Ethnomathematics study of Pandanwangi village: Schools mathematics instruction in rice farmer activities Pandanwangi

: This study aims to explore the hidden mathematical concepts behind the rice farming activities of Pandanwangi Cianjur. The research method is qualitative research with an ethnographic approach. The research location is in Pandanwangi Cultural Village, Bunikasih Village, Warungkondang District, Cianjur Regency, West Java. Pandanwangi Cultural Village was deliberately built by the Cianjur Regency Government to further introduce pandanwangi rice, which is the superior local variety of Cianjur Regency. Pandawangi rice farmers' cultural activities contain mathematical concepts that arise when determining seed class, number of seeds, nursery preparation, final seed selection with salt solution, seeding in nurseries, nursery maintenance, preparation of planting land, planting, fertilization in planting areas, planting maintenance, harvest, and post-harvest. The findings of this study show that there are mathematical concepts in agricultural activities on geometric content, including determining points, lines, angles, the area of flat shapes, the similarity of flat shapes, and algebra, including comparisons, percentages, and social arithmetic. The results of the research can be used as a teaching module to facilitate learning for students in the school curriculum.


INTRODUCTION
The Introduction presents the purpose of the studies reported and their relationship to earlier work in the field. It should not be an extensive review of the literature. Use only those references required to provide the most salient background to allow the readers to understand and evaluate the purpose and results of the present study without referring to previous publications on the topic.
Each ethnicity's unique process of human interaction gives rise to a culture (Nurjanah et al., 2021). Culture is a way of living, expanding, and growing as a group that is passed down from generation to generation (Dagan et al., 2021). The problems of human life that we do not realize come from culture cannot be separated from the role of mathematics. Mathematics and culture are branches of science that cannot be separated from human life (Nag Chowdhuri, 2022). Various activities that come from the customs and culture of the surrounding community that we are not aware of contain mathematical concepts. This relationship between culture and mathematics gave rise to the field known as ethnomathematics.
The first definition of ethnomathematics was introduced by Ubiratàn d'Ambrosio, an educator and mathematical historian born on December 8, 1932, in So Paulo. D'Ambrosio presented a paper titled "Science and Technology in Latin America" at a colloquium organized by the American Association for the Advancement of Science in 1977Science in (D'ambrosio, 1989. The scope of ethnomathematics is mentioned in the paper as being at the boundary between the history of science and technology concerning socio-economic phenomena and daily cultural life. "Mathematics is practiced among identifiable cultural groups such as tribal-national societies, workers' groups, children of certain age brackets, and professional classes." The term "ethnomathematics" is made up of the words "ethno," "mathema," and "tics" (D'Ambrosio, 1985). The prefix "ethno" is defined as an activity carried out by a group of people or communities, including ethnic groups in a country, as well as professional groups that exist in society, which includes language, jargon, symbols, codes of behavior, and other activities. Then "matema" has the meaning of knowing, understanding, explaining, and performing activities such as measuring, classifying, concluding, coding, and modeling, while the suffix "tics" means art in technique (D'Ambrosio, 1999) Ethnomathematics is defined as the mathematical cultural anthropology of mathematics and mathematics education (Vasquez, 2017). Ethnomathematics is the relationship between mathematics and socio-cultural reality (Brandt & Chernoff, 2014). The relationship between mathematical concepts and cultural artifacts can be formulated in the form of measurements, calculations, games, predictions, navigation, astronomy, and modeling (Eglash et al., 2006). Ethnomathematics views the importance of considering the cultural aspects of students to bring them closer to learning mathematical concepts used in everyday practice (Gavarrete & Albanese, 2021). The methods investigate and combine ideas, methods, and techniques developed by socio-cultural members or members of different cultures into an ethnomathematics study (Rosa & Orey, 2016). Rosa and Orey (2016) believe that ethnomathematics is a subset of the fields of cultural anthropology, mathematics, and modeling that are relevant to the pedagogical activities depicted in Figure 1. This means that the cultural component has a role as well as an influence on the pedagogical practice of learning mathematics in the classroom. The ethnomathematics carried out in various regions can be divided into 6 different dimensions, namely cognitive, conceptual, educational, epistemological, historical, and political, which are presented in Figure 2. These six dimensions are interrelated with each other and aim to analyze the sociocultural roots of mathematical knowledge (Rosa & Orey, 2016). As for the six dimensions, the first cognitive dimension focuses on the acquisition, collection, and dissemination of mathematical knowledge. Secondly, the Conceptual Dimension focuses on the creation of procedures, practices, methods, or theories by certain cultural groups to face the challenges of everyday life. The third Educational Dimension focuses on strengthening academic knowledge when students understand mathematical ideas, procedures, and practices that exist in their daily lives. The Fourth Epistemological Dimension focuses on the knowledge system, where a set of empirical evidence from observations is developed to understand and match with reality. The Fifth Historical Dimension directs students to examine the nature of mathematics in the form of understanding how mathematics is related to personal experiences or collections of experiences and the Sixth Political Dimension focuses on recognizing and respecting the history, traditions, and mathematical thinking developed by members of various cultural groups.
