ETHNOMATHEMATICS IN SASAKNESE ARCHITECTURE

This research is aimed to explore the cultural elements especially in Sasak architectures in Lombok Island such as a home living (Bale), worship building (masjid), lumbung (sambi) in ethnomathematics point of view. This research uses qualitative approach with cognitive (anthropology cognitive). The interviewees are the experienced custom leader and humanists who has conducted the research on Sasak society. Meanwhile, the data collection method used the participant, observation and documentation. Data analysis on this research is not only based on the researcher is interpretation but also the idea structure of the society. This research shows the evidence of sensitivity on the use of numbers practiced by Sasak ancestor long time ago in doing the measurement using their anthropometric ability (Ethnomathematics). The architecture products of sasak society also describe that sasak society is more focus on the process than the final products itself which describes the consistency in conducting role and cultural device which control the desire of individual construction.


Mathematics and Cultural Products
Mathematical and cultural integration means contextual and realistic mathematics.Various cultural products of our ancestors reveal artistic creativity that contains mathematics, for example in carved ornaments and architectural forms in traditional houses containing three-dimensional geometric formations (Kucuk, 2013).Likewise found by Nasir and Cobb (2007) and Orey (2000) that mathematical contextualization has been described as identification of mathematics that is practiced and developed in different cultural groups.So also stated by (Rius, 2000;Rosa & Orey, 2007) stating that if mathematics is seen as a cultural construct, then it is cultural development.Orey (2009) stated that mathematics in various cultural contexts confirms this as a demand.
Cultural products in the form of artifacts such as traditional buildings are given the opportunity to be developed through mathematical thinking.Mathematical creative thinking that is integrated with culture can also arise in economic behavior.The concept of calculating mathematics through a linear program to determine the critical point as well as meeting several variables becomes a solution when many needs must be met but funds are limited.Mathematical calculations here are an alternative problem solving.Humans appear to fulfill their creativity needs with limited funds.For that it is clear that mathematics is the product of the human mind.

Ethnomathematics
Ethnomathematics is a field study.D Ambrosio (1990) defined ethnomathematics as a very broad term that refers to the socio-cultural context including language, jargon, symbols, behavior and myths.In line with this definition, Orey (2003) explained ethnomathematics to explain, and understand the world to manage problems faced by people, a larger humanitarian problem.More specific again D Ambrosio (1993) stated that the mission of the ethnomathematics program is to recognize that there are different ways of doing mathematics where different cultures can negotiate in practicing mathematics.Furthermore, Borba (1997) described ethnomathematics as a way in which people use certain cultures in mathematical concepts in dealing with relational and spatial aspects in their lives.Thus, ethnomathematics emerges as a new category in the conceptual discourse of mathematics education and as an interaction between mathematics and culture.
One of the objectives of mathematics learning is to prepare students to use mathematics and mathematical mindset in everyday life (Soedjadi, 2000).According to Barta and Shockey (2006) ethnomathemathic is a complex and dynamic representation that describes the influence of cultural use of mathematics in its application.In mathematics learning in schools so far students still consider that mathematics is difficult, too abstract, many formulas and so on, this is because the mathematics learning in school is too formal and not in accordance with what is experienced by students in everyday life.Bandeira and Lucena (2004) investigated mathematical ideas and practices obtained by members of the vegetable farming community in the Northeast region of Brazil.They learn the mathematical concepts used by farmers to harvest, produce and commercialize vegetables.They found that the specific mathematical knowledge produced by farmers differed from the mathematical knowledge obtained in academic settings.Therefore, more researches are needed to explore the cultures that exist around us to find concrete mathematical concepts so that the concepts can be applied in school math learning.
From some of these opinions, it appears that in math learning at school there is a tendency that to explore the initial knowledge of students should begin by associating formal mathematics with the experience of students in everyday life.Therefore, in this study focused on exploring and exploring more about the customs (customs) of sasak community related to the calculation, measurement, modeling, designing especially related to the traditional buildings of Sasaknese society.According to Rosa and Orey (2016), ethnomathematics is the application of math skills, ideas, procedures, and practices applied in the past by members of certain cultural groups in different contexts, which are often used today in today's context.It is hoped that based on the findings of this study can be a reference for teachers and observers of mathematics learning in order to create textbooks and use local culture as a source of learning mathematics in schools, so that learning math is more interesting and meaningful for students.

