematics into contemporary mathematics learning models is also widely studied, especially in geometry learning (Hartinah et al., 2019;Lubis et al., 2021;Sudirman et al., 2020).Although ethnomathematical research continues to experience a positive trend in Indonesia, literature studies show the lack of ethnomathematical studies based on ethnic cultures in eastern Indonesia, especially North Maluku, settled by more than 10 indigenous tribes.Interestingly, the languages of these tribes come from two different roots, namely the North Hal-mahera family (Ternate, Tidore, Sahu, Tobaru, Loloda, Galela, Tobelo, Modole, Pagu, and Western Makian/Makian Luar) and the South Halmahera family (Weda, Sawai, Patani, Maba, Buli and Makian Timur/Makian Dalam/Taba) (Bowden, 1997;Taha, 2019;Voorhoeve C.L., 1982).
There are two fundamental reasons why this research examines the mathematical language of the Makian tribe.The reasons are related to the uniqueness and the threat of extinction.Makian Island is inhabited by one tribe with two different languages: Western Makian and Eastern Makian, with various dialects (Bowden, 1997;Voorhoeve C.L., 1982).However, on the other hand, the extinction of indigenous languages in North Maluku has become a real threat (Imelda, 2017).Therefore, a serious study of local languages and their rela-tionship with other aspects, including mathematics, can be considered essential for language preservation.
This study explicitly explores the two Makian tribal languages to find mathematical content and language that can be utilised as an entry point in integrating traditional mathematics into formal mathematics learning in schools.Mathematical content that will be discussed includes numbers, mathematical operations, areas, volumes and units of time.In addition, the comparison of the two Makian language variants will also be discussed in this paper.

RESEARCH METHOD
This study is ethnomathematical research which is part of an ethnographic approach.Ethnographic research aims to describe, analyze and interpret behavioral patterns, beliefs, and language of cultural groups, including language, rituals, economic and political structures, life stages, interactions, and communication styles that develop over time (Creswell, 2015).This definition is relevant to the research objective to explore the context of mathematics in the indigenous Makian language.Fraenkel & Wallen (2009) clarify that the emphasis in eth-nographic research is on documenting or describing the daily experiences of individuals by observing and interviewing them and other relevant people.Therefore, researchers conducted in-depth interviews and observations of participants contin-uously and continuously.For example, interviews were con-ducted with three traditional figures of the western Makian tribe from three regions: Waikyon, Waigitang, and Soma.In addition, interviews were also carried out with three traditional Makian leaders from Sabalé and Tafasoho.All of these sources are Makian natives who grasp the indigenous Makian language.
Observations were made in several places where the indigenous Makian tribe performed daily activities, such as in coconut groves, markets, and ritual events.In addition, literature studies are also carried out, such as regional language dictionaries and research reports.In general, the series of ethnographic data analysis processes begins with reading the data as a whole to build an in-depth understanding.The next stage is data reduction, describing the data and drawing conclusions and verification.Data reduction is carried out if data is found that does not correspond to some sources and some literature.Furthermore, detailed descriptions and interpretations are made to establish the context of the mathematical language used by the Makian people.

Results
The following describes mathematical terminology: natural numbers and fractions, number operations, indefinite quantities, and units measuring length, area, volume, and time.The language base used in the mention is Western Makian (WM) and Eastern Makian (EM).

The Mention of Natural Numbers 1-9
Based on Table 1, there are significant differences in the root pronunciation of natural numbers 1-9 between the Western Makian and Eastern Makian languages.However, these two words are often prefixed according to the object of the conversation or the noun that follows, for example: me minyé (WM)= one person, oma dimaedé (WM)=two children pso(EM) = one/a piece of fruit, sis wal (EM)= eight (animals).
In Western Makian, Nouns fall into two broad classes: Animate and Inanimate.In addition, they are divided into two smaller classes which are labeled Animate High (AH), Ani-mate Low (AL), Inanimate High (IH), and Inanimate Low (IL).Animate nouns denote people and animals, while Inanimate nouns denote plants, trees, and objects.Therefore, there are four sets of numbers in the West Makian language, namely: (1) numbers used to count Inanimate Low nouns, (2) numbers used to count Animate Low nouns, (3) numbers used to count objects Animate High and Inanimate High, and ( 4) the set of roots of numbers.This grouping ultimately leads to using different affixes placed before the mention of the number.
The classifier of nouns in the Eastern Makian language is divided into two: fruit and animal.This classification specifies the affixes used, namely p-for fruit and i-and sis-for 2-9 animals, such as iso = one (animal), silhim/sislim = five (animals).