Research in the field of ethnomathematics has been found in many countries. Several studies conducted in the field of ethnomathematics in 2021 include exploration of the Peruvian Aymara ethnic group in the 11th century developing a numbering system, according to the geographical context (Vilca-Apaza et al., 2021). Ethnomathematics of the Temple of Heaven is one of the famous cultural heritage sites in Beijing, China, which carries a lot of mathematical concepts, including geometry on the exterior, interior design, and building structure (Zhang et al., 2021). Finding mathematical concepts in the Quilombola community of ceramic craftsmen Amapá, Brazil for school mathematics learning as a concept from ethnomathematics (Sunzuma & Maharaj, 2021).
Indonesia is a country rich in cultural diversity. Many interesting ethnomathematical studies are found in Indonesian culture, one of which is the ethnomathematics of Baduy community which is Their way of thinking and life values are very interesting to study, especially their antirat technology based on mathematics (Arisetyawan et al., 2014). The discovery of mathematical and cultural concepts in 2021 in the Wayang kulit culture in Java found the concept of a set (Prahmana & Istiandaru, 2021). The Cigugur community determines the direction in seeking fortune using mathematical concepts, namely the concepts of pair order, relations, addition, and comparison (Umbara et al., 2021). There is a relationship between Surabaya regional music and mathematics in the analysis of block notation scores and number notation, namely the addition of the same numbered fractions, the addition of different fractions, the multiplication of fractions, data processing in the form of modes, and the presentation of data in the form of tables, bar charts, and line charts (Indrawati et al., 2021). Ethnomathematics in traditional Balinese dance hand movements, namely the scope of ethnomathematics discussed is limited to geometric objects, especially angles (Radiusman et al., 2021). The Minangkabau tribe in West Sumatra uses mathematical concepts in basic addition and subtraction calculations in livestock trade transactions in mathematical representations of finger symbols and gestures (Nurjanah et al., 2021). Candrasengkala pointed out that the ancient chronograms practiced in Bali and Java had an adequate understanding of place value .
Exploration of cultural buildings in Indonesia has become the object of ethnomathematical studies. Butonese society has practiced mathematical culture in the form of a Butonese traditional house called Banua Tadha on the concept of comparison (Kadir et al., 2021). The historical buildings of Ngawen Temple in Magelang resemble geometric shapes, including the shape of a cube, a rectangular pyramid, and a rectangular pyramid (Pamungkas et al., 2021). Components, ornaments, and objects at the Jami Sungai Jingah Mosque in Banjarmasin, Kalimantan, which contain many mathematical concepts of lines, knots, properties, circumference, and area, especially in the field of geometry (Fajriah & Suryaningsih, 2021).
However, several research results in various countries, including Indonesia, have explored mathematical concepts found in their native culture. Mathematical concepts found in culture can later be used for teaching materials in schools to be preserved for the next generation. One of the efforts made is by using an ethnomathematical approach as a teaching material in learning mathematics at school. The importance of school education that focuses on respecting local culture, which strengthens ethnic relations in seeking justice and building the preservation of arts and culture (Nurjanah et al., 2021) The purpose of this study was to explore the hidden mathematical concepts of activities of Pandanwangi rice farmers. Cianjur has its own culture, especially in the activities of pandawangi rice farmers. Pandanwangi rice is one of the varieties of Bulu rice. Because of the pandanscented rice (Trihaditia & Puspitasari, 2020), this rice and rice have been known since 1973 as "Pandanwangi". Pandanwangi rice is a superior product in Cianjur Regency, which is registered as a Geographical Indication and can only be planted in 7 sub-districts: Cisalak, Cibeber, Cianjur, and West Java, whose existence is necessary (Soetoprawiro et al., 2021). Cianjur Regency in the agricultural sector. There is one of the Pandanwangi rice cultural villages in Cianjur. The potential of Cianjur Regency's natural resources in the form of rice and a large area of rice fields is presented in the form of tourism in that place. This Cultural Village can introduce Cianjur's local wisdom, namely by introducing Pandanwangi starting from the Sundanese traditional house, a museum of traditional farmers' tools, the flow of traditional activities of pandanwangi rice farmers, Pandanwangi rice fields, along with Pandanwangi rice products and art performances (Malia et al., 2021).
The novelty of this research is the finding of mathematical concepts that exist in the activities of Pandanwangi farmers. So far, there has been no research that specifically examines the discovery of mathematical concepts in Pandanwangi activities. So it is important to explore ethnomathematics in the activities of Pandanwangi farmers in Cianjur, which have the potential to be used as a starting point for preserving culture and resources for learning mathematics. Cultural inheritance can optimize one of its functions as a cultural transformation in learning in schools and is implemented in everyday life by the younger generation of Indonesia (Carel et al., 2018). Describe a mathematics content that is found in the farmer activity rice Pandanwangi

