PERAN INTUISI DALAM MATEMATIKA MENURUT IMMANUEL KANT

Concluding Remark

Kant contributes significantly in terms from the philosophy of mathematics, especially for the role of intuition and concept construction mathematics. Immanuel Kant said that mathematics was not developed only with the concept of a posteriori empirical. But the empirical data obtained from sensing experience necessary to explore mathematical concepts that a priori the intuition-based construction of mathematical concepts of space and time. This is what makes mathematics as a science. Because if the mathematics developed just analytic methods will not be generated (constructed) a new concept, and thus will cause the math is just as science fiction. Kant tried to give a solution of extreme conflict between rationalists and empiricists in building the foundation of mathematics.
Kant argues that mathematics is built on pure intuition is intuition of space and time in which mathematical concepts can be constructed synthetically. Pure intuition (Kant, I, 1783) is the foundation of all reasoning and decision mathematics. If not then the reasoning is based on pure intuition is not possible.
Pure mathematics (ibid.), in particular the geometry can be objective reality when it comes to sensing objects. Concepts of geometry are not produced only by pure intuition, but also related to the concept of space in which objects are represented geometry. The concept of space (ibid.) is itself a form of intuition in which the ontological essence of representation can’t be tracked.
Intuition sensing itself is a representation which depends on the existence of the object. So it seems impossible to find such a priori intuition, because intuity a priori not rely on the existence of the object.
1. Intuition in Arithmetic
Kant (Kant, I., 1787) argues that the propositions of arithmetic should be synthetic in order to obtain new concepts. If you rely solely on the analytical method, then it will not be obtained for new concepts. If we call the "1" as the original numbers and only at the mention of it, then we do not obtain a new concept apart from the already mentioned it, and it certainly is
analytic. But if we consider the sum of 2 + 3 = 5. Intuitively 2 and 3 are different concepts and 5 is the concept differently. So 2 + 3 has produced a new concept that 5; and thus it must be synthetic.
2. Intuition in Geometry
Kant argues that the geometry should be based on the concept of pure spatial intuition. Concepts of geometry are not only constructed with pure concepts, but also based on pure intuition so as to produce pure results. For example in proving the 2 pieces of geometry are mutually congruent. Concept used in proving the need to use a synthetic step. Because if you do not use synthetic step that it will produce evidence that is not clear.
3. Intuition in Mathematics Decision
According to Kant, the ability to take a decision to be "innate" and have intrinsic characteristics, structured and systematic. The structures of mathematics decision according structure of mathematics proposition are linguistic expressions. Like the others, the propositions of mathematics connect subject and predicate with a copula. Relations subject, predicate and copula type is what will determine types of decisions.

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Mathematical Thinking Across Multilateral Culture