The Mention of Tens
Based on the mentioning tens numbers in Table 3, it can be seen that three elements make up words: the tens number class, times or measurement intervals, and numbers.The tens class in Western Makian is -Awe, and the measurement interval is -i.An illustration of the Western Makian language of forty ( 40) is Awe i fate, where Awe (tens), i (times), and fate (four).So in the structure of the Indonesian language, it can be interpreted as "ten times four".Meanwhile, in the Eastern Makian language, there are two types of mentions of the tenth grade: Beit, which is employed for animals, Yo for fruit, followed by Ha, which means times.For example, Beit lu = twenty (animals) where beit shows a multiple of 10, while Yo hatol means ten times three (30 pieces of fruits).

The Mention of Hundreds
The hundredth class in Western Makian is named Atus.This mention is similar to the mention in Bahasa.Meanwhile, in the Eastern Makian language, the hundredth grade is called Utin.One of the distinctions between "hundreds formation" and "tens formation" is that the number name directly follows the hundredth class (Utin) without including the ha-like the tenth class yo.Nonetheless, there are exceptions to units of measurement, such as meters.Therefore 400 meters in the Eastern Makian language is called "meter ha utin hot".The list of mentions of other hundreds of numbers can be seen in Table 4.

The Mention of Thousands
The thousandth class in both Western Makian and Eastern Makian is Calan.Nonetheless, there is a slight difference in the West Makian language, namely the class au (times/product) affixing.Some instances of mentioning a thousand numbers are provided in Table 5.Interestingly, when it involves mentioning larger numbers or quantities such as ten thousand, one hundred thousand, tens of millions, and hundred million.The pattern utilized is the largest number class at the beginning, followed by the smaller class, and ending by the numeral.For example, in the Eastern Makian language: six hundred thousand is called Calan Utin Wonam, where Calan is the thousandth class, Utin is the hundredth class, and Wonam is the numeral name of 6.In the Western Makian language, the word for "twenty million" is Juta Awedéng, where Juta is the millionth class, Awe is the tenth grade, and medéng reduced to édeng is the numeral of 2.

Complex Number
Complex numbers referred to in this study are number formations consisting of unit numbers, multiples of ten, and multiples of a thousand and so on.Based on Tables 6 and Table 7, the mention of complex numbers in both the Western Makian and Eastern Makian languages is constructed in successive addition using a numeral connector lo and frequently starting with the largest number class and terminating with the unit number.

Mention of Mathematical Operations
Makian natives have a special designation in mathematical operations, although their usage is not in formal mathematics, which is the context of daily life.The list of mentions of mathematical operations can be found in Table 9.Based on Table 9, it can be seen that the two Makian languages have similarities in the mention of addition and equal.Nevertheless, unfortunately, they do not have a specific term for the multiplication.

Length, Area, and Volume
The indigenous people of the West Makian and the Eastern Makian use a unique mathematical language to measure units of length, area, and volume of objects.
13. Sopo is used to express the volume of a liquid such as herbs or coconut sap.In addition, sopo is also used to express objects in the form of grains such as rice or grains measured by half a coconut shell.14.Gugum, this term is used to express the volume of a solid object that is the size of a human fist.15.Tugai is used to express the volume of a liquid that is measured using a measuring device.

Some Time-Terminology
The Makian community uses a particular mathematical language to indicate the adverb of time.Natural signs such as sunlight are often used to indicate time, especially for people who are occupied outdoors, such as farmers in coconut cultivation or fisherman.They know the time by recognizing these natural signs.The terminology mentioned below is a time terminology that native Makian frequently uses.

