MATH AND MATE IN JAVANESE PRIMBON : ETHNOMATHEMATICS STUDY

Marriage is an essential part of life for most people. In the Javanese tradition, great attention is paid to the weton of the couple through Javanese Primbon . It predicts the fate of the couple in the marriage. This prediction of the Javanese outcome after the wedding has some numerical values. Therefore, this study aims to uncover these numerical values using ethnomathematics. This research uses a qualitative method. Analyzing the Javanese Primbon documents is meant to explore the numerical value of Javanese people. Also, analyzing the data using the Javanese Primbon documents was not only based on the interpretation of the researcher but also the result of discussions with cultural and mathematical experts. This study proposes numerical values such as number bases, remainder theorem, modulo, and modulus of the congruence in formal mathematics, which is associated with matchmaking using Javanese Primbon.

Indonesia is a maritime nation with land and sea territories stretching from Sabang to Merauke.The geographical location of the country spans across a group of small islands making Indonesia a land with various ethnic and cultural characteristics (Sutarto, 2006).Culture is a phenomenon which is common in any society.Javanese has one of the most popular customs in Indonesia known for its noble character, as it is also the tradition of other Eastern religions (Ember & Ember, 2001;Hatley, 2008;Sutarto, 2006).
The Javanese culture is a well-known custom filled with mystical issues, with no scientific basis.Java's mystic beliefs came into the open since the early nineteenth century and a poem, Serat Centhini, composed in 1815 in the court of Surakarta, was an aspect of Java's mystic belief (Ricklefs, 2007).
Based on this mystical atmosphere, the Javanese culture is less explored scientifically.However, it contains various numerical values including ancestral civilization in terms of Mathematics (Maryati & Prahmana, 2019a;Maryati & Prahmana, 2019b;Supiyati, et al. 2019;Risdiyanti & Prahmana, 2018;Muhtadi, et al. 2017).The development of this subject started a long time in Java, although not yet to the level of formal mathematics or the Western ones.
The objects in Javanese culture contain numerical values in various forms of literature.Ambrosio and Rosa (2017) stated that the different types of culture appear in the form of the artifact, venti-fact, or socio-fact.One of the socio-fact in Javanese culture is the foreknowledge matchmaking in marriage.
Moreover, it is a general fact that marriage is something special in the lives of almost every individual, and it must be well planned, including with whom to marry.Before the wedding takes place, the Javanese usually find out about their next lives after the wedding.They carry out foreknowledge matchmaking in marriage before planning the married life.The traditional Javanese elders are the ones who usually start the whole process, guided by the Javanese Primbon, which is a life guide used by the people in their daily activities.The Javanese Primbon contains the human life guidelines from the womb, birth, adulthood, and even to the day of death.
The guide namely Javanese Primbon contains numerical values or mathematical knowledge from Javanese people.Although, the emergence of the Primbon did not have any connection with the formal mathematics taught in schools.However, there is a mathematical requirement when it comes to foreknowledge matchmaking in marriage as contained in this Primbon and Javanese marriage customs pay attention to the counting weton of the couples before they get married.It is usually used to predict the fate of the couple.The exploration of these numerical values in foreknowledge matchmaking in marriage as contained in the Javanese Primbon is an area of ethnomathematics studies.Tutak, Bondy, and Adams (2011) stated that the term of ethnomathematics was first introduced by D'Ambrosio in 1978 at the annual meeting of the American Association for the Advancement of Science (AAAS).Subsequently in 1985, D'Ambrosio, Gloria Gilmer and Rick Scott formed a group known as The International Study Group on Ethnomathematics (ISGEm), whose aim was to increase the understanding of mathematical practices on cultural diversity and apply the knowledge for the purpose of education and development (Tutak, et al. 2011).D 'Ambrosio (1985) stated that ethnomathematics is the mathematics which is practised among identifiable cultural groups, such as national-tribal societies, labor groups, children of a certain age bracket, professional classes, and so on.Furthermore, it defines ethnomathematics as the intersection of mathematics with the historical, cultural, and social roots of mathematic, and also that the ethnomathematics comes from the combination of two words -ethno and mathematics, where ethno denotes the socio-cultural context, and mathematics talks about mathematical knowledge such as counting, weighing, measuring, comparing, sorting, classifying, designing, and playing (Katsap, 2018).

