Konsep Pemikiran Plato Terhadap Matematika

Konsep pemikiran Plato berawal dari pertemuannya dengan para pengkut Pythagoras yang menyebar di segenap koloni Yunani di Sisilia dan Italia bagian selatan. Penemuan Pythagoras tentang hubungan antara angka dan harmoni musik telah membuatnya percaya bahwa angka-angka merupakan kunci memahami alam semesta. Segala sasuatu bisa dijelaskan dengan angka, yang barada dalam suatu realitas abstrak, diluar jangkauan kenyataan sehari-hari.

Teori tersebut berpengaruh amat mendalam pada diri Plato. Ia menjadi percaya bahwa realitas yang sebenarnya itu abstrak. Apa yang dimulai dengan angka dalam filsafat Pythagoras pun berubah menjadi bentuk atau idea-idea murni dalam filsafat Plato. Ciri utama filsafat Plato adalah teori Idea (atau bentuk) yang terus dikembangkannya selama hidup. Artinya, teori Plato yang sampai ke tangan kita sudah dalam berbagai versi, sehingga teori itu dengan sendirinya memberikan materi yang cukup untuk didiskusikan oleh para filsuf di masa-masa sesudahnya.

Bagi plato yang penting adalah tugas akal untuk membedakan tampilan (penampakan) dari realita (kenyataan) yang sebenar-benarnya. Menurutnya ketetapan abadi/permanent, bebas untuk dipahami adalah hanya merupakan karakteristik pernyataan-pernyataan matematika. Plato yakin bahwa terdapat objek-objek yang permanent, tertentu bebas dari pikir yang anda sebut “satu”, “dua”, “tiga” dan sebagainya. Bagi Plato Matematika bukanlah idealisasi aspek-aspek tertentu yang bersifat empiris akan tetapi sebagai deskripsi dari bagian realitanya.

Plato memiliki konsep sendiri bahwa matematika merupakan bayangan cermin struktur realitas yang sebenarnya. Hal ini dapat dicontohkan dari cara kita memandang sebuah lingkaran. Setiap kita menggambarkan lingkaran, kadang lingkaran tersebut berbentuk lonjong dan kita menganggap lingkaran tersebut tidak baik. Untuk menilai sesuatu pasti kita mempunyai dasar-dasar penilaian. Kita dapat menentukan dan menilai mana lingkaran yang yang baik dan tidak baik. Dan kadang kita meniai sebuah lingkaran itu sudah sempurna. Padahal seberapa teliti kita menggambar lingkaran dan ketepatan alat yang kita pakai pasti akan ada penyimpangan dari gambar lingkaran yang sempurna. Plato menyebut sesuatu yang sempurna sebagai forma (forms), dan dunia nonragawi yang mengandungnya dia disebut dunia forma (world of forms) atau dunia Idea.

Pemikiran Plato telah banyak menginspirasi para filsuf-filsuf lainnya untuk mengembangkan pemikiran-pemikirannya. Pemikiran Plato juga menyiratkan pesan moral dan religious, bahwa sesuatu yang sempurna hanya milik Tuhan. Walaupun ada yang setuju dan tidak setuju dengan pemikiran Plato, menurut saya Plato tetaplah filsuf yang sangat luar biasa!

Referensi :
http://pidisme.multiply.com/journal/item/3/Realita_Sejati_dalam_Dunia_Plato
http://naythea.multiply.com/journal/item/29/Antara_Matematika_dan_Filsafat