METHOD
The research method used in this study was a qualitative approach with the model of ethnography (anthropology cognitive) (Spradley, 1987).A new ethnography that focuses its efforts to discover how people organize their customs in mind and then use them in life.Informants used are the custom leader and cultural observers who already have experience in conducting research on the culture of the sasak community.While the data retrieval technique using participant observation and documentation.The analysis in this study is not only based solely on the interpretation of the researcher but also the composition of the idea of members of the community who are scraped out by the researchers, who then use four stages in analyzing the data such as an anarchic domain, taxonomic analysis, component analysis and theme determination.

RESULTS AND DISCUSSION
Architecture is an art and technique of designing and building and can be associated with construction (Irawan, 2016).The basic concept of sasak community building is a residential building called "bale" (house of residence), building of worship place "mesigit" (ancient mosque), and building of food store "granary" (sambi) is basically the same as Austronesia building in general which has a construction with poles and wooden beams both on the coast to the mountains.This spread leads to the emergence of vernacular structures that incorporate mound patterns with the construction of poles and beams according to the natural challenges encountered.

 House of Residence (bale langgak)
The house in the sasak language called "bale" is a space that is occupied as a residence settled hereditary in the hope of obtaining serenity, tranquility and welfare of the birth and the mind.
Home is one of the embodiment of cultural products and the development of human civilization (Fathurrahman, 2016).Spatial and home structures characterize the sociological dimension that reflects the social fabric of its supporting society.Classes and social functions in society are two elements that affect the shape, structure, and naming of space and home.Gedeng mention for the house of the nobles, cottage (bale jamaq) for ordinary people and bale bonter and mountain bale rate occupied by the religious teacher, village chief and the nobles.As for the concept of sasak architecture development always depart from pemole and semaiq concept which is then applied based on sasak custom system in example system of value, social, ritual and technical system.

 Bale Jamaq/Bale Tani
The concept of bale tani is built in accordance with the environment generally on the slopes of the hill; this bale has a roof of the back and side almost touching the ground and made with a slope that can launch the fall of rain water.Framework of the roof is made higher because basically this roof also functions to form space, because generally the bale tani wall is relatively low in example about 2 meters while the floor (floor) the dalem is higher than the ampik.
Space and function of this farm bale is divided into three spaces namely bale dalem, dalem bale and ampik.Bale dalem serves for the bedding of girls and dalem bale to store food and ampik divided into 2 ampik belo (long) and ampe konteq (short) which each function long ampik to place doing productive things like weaving and weaving while the short ampik is used for the boys resting place.All shapes can be seen in Figure 1.