Ethnomathematics Studies
However, Rosa and Orey (2016) explained that ethnomathematics includes ideas, procedures, processes, methods, and practices that are rooted in different cultural environments.Therefore, etnomathematics is so related to mathematics and culture in the nation.
There are several ethnomathematics related to studies carried out in other countries.One of such is the study conducted by Mohamad, Adam, and Embong (2010), which discusses an ethnomathematical study on weaving among the Malay tudung Saji or food cover weavers, focussing on investigating the mathematical ideas that are relevant to the weaving techniques, framework construction, and pattern formation.On the other hands, Fonseca (2010) discusses how youth and adult educators found ethnomathematics to be a resource useful in knowing their students better and producing an improved result in mathematics, as well as in intercultural studies related to ethnomathematics.This research offers a new perspective on conceiving mathematical knowledge and practices in youth and adult education.We also discuss the dimensions of the approach of teaching and learning practices to present a reflection about the relations among youth and adult education, ethnomathematics and the search for better understanding the teaching and learning of mathematics at schools, as well as making it an inclusion project.A related study was also conducted by Pais (2011), which clarifies the positions of ethnomathematics and its implications in the recent pedagogical research in the field.Meanwhile, François and Stathopoulou (2012) present the development of the political dimension of ethnomathematics and the researchers of critical mathematics education, also explore their similarities.
In other ethnomathematics related studies, D'Ambrosio (2013) explained about the position of ethnomathematics as a theoretical framework capable of guiding practice and serving as a curriculum for different educational projects.We also explained the fact that ethnomathematics is positioned as one which centers the children in a world of social equity and justice.Also, Matang and Owens (2014) discuss the role of indigenous traditional counting systems in children's development of numerical cognition in Papua New Guinea, and then Rosa and Orey (2015) discuss the curriculum for mathematics based on literacy, matheracy, and technoracy from ethnomathematics perspective.
Considering of all these existing articles, no author has discussed foreknowledge matchmaking in marriage guided by Javanese Primbon (the special book from Java) which is related to mathematics learning.Therefore, the research focus on to explore the ethnomathematics value of foreknowledge matchmaking in marriage found in Javanese Primbon, the body of knowledge from the ethnomathematics value of foreknowledge matchmaking in marriage found in Javanese Primbon, and the developed learning mathematics that can be used from the Javanese Primbon.

METHOD
The method used in this research is a qualitative method.The purpose of research method is to reveal ethnomathematics in Javanese Primbon.The design of this research follows the framework of ethnomathematics study from Alangui (2010) to conduct a qualitative method through ethnomathematics in Javanese Primbon.The framework is presented in Table 1.The significant value of culture, and mathematics Anthropology Describe the relationship between the two forms of knowledge (mathematics and culture).Write a new mathematical concepts found in the determining the matchmaking of the couple.

Gathering Data
To answer the research question, we analyzed the literature of Javanese Primbon.Analyzing the document involves activities like skimming (cursory examination), through reading, and interpretation (Bowen, 2009).The analyzed document produced data in quotations, themes or categories, and the examination, as well as the interpretation of the Javanese Primbon document, was carried out to obtain the scientific values in the foreknowledge matchmaking marriage and the experience after the wedding.
Interviewing informants were also carried out as supplementary data in the study.The informants are the traditional Javanese elders, who knew deeply about the Javanese tradition.During the interview, we made notes in the form of field notes and tape recorders.This interviews conducted was aimed at verifying the validity of data from the interpretation of the researcher.