METHOD
The research method used in this study was a qualitative approach based on the ethnography model (anthropology cognitive) (Spradley, 2016). A new ethnography that focuses on discovering how people organize their customs in their minds and then use them in everyday life. The location where this study was conducted is Cianjur City, West Java. selection of the location as the origin of the Pandanwangi Rice. The informants used are two farmers and two cultural observers who have previously conducted research on the culture of the Pandanwangi community. While participant observation and documentation are used in the data retrieval technique. The analysis in this study is based not only on the researcher's interpretation but also on the composition of the ideas of the farmer community who are scraped out by the researchers. This study employs the following design, which is based on the ethnomathematics research framework (Alangui, 2010) in Table 1.

RESULTS AND DISCUSSION
Pandawangi was introduced in 1970, Mr. Haji Nawawi from Cisalak Village, Mayak Village and Haji Damiri from Sadamaya Village, Peuteuycondong Village, Cibeber District, to Mr. Haji Jalaludin, a farmer who is also a rice entrepreneur and trader and a creative entrepreneur. Then he developed the rice and after it was successfully harvested he offered it to a restaurant in Jakarta (Soetoprawiro et al., 2021) Pandanwangi Cianjur rice itself is a type of aromatic rice belonging to the feather rice (javanica). The characteristic of Pandanwangi rice is that it has a long life of 155 days. In clumps that are 168 cm high, they are harvested and stored in panicles. The rice and rice have a pandan aroma. Pandanwangi rice is very suitable for growing in rice fields with air temperatures of 25 °C to 30 °C with an altitude of 450-800 meters. The Pandanwangi Cianjur rice grain is round in shape, golden yellow in color, has long fur resembling a keris, and has a pandan leaf aroma. Pandanwangi rice has been released as a superior variety based on the Decree of the The people of Pandanwangi village in Cianjur still preserve their cultural heritage, including in every activity carried out by traditional Pandanwangi farmers. The mathematical concepts found in Pandanwangi farmer's activities include:

Activities to Determine Land Areas
The activities of the Pandanwangi rice farming community, especially in the Pandanwangi Cultural Village, in determining the length is described in Table 2, it can be seen that there are several different names. Farmers use the length of the sample to determine the length of the rice field using the term "satampah", the size of the spacing of the term "sajeujeuh" which is along the sole of an adult's foot about 20 cm and the size of the water height with the term "sabuku" when planting seeds the water height is measured with 1 finger knuckle consisting of 3 book.
The mathematical concept of length is defined by Euclid as a line as "length without width," which "is equal to the points on itself (Brandt & Chernoff, 2014). Likewise, in measuring the area of the fields of Pandanwangi, farmers use the terms in Table 3. This will determine the number of seeds to be planted. Pandanwangi farmers often use the term "patok" to refer to the area of their fields. This is in accordance with the Sundanese cultural language used by the people of Cianjur. The activity of determining length and area contains a mathematical concept, namely geometry. The definition of area is a quantity that expresses the two-dimensional size of a clearly demarcated part of a surface, usually an area bounded by a closed curve. The process of determining the length and area in Figure 3 is what Pandawangi farmers use in their farming activities. The activity of farmers determining the length and area of a mathematical problem is presented in Figure 4.

