Understanding The Elements Supporting Ethnomathematics II - Ethnomathematics Reflection

Talk about intuition, everyone has intuition. Every people have intuition, but only few people use it properly. Intuition can grow up or grow dim depends on each personal and the area surround the personal. If surroundings do not support the development of intuition, then the intuition will grow dim or maybe die. Intuition is divided into two different kinds: space and time.

One thing we have to know that mathematics is mathematics, language is language itself. But Wittgenstein said that mathematics is a language. How come? Mathematics is the language of knowledge. Mathematics has structure that used in our daily life. If there is man, then there is language. Language grows because man grows perfectly. Language is used to communicate something: ideas, feelings. Language is the instrument of communication. So does mathematics. Language is used in mathematics. To deliver mathematics concept we need language on it. Indirectly we can say that mathematics is a language to deliver the mathematics concept itself.

Old times ago, people made temples, monument, yupa, and others. Temples tell us about the old stories. What our great-great-grandparents did, what they prayed to, and so on. Sometimes yupa or monuments told us about the old kingdoms, their kings, some wars, or maybe the queen. These archaeological remains are called artifact. For example papyrus. Actually, what is papyrus? Papyrus is thick paper-like material produced from the pitch of the papyrus plant. Old people write something, or may be draw something they saw in a cave, a rock, an animal’s skin, and the last era they write on papyrus. The first papyrus was found in the Nile Delta, Egypt. It was used at Mediterranean, to write something they believed, writing materials to make boats, mattresses, rope, sandals, and so on. Old times there is possibility people write the concept of mathematics in papyrus.

When I was at 2nd grade of elementary school, I had this kind of theater, and the story was about Aji Saka. When I asked my grandparent about Aji Saka, the things my grandparents told me are that Aji Saka came from somewhere in Middle East to the Land of Java to teach people about Islam. Aji Saka can defeat the ‘buta’ or a mythical gigantic demon named Prabu Dewata Cengkar who became a symbol of evil things in this world. Aji Saka helped by his loyal two servants named Dora and Sembada. From that story I get that the character of Javanese letter came from Aji Saka’s era. But from some source I got, Aji Saka came from a village named Medang Kawit, Majethi, Center Java. With his loyal servant, Dora, he went engage in adventure leaving Majethi Island and his other servant, Sembada. Aji Saka left his keris to Sembada and told him not to gave the keris to anyone, ever. Except Aji Saka himself asked for the keris. Sembada accepted; he will look out the keris.

That age, the land of Java was leaded by a king named Prabu Dewata Cengkar. Prabu Dewata Cengkar was a good and wise king, thus the land of Java became prosperous and citizenry lived happy. One day the chef for the king made a soup and accidentally he cut his finger. Prabu Dewata Cengkar ate the soup, and he felt that that soup was the best soup he ever tastes. Prabu Dewata Cengkar asked his regent to ask the chef about the soup. After that, the chef told the king that he accidentally cut his finger. After that moment, Prabu Dewata Cengkar always asked for human meat for his meal. After that moment too, his personality changed. He became cruel, strict, wicked, and sadistic. After quiet time, the land of Java became desolate because the king ate the civilian.

Aji Saka came to that land and offers his own body to be the meal for the king with one condition. Aji Saka asked for land as wide as his turban would expand. Prabu Dewata Cengkar was very happy to hear that, he thought he will have a great meal that day. He did what Aji Saka wanted. He spread out the turban until the south side of Java. Then Prabu Dewata Cengkar drowned in the South Sea and became a white crocodile, another mythical demon in Java. After that, Aji Saka became a king of that land. He delegated his servant, Dora to pick the Keris and his other servant, Sembada. Then Dora walked to pick up his friend, Sembada. After few days, Dora arrived and welcomed by Sembada. Dora asked for the Keris and asked Sembada to move to Aji Saka’s kingdom. But Sembada refused. He remembered Aji Saka’s order to not giving the Keris to anyone but Aji Saka. Dora only wanted the Keris and Sembada to follow Aji Saka’s order. Because both of them were very obedient, they chose to fight each other. But their ability was same, so they both died in war they made themselves.

Aji Saka waited for them for few days. He worried of them. But somehow he found out that his servants were died to prove their loyalty. Then Aji Saka made the Javanese word.

Ha Na Ca Ra Ka

Means “Ana utusan” or “There are messengers”

Da Ta Sa Wa La

Means “Padha kekerengan” or “Both preserve their own argument”

Pa Dha Ja Ya Nya

Means “Padha digdayane” or “Both are strong”

Ma Ga Ba Tha Nga

Means “Padha dadi bathange” or “Both are dead”

In this land of Java there are five days in a week. Starts with Legi, Pahing, Pon, Wage, and Kliwon. Javanese date system was brought by Aji Saka from India. It was actually started at March 14th, 78 A.D. Indian knew it by name Saka calendar. After Islam came to the area of Indonesia, people started to use Hijriyah calendar, But Hijriyah calendar was not as popular as Saka calendar. After that, Sultan Agung Hanyokrokusumo changed the system of Hijriyah calendar. He combinated the system of Hijriyah calendar and the system of Saka calendar.

The components of concept in the world there are two, namely containers and contents. No content without container, and no container without content. For example, the human body is the content. To cover the body, we need container, the clothes. The others examples, body is the container for the personal and the human soul. Like the number "two" had a concept, writing is a form of content.

In ethno mathematics, a theory can be built from the past theories. To built a new theory, we need a method to helped us collect the past theories. The method is named grounded theory. Sometimes ethno mathematics needs other knowledge to solve a problem. One of the knowledge is called ethnography. Ethnography is seeing knowledge from anthropology side.

Interaction is built between two or more people. The dimensions of interaction in a class are individual interaction, group interaction, and whole class interaction. In class, sometimes a teacher has to involve each personal to put something to the front. Sometimes teacher has to divide a whole class into smaller groups and let the pupils make their argumentation, do discussion, and do problem solving. And sometimes teacher has to do the classical way to teach, by involving the whole class is a whole class discussion or maybe by giving sermon to pupils.

From social side, there are two kind of knowledge: subjective and objective.

The beginning of knowledge is awareness. If people aware to every inch of this world then there are millions knowledge can be made. If people aware then knowledge are absorb into their mind easily.

There are two kinds that cannot be explained in mathematics: primitive knowledge and intuition. Primitive knowledge came from something primitive, where people didn’t really know how to make fire, to engage in planting or cultivating, or maybe to speak. Primitive people lived primitively, lived moving from a place to another place and they only can harvest and hunt for their meal. Intuition came from the deepest heart. Mathematics definitely cannot explain it.

Some things can be explained by mathematics. Some things cannot. This is our job to group and keep on doing research to know which one can be explained, which one cannot.