The Data Analysis
This research is limited to the rules the determining the matchmaking of the couple.The data analysis technique used in this study is taxonomic analysis.The taxonomic analysis is conducted to analyze the determining of the matchmaking of the couple, and the values of school mathematics that can be taught.

RESULT AND DISCUSSION
The foreknowledge practice through Javanese Primbon is still a common act among the Javanese people, and it is carried out before a wedding could take place.Foreknowledge is known in Javanese as Petung, and the real meaning of this word in English is called computation.However, petung in the Javanese language does not always mean computation.It means consideration in determining something.
The weton of the couple is critically considered in matchmaking using the Javanese Primbon.
Weton is a calculation of birthdays based on days in the Javanese Calendar.Weton is a composite calculation of neptu dina and neptu pasaran from the two mates.Neptu is certain calculation numbers.
It means that consideration in matchmaking in Javanese society is not permissible for a prospective couple who have a neptu wage and pahing for the wedding.
The major consideration in matchmaking through Javanese primbon uses computation, and there are two types of matchmaking computations.The first one is the computation with the couple weton, and the other is computation with the names of the couple.This study focuses on the computation of matchmaking based on weton from the couple.In Javanese culture, the weton of the couple needs to be paid attention to before the wedding, and when it is computed, it helps to predict the fate of the couple during the wedding.

Computation in Predicting the Future of the Bride based on Weton of the Two Brides
There are many computations in predicting the future of the couple based on their weton.Also, this weton is a compilation of dina and pasaran.Dina (Days) is Akad (Sunday), Senen (Monday), Selasa (Tuesday), Rebo (Wednesday), Kemis (Thursday), Jumuah (Friday), and Setu (Saturday).Table 2 present the correlation between days (Dina) and Neptu namely Neptu Dina.Pasaran is Kliwon, Legi, Pahing, Pon, and Wage.However, determine the match matching to predict the future of the couple after the wedding must be attention to the neptu dina and neptu pasaran of the bride and groom.Hence, attention must be paid to Table 3, for a proper discussion on computation in predicting the couple's future based on their weton (Tjakraningrat & Soemodidjojo, 2017).There are four types of the computations in predicting the future based on weton of couples, such as.

Type 1
The computation is performed by summing up of each neptu dina and neptu pasaran of both the bride and groom and then divided by 9.Then, the foreknowledge decision is made using the remaining value after the division.Therefore, the conclusion is based on the meaning shown on Appendix: The Meaning of the Remain Type 1, and the part of it shown in Table 4.Then, after the computation, if the remainder has a good meaning, according to the Javanese Primbon, then the wedding takes place.However, the wedding is canceled if the result is bad.
The first example of the computation is a situation where the bridegroom is born on Kliwon Hence, the computation is (6+9) 9 = 1 and the remainder is 6.Considering the computations above with the remainders of 5 and 6, the conclusion based is based in Table 4, which is easy of fortune.In other words, if they get married, they probably have a better life, easy of fortune.
Another example is a situation where the bridegroom is born on Kliwon Friday, and the bride born on Pahing Thursday.Then, the foreknowledge of the two brides is determined as follows: a. Weton of the bridegroom born on Kliwon Friday means: Friday = 6, and kliwon = 8 Hence, the computation is Hence, the computation is (8+9) 9 = 1 and the remainder is 8. From the computations, the remainders are 5 and 8. Checking these with the meanings in Table 4, we have many obstacles.In other words, if they get married, probably their life will be many obstacles.