 Bale Bonter
The concept of bale bonter is a residence for the citizens who have the function and status of the middle nobility, this building is made to be more authoritative than bale jamaq with symbols such as peduncles and the use of jejait on the frame.Bale bonter construction is more robust compared to other bale-bale poles and blander-blander and its doors use carvings.Bantaran (foundation) bale bonter built rather high so that built steps (steps) made of soil.In general, this type of house is equipped with a six (berugaq bertiang six) or bale jajar also called bencingah.
Space and bale bonter functions have in common with the bale jamaq that is applying the concept of dalem bale, dalem bale and ampik that can be seen in Figure 2.There is little difference in the shape of the roof.Construction of bale mountain roof rate using tunjeng and bumbungan generally decorated with carvings this hole usually has a length of 2 meters is used as a pedestal four pieces ujuk-ujuk same length.This type of building has a wall of yard so everyone who wants to enter it does not apply haphazardly.They will maintain the attitude or etiquette, especially because of the gate to the yard.The Bale Gunungrate and its sketch can be seen in Figure 3.The building of the mosque uses the pattern of the mound foundation with the low pillars and walls and the towering roof extends downward as if it were almost touching the ground, so everyone who will enter must be in a downcast position.The size of the customary mosque is generally 7 x 7 meters or 9 x 9 meters on the floor, in the middle of the mosque space, stands 4 main pillars that directly into a crown pole or cone.
Around the wall is built 20 poles tied with gelampar components and jejait using a system of purus (knockdown) and wooden pegs of roofing materials are usually made of reeds and some are using bamboo, and the roof is mounted through the wall about one meter above the floor, so people enter the mosque should bow down.Downward attitude is interpreted as a form of homage to the mosque or the people in it.Mosque buildings are usually placed in separate locations separated from housing or settlements (Figure 4).Setia Sopandi (2013) identifies sasak granary building technology in Lombok dating from 3500 years BC.Banguanan barn consists of two parts, namely the top and bottom which each has its own function of the top serves as a place to store the rice so that it is made closed.This upper space is formed by the roof with a symmetrical dome pattern if viewed from the front and rear.At the bottom consists of four poles with the arrangement in a clockwise direction, ranging from nyake, teacher, pendite, and kire.The illustration can be seen in Figure 5.
Above the four pillars are formed jelepeng which serves to prevent rats rose into the barn through the pole, in addition to increase the beauty.Above jelepeng is placed coral reef-shaped place where laying gelampar bottom that serves as a base with foot footprint women (selampak nine).The form of a granary developed by the sasak community is called "mekadal meteng" which in sasak society symbolizes the frugal attitude (frugal).The location of the granary in the yard is always in the right position of the house, as a sign of appreciation for the rice that is the fortune of the God.

The concept of mathematics in the cultural architecture of the sasak society
There are some concept of mathematics in the cultural architecture of the sasak society, such as measuring and measurement, designing, and geometric form.The explanation of the concept explained in the following.

 Measuring and measurement
In forming sasak community building structures, there is a feature known as "sikut/elbow" which means size, but in this case size is not related to length, width and height (numerical), but also relates to elbow time, elbow space and elbows ramon.Elbow length corresponds to the length to the power (north), width towards the andang and mudi (front -behind), high elbows associated with the nature of the building is determined by the size of the owner of the building while the elbow time related to the start building.All of these elephants are termed anthropometry (a measure that refers to the size of a human body).
The use of the concept of size (elbow) in determining the size of buildings in the community sasak use some terms in accordance with what will be measured.
1. Elbow size: the size of the construction of a house that refers to the size of the human body known as anthropometry, this measure consists of seperunjung, sedepa, sejengkak, sekepal, sehasta, and senyari (Figure 6).
2. Elbow andang: measurement to ensure the accuracy of direction that refers to the environmental layout, the accuracy of the determination of the direction of doors and windows tailored to the comfort and security of the inhabitants of the house.
3. Time elbow: precise time planning measurements to construct buildings such as houses, mosques, barns or other buildings.
4. Elbow of space: measurements related to the position of the planned room and determine the proper position to be made the core room in accordance with the traditional buildings that apply in the community.

 Designing
Sasak community activities related to the designing in the activities of building design such as establishing houses of residence, places of worship, and buildings related to the social life.In implementing the values that must be upheld in designing or planning development, the sasak community realize the four basic concepts those are: 1. Semaiq, not excessive in accordance with the needs so that the main size used is the size of the owner.
2. Hardened (sturdy), logical in applying the correct structure concept 3. Pantes (ethical), meets standards of decency 4. Solah (aesthetic) satisfies the owner's heart and others who see it.

 Geometric form
Geometry form that exists in the construction of buildings founded by Sasak community.It can be seen in Table 1.

Figure 5 .
Figure 5. Granary (sambi) This elbow is used to select the right building material and placed in the right position especially wood and bamboo materials.

Table 1 .
Mathematics concept and its application in Sasak' building ornament