Task Design
Ujang is a 7th grade junior high school student. Ujang's father was a Padangwangi farmer. On Sunday, Ujang helped his father do farming. Ujang observes the area of the rice fields that his father cultivates to form a rectangle with a length of 15 tengkah and a width of 5 "tengkah". How much land did Ujang's father work on if he wanted to express it in terms of the area of "meters"? (information 1 "tengkah" = 50 cm).

Activity to Determine the Amount of Seed Needed
Pandanwangi Cianjur rice farmers still use conventional methods in determining the amount of seed needed. The seeds used by farmers are labeled with blue labels or seeds selected by breeder farmers whose seeds are found in the agricultural office. In determining the amount of rice seed needed for planting, the planting hole is determined based on the land area. Usually, farmers determine by predicting 3-4 stems that the need for seed per ha is 25-40 kg/ha. In the activity of determining the number of seeds, mathematical concepts were found in the comparison material of worth. Mathematical problem activities often used by farmers to calculate the number of seeds needed are presented in Figure 5.

Task Design
Pandanwangi farmer owns a patch of rice fields. The rice field has an area of 1,500 bricks. How many rice seeds must farmers prepare if, in one hectare, 40 kilograms of seeds are needed? (Information 1 "sabata" equals 14 m 2 ).

Solution
It is known that the area of the rice field is 1,500 bata = 21,000 m 2 . In a rice field area of 1 hectare = 10,000 m 2 , it takes 40 kg Comparison Concept

Activities in the Seed Nursery
Farmers' activities Before determining the number of seeds, and before sowing, the seeds are first sorted with 4% kitchen salt solution to separate the grain or seeds that are empty and less nutritious. The pithy and good grain/seed will sink, while the empty and less pithy will float. Furthermore, the seeds are soaked in water for 24 hours, ripened for 48 hours, and every 12 hours, watering and reversing are carried out. Seeds that are ready to be seeded after coming out will root 0.5-1 cm.
After the seeds have roots of 0.5-1 cm, the seeds are sown in a nursery covering an area of 400-500 m² (4-5%) of the planted area, so that the average seed spread is 15 m² for each kg of seed. Before the seeds are sown in the soil for nursery, they are plowed and harrowed until they are completely muddy or soft. Then make beds with a width of 1-1.5 meters, the length of the beds in accordance with the length of the rice field box. Sprinkle the rice seeds in each nursery evenly, try not to pile up the rice seeds in the nursery as shown in Figure 6. Close the In this activity, there are mathematical concepts that appear, namely geometry in determining the area of the nursery, the concept of comparison in measuring the area in calculating the number of seeds per kg in the nursery area, and the concept of rows and series when observing predictions of growing seed size. The mathematical problem activities used by farmers are in Figure 7.

Task Design
A field of 150 acres requires 60 kilograms of seeds, to determine the area of the Pandanwangi farmer's nursery, which is 5% of the rice field area. So how much area is needed to make a 150 acre nursery? (information 1 are = 100 m 2 )! Solution Rice field area 15 are = 15,000 m2 Nursery area = 1.5000 x 5% = 1.5000 x 5/100 = 750 m2 The need for nursery area is 750 m 2

Figure 7. Task Design on Nursery Area
In mathematical concepts, what is meant by similarity are concepts that describe whether two forms have similar characteristics. In Euclidean geometry, the term "similarity" is used to describe objects that have the same shape. The basis of this concept is that farmers use it to complete solutions in determining the area of the nursery (Libeskind, 2008).

Activities in Land Management
The next activity of the farmer is tilling the soil until it becomes muddy by plowing and harrowing using buffalo, as shown in Figure 8. Straw and grass are immersed when plowing. The time interval between plowing/harrowing and planting is about 15 days (2 weeks). After slicing the paddy fields, the ripe organic fertilizer is spread, along with phosphate fertilizer. It takes 2 people to spread the fertilizer over an area of 1 hectare. The soil is left for a few days until the muddy, thickened soil is ready for planting to facilitate seedlings. In this activity, there are mathematical concepts that appear, namely geometry in determining the area of land cultivation, and the concept of comparison of turning values in plowing time activities related to the number of workers and the number of buffalo. The mathematical problem activities used by farmers in task design are in Figure 9.