Discussion
The description of the variety of Western Makian and Eastern Makian languages that contain mathematics includes mentioning the names of natural numbers (from small to large), indefinite numbers, and terms that represent the context of the area, the volume of objects, and time are not focused on comparing the two language variants.However, it is intended to introduce and understand teachers and students who are part of the local inhabitant about the mathematical context in their everyday words.Hence, mathematics educators can explore and exploit sociolinguistic and epistemological problems that arise when the native language is elaborated and combined with formal language that is often used in learning mathematics (Parra & Trinick, 2018).Furthermore, teaching indigenous languages and incorporating indigenous cultural knowledge and modern worldviews in the mathematics curriculum makes it possible to improve the performance of indigenous students in mathematics education (Aikenhead, 2018).In addition, Riccomini(2015) also confirms that learning students' mathematical vocabulary is a crucial part of students' language development and, ultimately, mathematical abilities because vocabulary comprehension is a significant contributor to overall understanding in many content areas, including mathematics.
In the local scope of North Maluku Province, there has been no similar research related to the ethnomathematics of the Makian tribe, especially the implementation of Makian culture in school mathematics learning.However, there have been many ethnomathematical researchers who have documented their research reports on the positive impact of internalizing local culture in learning mathematics in primary and secondary schools, such as the use of cultural contexts in improving mathematical literacy (Zaenuri et al., 2020), exploration of art as a source of learning mathematics (Budiarto et al., 2020;Sugianto et al., 2019), internalization of ethnomathematics into mathematical activities such as estimation, measurement, and finding patterns (Muhtadi et al., 2017) and even mathematics learning design using traditional games (Roza et al., 2020).

CONCLUSION
The indigenous languages of the Western Makian and Eastern Makian are rich in knowledge and values, including mathematical content such as natural numbers, indefinite quantities, measurement, and time display.The involvement of native languages in learning mathematics is a step toward bringing students from indigenous communities closer to formal mathematics.This integration can be done through learning designs containing activities such as traditional games, works of art, and native languages.Furthermore, this research can be a good entry point for mathematics teachers in North Maluku Province to bring mathematics learning closer to their native language and culture as a bridge to foster student understanding.

Table 1 .
Names of Natural numbers 1-9In the mention of the numbers 11-19, both in the western Makian language and the eastern Makian represent it in the addition of 10 with the unit numbers 1-9.The pronunciation of the number 10 in Western Makian is Ainyé, while it is called Yo ha so in Eastern Makian.In addition, a numeral connector is also used in the designation pattern, namely, lo, which means and or plus.That applies not only to the numbers 11-19 but also to larger integers.The numeral connector "lo" is operated in Western and Eastern Makian.An example of mentioning the numbers 11-19 can be seen in Table2.

.
List of Tens Mention

Table 4 .
The Mention of Hundreds

Table 5 .
The Mention of Thousandths

Table 6 .
Illustrations of expressing complex numbers in Western Makian

Table 7 .
Illustrations of expressing complex numbers in Eastern MakianIndigenous people often recognize Zero as empty/nothing.For example, the Western Makian people call empty with momua, and the Eastern Makian people call it molo/nol.Theonly known mention of the fraction is half, which in Western Makian is called eta, and Palo in Eastern Makian.Subsequently, it is known to say indefinite quantities such as many, few, and some, as in Table8.

Table 8 .
An example of Mention of some Indefinite Quantities

Table 9 .
The Mention of some Mathematics Operation

1 .
Kaman, this term indicates the night.2. Kama gola is used to indicate the time at midnight.3. Osufi, this term indicates the early morning time.4. Win uwai, this term is used to indicate the time of noon. 5. Iseba ibulang, this term indicates the time before noon.6. Mararing, this term indicates the evening.Maddiding is used to indicate the time of the evening before sunset.2. Galmumite is used to indicate the time of night.3. Musama-Halaim is used to indicate the time of midnight 4. Gagal-mumto is used to indicate the time of dawn. 5. Daking-mauwa is used to indicate the time around 3 o'clock at the early morning 6.Galumto is used to indicate the morning time after sunrise 7. Ngan-halaim is used to indicate the time of noon.8. Laimone is used to indicate the time of today.