Refleksi Ethnomathematics - The Reflection of Learning Mathematics

Ethnomathematics was one of the courses which teach us about how to understand mathematics from different sides. Especially the way we see mathematics from our culture. Indonesia is one of the countries with the richest culture. This makes us need to choose the culture we use to see the mathematics. Since I am a Javanese, then I use to see mathematics in Javanese way. Very traditional maybe, but that day Mr. Marsigit did question-answer session again. But this time he made me realize that the traditional way sometimes not good or not good enough to deliver the content of mathematics.

The first question came from Brigitta Dini Laksitasari who asked Mr. Marsigit about ethno mathematics in abstract mathematics and how to apply it.

The relationship between two humans has a dimension. Every relation is on its own phase. For example is the dimension of the relation between parents and children, and between teachers and their pupils. Even for food, it has dimension. First was the simplest material, water. We can divide water into some classes; maybe the water is (berasal dari sumur, atau air hasil sulingan). Then we go higher to (bubur) then even higher, food. So does the education itself, it has dimension. Ethnomathematics came from the culture of a nation. Behind the history, every history, there was a mathematics used on a nation. Mesopotanian, Babylonian, Egypt; they had their own history, and also their own mathematics on their culture, which was not named mathematics yet. But the culture was the inspiration for people so they knew what mathematics is. From these cultures, it can be found the formal mathematics, which is used in pure mathematics. The pure mathematics is the abstract one. This mathematics is used in college, and this mathematics is out of the culture. Pure mathematics is nothing to do with ethno mathematics.

Mathematics is not an art. Pure mathematics for exactly has nothing to do with concrete items. The formal mathematics, which is the pure one, is built from the agreement among mathematics specialist. Except the definition comes from the decision of us. From our own decision we made axioms, after some research and test the axiom can be a theorem.

Ethnomathematics is quite dangerous, if ethno mathematics face the children. For sure children don’t really understand what mathematics is. Even children don’t really understand or admit that mathematics is beautiful. The one who knows that mathematics is beautiful is only us. Teacher cannot force the pupils to admit that mathematics is beautiful or mathematics is needed until the pupils admit it their selves.

Pure mathematics came from the researcher in mathematics. Mathematicians are free to use any method, any science that will use on their research. The researcher has no connection with mathematics education. It has no problem to make new research in mathematics.

The method we used is different to each problem. Even for a problem we use several methods. For example someone wants to jump down from outer space to the center of the Earth. He can do this experiment by using different methods for each section or each part. From the outer space we use the rocket. By moving slowly and carefully, the rocket is changed become a capsule. It has to move very carefully so there is no collision among the molecules from the capsule and the atmosphere. Does the capsule want to land on a field or a sea? If the capsule lands on a field then the astronauts will use parachutes, and landing slowly to the Earth. If the capsule lands on a sea then the astronaut will use buoys which are open when touch the surface of the sea. Then the effort to access the center of the Earth is just by using different method. We cannot use the parachute or a buoy to access the center of the Earth. If we use the same method with what we use in outer space then the center of the Earth cannot be accessed. The key is using the appropriate method on a condition. In our daily life, for example by using the appropriate words on the conditions given. We cannot use the words we use to talk to our friend to our parents, or maybe our elder.

Education itself is flexible, dynamic, and creative. Education is using method and intuition. If people learn something with distressed, disappointed, and anger, then people will lose their intuitions. If people do learning process with distress and afraid to the teacher, they will lose their intuitions.

Learning problem came from the elder. The problem of the children came from their parents. The problem of the pupils came from their teachers. The problem of the little sister or little brother came from their older sister or older brother. The problem of the citizen came from their government.

So the conclusion is that ethno mathematics is not effective for senior high school’s students. The material of the mathematics for senior high school is abstract, so the ethno mathematics cannot be used on learning process. For knowing the relevance between ethno mathematics and mathematics in senior high school, we need the research between them.

Still the question from Brigitta Dini Laksitasari, about the advantages and disadvantages of learning mathematics using ethno mathematics. But first we have to know that the Minister of Education doesn’t even know what ethno mathematics is. So how the Minister cans implement the material of ethno mathematics in Indonesian education system? Logically, people want to use the innovative learning process, which is centered on the students. The students are the actor of our education system. The teacher has to develop the method of learning and the sources of learning. The curriculum of Indonesia still stressed on The Final Exam, it doesn’t look at the process of learning.

The next question came from Erni Anitasari about how to implement ethno mathematics to the students. Still the normative question. The next question came from Gamarina Isti Ratnasari. Does the teacher can force the manner of study of each student? That is the arrogance of the teacher to force the way of study of each students.