Task Design
If a plot of rice field measuring 1 hectare is worked on by four workers, it will be faster than two workers covering the same area of the rice field. So, it can be concluded that the more workers who work, the faster the time needed is needed and vice versa. Usually, the workers work a day with the term "sebedug" in the sense of working from 06.00 to 12.00 a.m. A seed dispersal project can be completed in 3 days by 12 workers for a rice field area of 20.000 m 2 . How many days will the project be completed if it is done by 18 people?  This concept in mathematics is known as the inverse ratio of values, defined as follows: The inverse ratio is a comparison in which a change in the value of one quantity is followed by a change in another quantity, with the opposite value changing (Lamon, 2007).

Activities in rice cultivation
The activity of planting rice begins after the soil is processed and seedlings aged 15-25 days are transferred to land that has been prepared previously. The spacing used is about 25x25 cm or 30x30 cm using "caplak" tool. Then the number of seeds planted is 2-3 stems/planting hole with a planting depth of 2-3 cm.
In this activity, there are mathematical concepts that appear, namely the geometry of points, lines, and planes. The Caplak in Figure 10 is used by farmers to help make lines for the spacing pattern of rice. Using Caplak is to pull them vertically and horizontally, so that the meeting of the lines printed by the Caplak will form a checkerboard line. In addition, the concept of straight lines is used by farmers when "tandur". In the process, the "tandur" produces a set of points that become a set of parallel lines. Farmers do not realize that they are using geometric concepts, namely points, angles, and lines in Figure 11. This mathematical concept of points, angles, and lines helps farmers in arranging crops and determining the number of plants that can be planted in the area of rice fields. One of the activities of farmers is solving mathematical problems in Figure 12.

Task Design
If the farmer has an area of 3,6 hectares of rice fields, how many plots are formed using ticks if the area of the square (plot) is 30 x 30 cm?

Solution
It is known that the area of rice fields is 3,6 hectares = 36.000 m 2 Area of the plot 30 x 30 cm = 900 cm = 9 m 2 Asked the number of plots? Number of plots= (field area)/(plot area)= 36.000/9 = 4.000 So, the number of rice fields is 4,000.

Activity in fertilization
Farmers also pay attention to the dose of fertilizer used during the growing season, which is 60-90 kg N/ha or equivalent to 125-195 kg/ha urea, 45-60 kg P2O5/ha or equivalent to 100-133.3 kg/ha sp. 36 and 25-37.5 kg K2O/ha or equivalent to 50-75 kg/ha KCL.
The dose of fertilizer per application and time of fertilization is the first fertilizer, including 33.3-65 kg of urea (30% dose) plus 100-133.3 kg of SP 36 fertilizer (100% dose) and 50-75 kg of KCI fertilizer (100% dose of fertilizer). is applied no later than one week after planting. The second fertilizer is given at the age of about 39 days after planting, including fertilizer given in the form of 50-70 kg of urea (35% dose) around the age of about 60 days of 50-60 kg of 30 cm 30 cm 30 cm urea (35% dose). Additional liquid organic fertilizer, whether applied through the soil or leaves, is adjusted according to the recommendations of the fertilizer manufacturer.
In this activity, a mathematical concept appears, namely the comparison of worth to determine the amount of fertilizer according to the area of the field, the percentage of the amount of fertilizer used, in determining the amount of fertilizer as in the previous farmer's problem.

Activities in irrigation
Irrigation activities are carried out using intermittent irrigation technology. The first drying of the paddy fields is carried out at the age of 25-30 days, at the time of the first weeding. After weeding and fertilizing, the paddy fields were flooded again at the age of about 45 days. The paddy fields were dried again for weeding and fertilizing. After weeding and fertilizing, the paddy fields were flooded again at the age of 46 days. The water level was raised by about 10 cm with the aim of suppressing unproductive tillers. Furthermore, irrigation can be carried out at any time. The water that is put into the plot is accompanied by the soil because it seeps into the soil or is used by rice plants. About 10 days before harvesting, the paddy field is dried. This system is known as the "dry base system," which is depicted in Figure 13. In this activity, a mathematical concept appears, namely geometry, in calculating the volume of water flowing into the fields. Constants, variables, functions, equations, namely making a mathematical model to determine the volume of water by taking into account the magnitude of the change in water level, the length of time of inundation. Mathematical concepts are only used by farmers in predicting water levels adjusted to water flow. No farmer has yet calculated the volume of water mathematically.