Type 2
This computation in Type 2 is carried out by summing up all the neptu dina and neptu pasaran of bride and groom, then divided by 4. The foreknowledge decision in this is also made using the remaining value after the division.The conclusion of the computation based on the meaning from the Javanese Primbon in shown in Table 5. Punggel, mati siji (one died) The first example here is a situation in which the bridegroom is born on Kliwon Friday, and the bride is born on Pahing Friday.Then, the foreknowledge of the couple is determined as follows: Weton of the bridegroom born on Kliwon Friday means Friday = 6, and kliwon = 8, and then weton bride Pahing Friday, means Friday = 6, and pahing = 9.Hence, the computation is = 7, while the remainder is 1.
Since the remainder is 1, the conclusion of the computation as shown from the meaning in Table 5 is rarely have children.Therefore, in a situation where the bridegroom is born on Kliwon Friday and the bride born on Pahing Friday, there is no good future for them.
The second example is a situation where the bridegroom is born on Kliwon Friday, and the bride born on Pahing Thursday.Then, the foreknowledge of the couple is determined as follows: Weton of the bridegroom born on Kliwon Friday, means Friday = 6, and kliwon = 8, and the weton of the bride born on Pahing Thursday, means Thursday = 8, and pahing = 9.Hence, the computation is = 7 and the remainder is 3.
The conclusion with the remainder of 3 as shown from the meanings in Table 5 is lots of fortune.
Based on this, the bridegroom born on Kliwon Friday with the bride born on Pahing Thursday has a good future, lots of fortune.

Type 3
Predicting the future with Type 3 is similar to Type 2, which involves summing up of all neptu dina and neptu pasaran of bride and groom.However, the divider is 10 or 7, and the remainder of the division starting from 1 to 7.Then, the conclusion is drawn from the meanings of the Javanese Primbon shown in Table 6.Based on this, the conclusion is drawn from the meanings in Table 6.Since the remainder is 1, it is easy to forgive, accept suggestions.In other words, a bridegroom born on Kliwon Friday will have a good future with a bride born on Pahing Friday.
Also, just like the second example in Type 2, the bridegroom is born on Kliwon Friday, and the bride born on Pahing Thursday.Kliwon Friday means Friday = 6, and kliwon = 8, and Pahing Thursday means Thursday = 8, and pahing = 9.Hence, the computation is = 3, while the remainder is 1.Checking for this remainder with the meaning shown in Table 6 gives easy to forgive, accept suggestions.Therefore, it is concluded that the bridegroom born on Kliwon Friday will have a good future with a bride born on Pahing Thursday.

Type 4
The computation of Type 4 is the same with type 2 and 3, with the summing up of all neptu dina and neptu pasaran of bride and groom.However, the divider is 5, and the remainder of the division starts from 1 to 5.Then, the conclusion is drawn from the meanings shown by Javanese Primbon in Table 7. = 5 and the remainder is 4.
Based on the remainder, which is 4, and checking it with reference to the meanings shown in Table 7, it is pati, meaning died.Therefore, it is concluded that the bridegroom born on Kliwon Friday will have bad marriage experience with the bride born on Pahing Friday.
Also, like the second example in Type 2 and Type 3, the bridegroom is born on Kliwon Friday, and the bride is born on Pahing Thursday.Kliwon Friday means Friday = 6, and kliwon = 8, and Pahing Thursday means Thursday = 8, and pahing = 9.Hence, the computation is = 6 and the remainder is 1.
Considering the remainder, which is 1, the conclusion is drawn from the meanings shown in Table 7, and this is noble.Therefore, there is a good future between the bridegroom born on Kliwon Friday and the bride born on Pahing Thursday.If they get married, probably they will be very rich.
Considering this foreknowledge presented above, we could deduce that the results are inconsistent.However, the focus is not to discuss these inconsistencies; it is an indication that foreknowledge is someone's estimate, which is not necessarily truenevertheless, it showed that numbers have a mystical aura for the Javanese and this does not only occur in Java.There was a pair of friendly numbers in the ancient Greeks, which attained a mystical aura, and superstition.Then, it later maintained that two talismans bearing these numbers would have a perfect friendship.According to Eves (1969), these numbers came to play an essential role in magic, sorcery, astrology, and the casting of horoscopes.