Alfian Tyas Kurniawan
07301244016
Pend.Mat NR C 07

Konsep Matematika Dienes

Zoltan P. Dienes adalah seorang matematikawan yang berpendapat bahwa pada dasarnya matematika dapat dianggap sebagai studi tentang struktur, memisah-misahkan hubungan-hubungan diantara struktur-struktur dan mengkatagorikan hubungan-hubungan di antara struktur-struktur. Dienes mengemukakan bahwa tiap-tiap konsep atau prinsip dalam matematika yang disajikan dalam bentuk yang konkret akan dapat dipahami dengan baik. Ini mengandung arti bahwa benda-benda atau obyek-obyek dalam bentuk permainan akan sangat berperan bila dimanipulasi dengan baik dalam pengajaran matematika.
Dienes berpendapat bahwa konsep-konsep matematika akan berhasil jika melalui beberapa tahap, antara lain :
1. Permainan Bebas (Free Play)
Dalam tahap ini anak didik diberikan kebebasan untuk bermain. Anak didik tidak perlu diarahkan dan dikonsep. Sebagai contoh anak didik diberikan permainan mengelompokkan kotak sesuai dengan warnanya. Dari kegiatan ini anak didik mulai dikenalkan dengan konsep warna dan tebal tipis suatu benda.

2. Permainan yang Menggunakan Aturan (Games)
Setelah dikenalkan dengan berbagai bentuk benda, anak didik diminta untuk mengelompokkan benda-benda tersebut sesuai bentuknya atau ketebalannya. Anak-anak akan mulai mengenal suatu konsep bentuk benda dan akan mulai berpikir serta menolak bentuk benda yang tidak sesuai atau sama.

3. Permainan Kesamaan Sifat (Searching for communalities)
Tanpa mengubah keabstrakan benda, anak didik diminta untuk mencari sesuatu yang sama dari benda tersebut. Dari kegiatan ini anak didik dapat mengenal dengan sendiri konsep kesamaan sifat dari suatu benda.

4. Permainan Representasi (Representation)
Merupakan tahap pengambilan sifat dari beberapa situasi yang sejenis. Para anak didik menentukan representasi dari konsep-konsep tertentu. Setelah mereka berhasil menyimpulkan kesamaan sifat yang terdapat dalam situasi-situasi yang dihadapinya itu. Representasi yang diperoleh ini bersifat abstrak, Dengan demikian telah mengarah pada pengertian struktur matematika yang sifatnya abstrak yang terdapat dalam konsep yang sedang dipelajari. Contoh kegiatan anak untuk menemukan banyaknya diagonal poligon (misal segi dua puluh tiga) dengan pendekatan induktif seperti berikut ini.

5. Permainan dengan Simbolisasi (Symbolization)
Merupakan tahap merumuskan konsep-konsep yang dipelajari dengan simbol matematika atau perumusan verbal. Dari kegiatan menghitung banyaknya diagonal poligon, anak didik diminta membuat rumus jumlah diagonal poligon dari pola dan pengalaman yang didapatkan.

6. Permainan dengan Formalisasi (Formalization)
Merupakan tahap akhir pembelajarandan anak didik diharapkan mampu membuktikan teorema dan aksioma secara induktif.

Dienes menyatakan bahwa proses pemahaman (abstracton) berlangsung selama belajar. Untuk pengajaran konsep matematika yang lebih sulit perlu dikembangkan materi matematika secara kongkret agar konsep matematika dapat dipahami dengan tepat. Dienes berpendapat bahwa materi harus dinyatakan dalam berbagai penyajian (multiple embodiment), sehingga anak-anak dapat bermain dengan bermacam-macam material yang dapat mengembangkan minat anak didik. Berbagai penyajian materi (multiple embodinent) dapat mempermudah proses pengklasifikasian abstraksi konsep.

Konsep matematika yang disampaikan oleh Dienes merupakan sesuatu yang baru dan dapat diadopsi dalam pembelajaran matematika di Indonesia. Konsep tersebut mempermudah dalam proses pembelajaran matematika yang bersifat abstrak dan sulit untuk dipelajari. Selain itu konsep Dienes juga membuat belajar matematika menjadi lebih menarik dan menyenangkan. Sehingga anak didik tidak lagi takut dan alergi terhadap matematika. Dan matematika dapat lebih mudah diterima oleh semua kalangan.