Activities in Harvest and Post Harvest
Harvesting is done when 80-90% of the rice grains have turned yellow, the stalks are still fresh, not dry and not broken, and the harvest age is around 145-155 days. Harvesting is done using "ani-ani", cutting the "malay" stalks as shown in Figure 14. Malay that have been harvested are dried in the sun for 2-4 days and carried out in the hot sun until they reach 14-15% water, which is referred to as milled dry malay (MKG) in Figure  15. MKG is stored in rice storage warehouses for no more than 3 months so as not to reduce the level of fragrance. MKG storage was carried out in sacks for short malay and long malay. In this activity, a mathematical concept appears, namely the concept of comparison in harvesting activities related to the number of workers, the number of grains, or panicles, produced in the area of rice fields. These activities can be used in other mathematical problems that contextual farmers use.

Activities in Processing, Sorting, and Packaging
MKG processing is carried out after being stored for at least 1-2 weeks to avoid the high percentage of broken rice. MKG is processed using a thresher to produce milled dry grain. Rice is sorted and graded to produce quality I and II rice based on the Indonesian National Standard (SNI 6128:2008). Packed in packs of 1-25 kg as in Figure 16 labeled, "Logo and Traceability Code for Cianjur Pandanwangi Rice." The packaging is stored in a good warehouse using a pedestal so that the packaging of Cianjur fragrant pandan rice does not directly touch the floor. In this activity, a mathematical concept appears, namely the concept of comparison in milling activities and packaging related to the amount of rice produced from how many kilos of dry panicles into rice that is ready to be packaged. The concept of social arithmetic is used in determining the percentage of profits and losses. Recapitulation of the profit description of Pandanwangi Dry Milled Malay Production by cultivators Until Harvest with a rice field area of up to 1 hectare as follows: Benefits of Pandanwangi Rice Farmers with Cultivators Harvested in the form of Milled Dry Malay for sale at the harvest location. Selling Price of Milled Dry Malay Paddy Pandanwangi Rp. 6. 000/kg. Total Selling Price 7,500 kg x Rp 6,000 = Rp 45,000,000 Procurement of Certified Rice Seeds = Rp 6,235,000 Cost of Soil Processing to Planting = Rp 6,670,000 The advantage of this cultivator is if it is carried out in a land rental system. However, there is also a tradition of Pandanwangi farmers, namely the Sundanese term "mamaro" which means farmers who work and landowners for the profits from farming. So for the above case the land rent is not taken into account so that the profit of the farmer and the owner of the field becomes Rp. 23,525,000 so that the profit of each farmer and the owner of the field is Rp. 11,762,500. This "mamaro" tradition is also carried out by other Indonesian farmers with the terms "maro" in Pekalongan and "guise" Mulyerejo as a form of community solidarity (Malia et al., 2021;Wahyuningsih, 2013).

CONCLUSION
Pandanwangi farmers in every activity use mathematical concepts. Mathematical concepts are carried out by farmers without their knowingly learning mathematical concepts. Bringing up mathematical concepts when farming activities start from determining the area of rice fields used when farmers determine the number of seeds to be planted, determining the amount of rice seed needed for planting, planting holes are determined based on land area, determining the area of the seedbed with the concept of geometric similarity, soil management activities, giving fertilizer, and post-harvest and harvesting with the concept of comparison, the activity of growing rice with ticks using the concept of points, lines and angles, the activity of irrigating the fields with the concept of geometric series, and processing, sorting and packaging activities with the concept of social arithmetic. The mathematical concepts contained in agricultural activities can be used as teaching materials for teachers and give students' insight that mathematics is always related to life in various activities. For further research, it is hoped that researchers will dig deeper into the agricultural sector. Because there are still many ethnomathematics that have not been explored. So that it can add to further research studies and participate in preserving culture.