Relating Mate and Mathematics
The act of getting a mate and the prediction of future based on the weton of the couples through Javanese Primbon has a numerical value within the Javanese community.These computations in predicting the future have similarities in the case of repeating numbers.Ascher (1991) stated that numbers are only names given for the series formed, and the capacity to calculate is universally related to human language.Furthermore, when writing or naming numbers for each culture, it may be different from what it means in the other culture (Van Maanen, 2011;Abdullah, 2017).However, numbers usually have patterns and have implicit relationships in arithmetic.
In addition, Eves (1969) states that the calculation process must be systematized in a number base.Human fingers are more comfortable to use.Hence, it was not surprising that base 10 was chosen.
Besides base 10, Eves (1969) suggests the use of 2, 3, and 4 as number bases.In line with this, certain tribes of Tierra del Fuego have several first number names based on 3, and some South American tribes also use 4. Eves (1969) also suggests that base 5 could be used extensively.There are some South American tribes that currently count by hands, such as "one, two, three, four, hands, hands and one,." Yukaghir Siberia uses a mixed scale by counting "one, two, three, three and one, five, two three, one Moreover, calculating through Javanese Primbon could be performed using other mathematical elements, as we could symbolize the calculation on Type 1 in the formal mathematical sentence.If neptu dina of the bride is symbolized as , and neptu pasaran of the bridge is symbolized as , and divisor 9 is symbolized in , and the remainder of this calculation is symbolized by , then it can be written as: and remainder , where  = {3,4,5,6,7,8,9} and  = {4,5,7,8,9}.
Also, we also could symbolize the calculation in Type 2, 3, and 4 in the formal mathematical sentence.If neptu dina of the bride is symbolized as , neptu dina of the groom is symbolized as , neptu pasaran of the bride is symbolized as , neptu pasaran of the bride is symbolized as , and the divisor is symbolized in , and the remainder of the calculation is symbolized as , it can be written as: +++  and remainder , where  =  = {3,4,5,6,7,8,9} and  =  = {4,5,7,8,9}.
In the general form, the result of the sum is symbolized as  then divided by  and remainder  or written as  =  + .This is referred to as the remainder theorem in formal mathematics.In other words, one of the mathematical elements in the foreknowledge is a remainder theorem.
This theorem is also known as the division algorithm (Fine & Rosenberger, 2007).We take the following examples of the division algorithm: (i) 22 divided by 5 is 4, remainder 2, so we can write 22 = 5 • 4 + 2 (ii) 26 divided by 4 is 6, remainder 2, so we can write 26 = 4 • 5 + 2 (iii) 28 divided by 3 is 9, remainder 1, so we can write 28 = 3 • 9 + 1 Another commonly used notation is    =  (read "a modulo m"), which denotes that  is the remainder obtained when  is divided by .Suppose that  is an integer and  is an integer more than 0, hence: = , so that  =  + , where 0 ≤  < We can take the following examples of the modulo arithmetic: Furthermore, the mathematical element in the foreknowledge is a congruent modulo n.In the definitions and fundamental properties, let  be an integer ≠0.The integers  and  are said to be congruent modulo , or for the modulus , when their difference  −  is divisible by .To express this mathematical element: Where the symbol ≡ is to be read "is congruent to" , and the number  is the modulus of the congruence (Nagell, 1952).We take the following examples of the congruent modulo: (i) 22  5 = 2 and 17  5 = 2, so 22 ≡ 18( 5) (ii) 26  4 = 2 and 30  4 = 2, so 26 ≡ 30( 4) (iii) 28  3 = 1 and 25  3 = 1, so 28 ≡ 25( 3) Therefore, we could conclude that foreknowledge computations contain mathematical elements including number bases, remainder theorem, modulo, and modulus of the congruence.