Referensi :
http://ikanoradhany.wordpress.com/
www.google.com

Alfian Tyas Kurniawan
07301244016
Pend.Mat.NR C 07

Konsep Matematika Al Khawarizmi Terhadap Istilah Bilangan

Pada suatu kesempatan saya bertemu dengan adik sepupu saya, Raihan, yang masih duduk di bangku taman kanak-kanak. Kemudian saya tertarik untuk mengetahui kemampuan matematikanya. Saya ambil secarik kertas dan menuliskan beberapa soal penjumlahan dan pengurangan. Dengan mudah Raihan dapat menjawab soal-soal tersebut dan menuliskan jawabannya di kertas. Rasa penasaran saya kemudian muncul apakah dia bisa mengerjakan soal-soal perkalian. Kemudian saya menuliskan soal perkalian : 6 X 7. 3 X 9, dan 5 X 3. Pada dua soal pertama ternyata dia tidak kesulitan untuk menjawabnya. Tetapi pada soal ketiga dia bertanya kepada saya, 15 itu yang ditulis angka 1 atau angka 5 dulu. Saya sungguh terkejut dengan hal tersebut, begitu lancar dia menjawab soal-soal penjumlahan, pengurangan, dan perkalian. Tetapi satu keganjilan ternyata muncul ketika dia kesulitan menuliskan angka 15.

Hal tersebut kemungkinan dikarenakan penyebutan istilah bilangan yang sering dipakai. Anak-anak tidak akan sulit ketika dia disuruh untuk menulis angka 46 (empat enam), karena mereka dapat berpikir setelah angka 4 pasti angka 6. Tetapi ketika mereka disuruh untuk menuliskan angka 11, 12, 13, 14, 15, 16, 17, 18, 19, mereka akan kesulitan. Sebagai contoh apa yang terjadi dengan adik sepupu saya ketika kesulitan menuliskan angka 15. Hal ini dikarenakan peta konsep pemikiran mereka sesuaikan dengan penyebutan istilah bilangan tersebut ( lima belas ). Dia akan kebingungan angka mana yang harus ditulis terlebih dahulu, apakah angka 1 atau angka 5.

Kesulitan ini mungkin akan dipermudah dengan adanya konsep matematika Al Khawarizmi tentang istilah bilangan. Di bawah ini contoh konsep Al Khawarizmi tersebut :
11 bukan sebelas tetapi sepuluh satu
12 bukan dua belas tetapi sepuluh dua
13 bukan tiga belas tetapi sepuluh tiga
14 bukan empat belas tetapi sepuluh empat
dan seterusnya.

Dengan cara di atas, kemungkinan anak-anak akan lebih mudah menguasai matematika. Hal tersebut memang sangat sederhana, tetapi dampaknya akan luar biasa dalam proses belajar matematika anak-anak. Anak-anak akan lebih mudah menuliskan angka belasan. Jadi tidak ada salahnya jika mengenalkan cara tersebut disamping tetap mengajarkan cara yang lama. Semoga hal ini dapat dijadikan wacana bagi pemerintah dan pihak terkait demi kemajuan pendidikan di Indonesia
.
Referensi :
http://apiqquantum.wordpress.com/category/matematika-populer/page/2/
www.wikipedia.com
www.google.com

Alfian Tyas Kurniawan
07301244016
Pend.Mat.NR C 07

Psychological Analysis of Junior High School Student

This day, Friday, 2 January 2009, one day after new year, because holiday, I visited my grandmother and grandfather at Purworejo. In here, I meet with my nephew, Syahida, she had a holiday also. She was first grade in Junior High School. When I chat with her, I remember with my Psychology of Mathematic Education assignment about Psychological Analysis with Junior High School student. Spontantly, I put a paper and pen, I make mathematic problem:
There are a scout group with 18 personal. In one moment, 11 person is assigned to bring stick, 8 person bring ropes, and 5 person do not bring both of them. How many person that bring both of them?