The relationship between the elder and the younger has a dimension. The worst dimension came from the brutality of a mother who killed her own child. The best dimension came from the parents who pray for the kids, the parents who would carry the kids, giving what the kids need, like food, home, clothes, love, and education. It is the arrogance of elder to force something to the younger people like everyone was like the elder. Whereas the younger is different to each other, they have their own characteristics. Just like the teacher cannot force and control the way the pupils study. Teacher only can facilitate the students to study by giving the sources and the material what they need. The teacher who did or said something vulgar will get the same type of students, who did or said something vulgar too. To manage study process is to be a dynamic person, because the way we learn something is always different to other way we had already did.

The next question came from Gamarina Isti Ratnasari, how to manage studets who has different way to learn something? There is no disadvantages to have a different students. One thing we have to understand, from 40 pupils in a class, there are 40 different ways of learning process of pupils. The teacher cannot possibly fullfil her/his students needs. If a student learns a material at 10 pm, the other student learns a material at 2 am, then does the teacher has to complete the request to have a class at 10 pm or 2 am? The way they learn something is helped by a technology called by internet.

The next question came from Aisyah Purnama Dewi, does the formal education has something to do with the quality of a personal? We can simplify the question become: do we need the formal education?

This is the good side of mathematical thinking, and for general: thinking. The travel of idea and thinking is amazing, since our mind can think about the universe even the afterlife, but the technology cannot reach the whole universe yet.

In this globalization era, it’s needed to have a formal education. To be admitted in this socialization, the formal education is needed. Although professors or teachers give the lessons to be learned by the students. In this globalization era formal education is needed not only as a source of formal learning, but also as a marker of human social life.

Education should liberate students' thinking. In such education, learning that the teacher must be innovative. In the learning process there is no arrogance of teachers to students. Teachers continue to dodge when the student asked. For many teachers avoid arrogant and vulgar, should be held for the training of teachers in order to develop innovative learning and to keep an open mind.

The components of each material 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. Formal education is a place for every human thought. How does one acknowledge you if you have no formal training? As the list of attendees at the lecture is a sign that education is being implemented formal education. 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.

Necessary and sufficient conditions are best behavior and the behavior of worship is the container. To perform worship to God, we also need a container. We cannot possibly perform Isha at Duha. We cannot possibly carry the current Ramadan fasting in the month of Shawwal.

The next question came from Medina Rendani Sabana, it was about the best learning method for high school students. Nothing is right in this world. Something right is relative, because the right has a different definition for each person. For example, sharp. The sharpness of the blade is only in the mind. The knife is not sharp as a knife edge is a molecule. End of the molecule is an electron, which is moving in a circle.

There’s no best way to educate. But according to religion, the best way is to educate people in each religion. Appropriate learning is an innovative teaching, with different methods, different sources, and various interactions. The method is an assortment of discussion, reflection, presentations, lectures, do the problems, case studies, and so forth. Learning resources can be obtained from the library, books, journals, and open references online. As for the interaction of a variety is to learn individually, in groups, and a sermon by the teacher.

The next question is about the combination between mathematics and language. One thing we have to know that mathematics is mathematics, language is language itself. Speech quality can be improved. For example, when we are making coffee for our fathers, we would say, "Dad, I make coffee latte." Then Dad would know that we made ​​a drink from a mixture of coffee, milk, water, and sugar. If we say, "Dad, me to make drinks from the chemical reaction of coffee, milk, water, and sugar." then Dad will be confused, maybe a little frightened by our words. If we experimented with cooking coffee, milk, sugar and water to boil in a kettle and we provide results on the dad, and we said,”Dad, I made a mixture of reaction coffee, milk, sugar, and water in the kettle to boil and the kettle get mixed. The coffee contains iron so that dad always healthy and smart." Dad will get scared. And only certain substances can dissolve in water directly.

The stupid way to make a coffee latte is to combine the way to make coffee latte with making the fusion of energy from coffee, milk, sugar, and water in a kettle. The same thing also happened on the language and mathematics. They cannot put together. Given that mathematics is a language, we do not need to collaborate on language and mathematics. Mathematics is a language game. As we know that limestone is a rock.

Curriculum of 2013 is very tragic because the curriculum was not handled by experts and skilled people are unable to manage this curriculum in 2013. Should people who manage the curriculum in 2013 asked education experts.

The last question came from Valeria Kartikaningtyas, how to respond to curriculum change in 2013? It seems there is no difference between the KTSP curriculum and the curriculum in 2013. Teachers are required to remain innovative in learning activities. Let the students develop according to his ability. Teachers should be glad if an advanced student is smarter than the teacher. In traditional teaching, there is only material transfer from teacher to student. Pupils are not given the opportunity to argue in public. In an innovative learning process, students compared with seed plants. Water and fertilizer is knowledge. Prior to the interaction between teacher and student, the seeds do not have roots and even leaves. At the initial meeting of the seed, grow roots. Until one day the seeds turn into plants that can produce fruits useful knowledge.