Proposed a Mate in Javanese Primbon as a Contextual for Teaching Mathematics
A mate in Javanese Primbon is a contextual problem for Javanese students.Learning uses a context that can provide comprehensive understanding and links to students to provide direct experience with hands-on experience in real life.Cultural context issues can be used in learning through ethnomathematical problems.Hence, mate or foreknowledge matching in Javanese Primbon can be used as an ethnomathematical problem.Ethnomathematics problems are mathematical problems in which verbal texts use narration to describe mathematical practices that exist in daily habits, traditions, and experiences of various socio-cultural groups, and solution to the problem must be examined in its social context (Katsap & Silverman, 2016;Risdiyanti & Prahmana, 2018).
Problem's text using ethnomathematics can be built by integrating problems related to a culture which contain mathematical content.Katsap and Silverman (2016) argue that the problem contains two parts; the first part contains a prelude, which is a segment of information related to the culture, tradition, or habits of society.The second part of the problem's text contains mathematical questions (the solution is discussing mathematical objects and structures requires investigation or evidence) and nonmathematical questions (referring to social problems or facilitating mathematical practices in the community).Here is an example.

Problem: Prediction of fate marriage through base and modulo
Read the prelude before you answer the following questions.

Prelude
In the tradition of marriage in Javanese, various things need to prepare, including determination about the compatibility of the two brides.Traditional Javanese elders usually do match matching between the two brides.The determination of the compatibility of the two brides contains predictions about life later after marriage based on the weton.If the foreknowledge results are good, then the determination continues on the search for a good wedding day for the bride and groom.However, if the foreknowledge results are not good, the marriage of the two brides will not take place.

The task
1. Describe in your own words what you've learned about the rural setting of the prediction of fate marriage from the prelude information.
2. A girl of sufficient marriage (a mature woman), has Tuesday Legi weton.The girl's parents looking for a partner to her daughter.If the forecasting used is to use the modulo base 4, the computation is carried out by summing up all the neptu dina and neptu pasaran of bride and groom, then divided by 4.Then, the foreknowledge decision is use Table 8.Furthermore, find weton of a man, who has a good prediction if he is married to the girl.

CONCLUSION
The use of Javanese Primbon in marriage is something unique in predicting the future.We have shown that matchmaking of mates using foreknowledge through Javanese Primbon is attributed to number bases, remainder theorems, modulo, and modulus of congruence in formal mathematics.Hence, the matchmaking of mates using foreknowledge through Javanese Primbon has potential material as a context in mathematics learning, such as the context in making an ethno-mathematical problem.The limitation of this study is needed to be continued for further research on its empirical use in mathematics learning by the topic.

Friday, and the
bride born on Pahing Friday.Then, the foreknowledge of the two brides is determined by calculating the weton of each bride: a. Weton of the bridegroom born on Kliwon Friday means: Friday = 6, and kliwon = and the remainder is 5. b.Weton of the bride born on Pahing Friday, means: Friday = 6, and pahing = 9 and the remainder is 5. b.Weton of the bride born on Pahing Thursday means: Thursday = 8, and pahing = 9 more, two four, ten with one missing, ten."Like calculations from other cultures that use bases, computation in predicting the future of couples based on weton also uses number bases.If we look at Type 1, foreknowledge used base number 9, Type 2 used base number 4, foreknowledge in Type 3 used base number 7, and Type 4 used base number 5.This shows that the computation in predicting the future of couple based on their weton, use different number bases for different types.In other words, Javanese Primbon recognizes more than one base.

Table 4 .
The Part of the Meaning of the Remainder in Type 1

Table 5 .
The Meaning of the Remainder in Type 2

Table 6 .
The Meaning of the Remainder in Type 3 Like the first example in Type 2, the bridegroom is born on Kliwon Friday, and the bride born on Pahing Friday.Kliwon Friday means Friday = 6, and kliwon = 8, and Pahing Friday means Friday = 6, and pahing = 9.Hence, the computation is

Table 7 .
The Meaning of the Remainder in Type 4 Like the first example in Type 2 and Type 3, the bridegroom is born on Kliwon Friday, and the bride is born on Pahing Friday.Kliwon Friday means Friday = 6, and kliwon = 8, and Pahing Friday means Friday = 6, and pahing = 9.Hence, the computation is

Table 8 .
The Meaning of the Remainder in Modulo 4