I give this problem to her. Initially, she was only look into the problem. I gave a moment to think and finish the problem. After a few moments, I am only seeing him read that problem repeatedly. Then I ask to her, why she was only read that problem repetedly. she answer that she confuse with the purpose of that problem. Later, I ask again to her why she didn’t ask to me. She ask that she was shy with me.

From this occurrence, I get two conclusion, that is :
• The student still confuse with story problem. They didn’t know the purpose of this problem. It is because the student didn’t usual with story problem. Because in story problem, the student must know the purpose of the problem then finishing it.
• Although with the close people, like cousin, for study problem, the student still shy to ask. This matter can be caused by the average student do not want to know about their problem, they still ashamed and closed. In here need aid from closest people to ask more often again.

Alfian Tyas Kurniawan
07301244016
Pend.Mat. NR C

Learning Motivation

Everyone must be have a expectation and dream. to make it come true, someone need the hard effort and never give up spirit. At the behind of the expectation and dream there are a spirit which is being the dream and expectation background called motivation. There are some definition of motivation :
• according to Mc. Donald, motivation is energi change in the self of someone marked with feeling appearance and preceding with comments to existence of target.
• motivation is the overall of locomotion in the self of student,generating activity of learn,which guarantee the continuity of activity learn ( Sardiman, 2006:75)

From definition that told by Mc. This Donald, contain three element / fundamental characteristic in that motivation, namely motivation be first the happening of energi change, marked with existence of feeling, and stimulated caused by target. While according to Sardiman, learn motivation represent the psychical factor which have the non-intellectual character . A student which have high intelligence can fail because less the existence of motivation in learning.

Someone must be have different motivation with others. The factor that differentiating motivation of someone are :
• Physiological difference (physiological needs), like feeling peckish, thirsty, and sexual ambition
• Security difference (safety needs), as mentally, physical, and intellectual
• Affection difference (love needs) accepted
• Selfregard difference (esteem self needs). Example : the presstige have luxuriant house or car, position, etc
• Self actualization difference, available of opportunity to someone to develop potency which there are in theirself so that turn into ability of reality

There are 2 factor that can mke someone motivate to learn, that is:
• First, learn motivation come from internal factor. This motivation is formed because awareness of theirself of understanding what a important learn to develop theirself and stock for endure their life
• Second, learn motivation from external factor, that is can be the form of excitement from others, or vinicity environment that able to influence psychologically to relevant persons.

One of the factor from within student self that determining succeed or not the student in teaching learning process is motivation to learn. Motivation have important role in teaching learning process for student and teacher. For teacher, to know motivation to learn from student very needed to utilize to protect and improve the learning spirit of student. For student, the learning motivation can grow up the spirit of learning so that student shoved to learning.

Student do learn activity with pleasure because shoved by motivation. To evoke the motivation it is required aid of others. In here role of people around student to give motivation and congeniality to student. When at home, the parents give congeniality for the importance of education to the future of student. When student get bad mark, the parents don't give penalization to student, however give spirit to more harder to learn. With that, the student do not feel brought to corner and do not break student motivation. When in school, the teacher consort the student in learning. Teacher have to be more diligent again enquire to student concerning difficultys learn. Any result of which is got by student, teacher have to give support to student to harder learn.

From here we earn to conclude that someone motivation do not only coming from within someone self but coming from outside also. for that required the balance relation between all aspect outside self and in self. So that someone motivate can awake and even can increase along time.

Referensi :
http://www.anneahira.com/motivasi/index.htm
http://www.bruderfic.or.id/h-129/peran-guru-dalam-membangkitkan-motivasi-belajar-siswa.html

Alfian Tyas Kurniawan
07301244016
Pend.Mat.NR C

My Psychology Experience

I live in a family which is very hold high a manner and ethics. Since I was child I inculcated by courtesy values and moral. My parents always defin good things and very prohibit negative things. My family is stringent in the case of manner and religion. Since I was child I must to listen willingness of my parents. Its effect to my willingness is bridled and I grow to become someone who is prude, my mentality also less forged. This matter is happened until I am in junior high school.

When I was in senior high school, I made bold to follow organization in school. In here my mentality were forged and I start dare to have socialization with others. I start to talk ahead of many people. This is very different with personality of me before. My fear little by little start to lose. That fear turn into bravery. My confidence is sprout. And it is very useful for myself till nowadays.

My confidence must to improve day to day. I do it by always talking and asking enquire when presentation in class. I hope that thing earn to become my stock when I teach later. A teacher claimed must to have to steel mentality and high comitment. It must be learned continously and deepen with me. So that I earn to become good teacher later. It is of course not easy to do and require many experiences. From my experience I earn to conclude that the confidence is very important and will become our stock further.


Alfian Tyas Kurniawan
07301244016
Pend.Mat. NR C

ACTIVITY REPORT AND MY RESULT IN SEARCHING, COLLECTING, STUDYING, ANALYZING, DISCUSING MATHEMATICS HISTORY DURING THE TIME

1. Activity
At first time I'm join university lecture I'm interest with mathematics history subject. In my opinion history interesting to be studied, moreover relate to mathematics. When finding of theorems, how to find it, who is the inventor figure. It's my reason want to know more and understand what mathematics history is.

In Junior High School, first mathematician that I know is Pythagoras. It’s because of in Junior High School teach how to find hypotenuse of right triangle if the other side are known. And his theorem was used in here. It’s the begin I know mathematic history.

In Senior High School, my knowledge about history mathematic be promoted. I know more the mathematicians, like Pascal, Aristoteles, Algebra, etc. Although I know them in other subject not in mathematics. In that time, I’m very amazed with them because in all limitation they can discover new things that amazing at this time. I can’t imaging how to expand their thinking and realize it with their experiment.

In both time, I’m only limited to know the formula and the mathematician who discover it. I’m only know how to use formula, I don’t know how to prove it.

In college, I meet with mathematic history subject. I feel it’s very interesting, in there I can know the prove of the mathematics theorems. At this time, my lecturer use group presentation in the class. So that the class let to make the group and discuss the problem sets. One group give one discussion material and must present it in the front of class.

From the presentations, I know more about mathematics history. And my admiration with the mathematicians more over. I know how they can discover the theorems and the prove of it. And I know the growth of mathematic history from the past to this time. They do wonderful things that very rare people do at this time, it’s very amazing!

2. Result
The profit that I get from studying mathematic history is when I must make the paper. In here, I must have concept, look for reference, and arrange the paper. At first, I feel it’s very difficult and tiring. But at least I know the benefit from it and enjoyed it. My lecturer always teach me how to make good paper, so, there no reason for me can’t make the paper.

With Mr.Marsigit, my mathematic history lecturer, mathematic history class always interesting. There are new things that I know every meeting. Not always the reference from the book, but it can be from encyclopaedia software from computer. It’s really outside idea of me, what possible only have directive to books and articles. In this software, not only past history but also the history until 2007. How to discover it, what is the discovery, who is the discoverer, all of it avalaible in this software. It’s very amazing and facilitating for me.

Now, I can answer question one who enquire about mathematics history, although only limited to ability of me. A lot of things which I can study from mathematic history, like philosophy, spirit, intuition of mathematics figure, giving my spirit to study mathematics.

3. CONCLUSION
Mathematic history is the interesting lesson for me. A lot of things that can be studied in mathematic history. How to we can recalling and say thanks if we don’t know who mathematician is. We not only use the formula and theorems, but also we can prove it and know the forming of it. So, we can recalling mathematics and mathematicians which have meritorious.

My ability increasing with studying mathematic history. I learn how to make paper from mathematic history. Mathematic history have open my mind, that source of science not only from books but also can be from the other media. I’m really grateful that my chance to studying mathematic history. More over ridde that I don’t know. More question which not answered yet. And I can know all of it with continue to learn and curious.