Kesimpulan Membaca

Bertukar pandangan dan pemikiran tentang matematika adalah hal yang dibutuhkan dalam ilmu pengetahuan, teknologi, pertumbuhan perekonomian dan pengembangan perekonomian anggota APEC. Berdasarkan pada rapat menteri Pendidikan para anggota APEC ke-tiga yang diselenggarakan 29-30 April 2004 di Santiago tentang prioritas dalam aktivitas- jaringan-masa depan untuk tujuan stimulasi pembelajaran dibidang Matematika dan ilmu pengetahuan, maka dibuatlah suatu rancangan kegiatan oleh APEC yang bekerjasama dengan Tsukuba University of Japan dan Khon Kaen University of Thailand brupa kolaborasi studi untuk inovasi belajar mengajar Matematika dari berbagai kultur budaya yang berbeda. Kegiatan ini membahas mengenai ide dan cara berpikir Matematika.
Pemikiran matematika adalah dasar bagi berbagai macam tipe berfikir. Dengan mempelajari matematika siswa dapat belajar tentang logika dan cara berfikir yang rasional. Selanjutnya akan dibahas mengenai beberapa karya dari para pemikir di dunia pendidikan berdasarkan pada berbagai macam konteks dan budaya untuk memberikan pandangan tentang pemikiran matematika.
1. Konteks Orang Australia: Karya Stacey Kaye
Dalam konteks orang Australia, Stacey,K mengungkapkan bahwa guru harus memahami bahwa untuk dapat menyelesaikan masalah dengan matematika dibutukan kemampuan dan kecakapan termasuk diantaranya: memiliki kemampuan matematika yang memadai, berfikir secara umum, pengetahuan tentang strategi heuristik, kepercayaan dan tingkah laku yang baik, kapribadian, dan kemampuan untuk menyampaikan solusi.
2. Konteks Orang Inggris: Karya David Tall
David Tall mengungkapkan sementara guru berusaha meningkatkan prestasi dalam tes di samping itu juga harus mengembangkan realisasi dari prosedur latihan yakni membentuk cara berfikir matematis yang kuat.
3. Konteks Orang Taiwan: Karya Fou Lai Lin
Fou Lai Lin membuktikan bahwa kegiatan mengira atau menerka dalam pemikiran matematika merupakan proses yang dibutuhkan dalam penyelesaian masalah, dan mengembangkan kemampuan membuktikan.
4. Konteks Orang Jepang: Karya Katagiri
Katagiri menegaskan bahwa kemampuan yang paling penting yang dibutuhkan oleh seorang anak untuk bertahan di masa sekarang maupun di masa yang datang bukanlah kemempuan untuk menjalankan tugas dan perintah dengan benar dan cepat tetapi lebih kepada menetukan sendiri apa yang harus mereka lakukan.
5. Konteks Orang Singapura: Karya Yeap Ban Har
Yeap Ban Har menggambarkan bahwa di Singapura, pendidikan mempunyai fungsi ekonomi. Pendidikan mempersiapkan siswa untuk mengembangkan kompetensi yang dibutuhkan untuk menghadapi dunia kerja.
6. Konteks Orang Malaysia: Karya Lim Chap Sam
Lim Chap Sam mempelajari bahwa di dalam konteks orang Malaysia ada 3 komponen utama pemikiran matematika, diantaranya adalah: pengetahuan matematika, kegiatan metal dan perkiraan.
7. Konteks Orang Indonesia: Karya Marsigit
Dalam konteks Indonesia, tujuan pendidikan matematika sekarang ini dan yang masih mendesak adalah untuk membiasakan berfikir matematis dan mewujudkannya dalam tindakan. Hasil pengamatan mengindikasikan bahwa matematika harus diterapkan dalam situasi alami, setiap masalah nyata yang muncul dalam menyelesaikannya diperlukan suatu metode matematis.
Jadi konsep berfikir matematis memiliki banyak makna bagi banyak pemerhati pendidikan matematika karena terkait dengan latar belakang budaya dan tujuan nasional pendidikan negaranya.

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Memanfaatkan Microsoft Word 2007 Sebagai Media Pembelajaran Geometri di SMP

Concluding Remark

In learning process mathematic teachers can use various media to help them. Teachers can select the appropriate media with material that will be studied. Teachers should choose learning media that can facilitate students to learn the material, besides that learning media should make students become attracted and delighted in learning the material. Nowadays, technology advances very rapidly. We can use technology as a media of learning mathematics. One of media we can use is computer. With computers we can access the Microsoft Word 2007 as a media of learning geometry in junior high school.

With Microsoft Office 2007 we can develop Geometry learning in school. Microsoft Office 2007 completed with SmartArt Graphic so user can make many kind of graph. With SmartArt Graphic we also can do animation to shapes and adding kind of text for picture explanation. Expected, media learning geometry by using Microsoft Word 2007 can make grow and improve student’s creativity. By utilizing Microsoft Word 2007 we can also develop the material geometry. We can make many aspects by utilizing the basic geometry of the wake, make tile, create a tangram, make triangles based on the size of the angle, determine the steps to find a formula or a large volume of space built with the help of pictures.

Using Microsoft Word 2007 can do easily because this software available in every new generation computer. It also make student enjoyable learn math. Student can learn geometry independent or in group. It also gives clear vision of geometry shape. And the most important is increasing the student’s achievement. But, first step that we must take is increasing the teacher’s skill to use various facilities that’s served Microsoft Word 2007. In here, the teacher is claimed to have high skill in using Microsoft Word 2007, to make complex geometry shape and also explained it to all of student. So, geometry comes closer to us and useful in our daily life.

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English Assignment (Make an Issue related disaster)

Created by Ambar Sito Jati (10305144042)

What is the main goal of teaching mathematics? The answer is problem solving. In our daily life, there are so many incidents happened, the example is natural disaster. Natural disaster made various problems appear. It is possible to make mathematic models from the problem caused by natural disaster. And may be it can help us to solve the problems.

There are so many mathematical thinking that has relation with problem caused by natural disaster. But in here, I will raise a problem about how we can find the best solution to make a decision related with natural disaster especially about cope the victims of natural disaster.

Cope the victims of natural disaster is important. I have an example problem that may happened in the process cope with the victims of natural disaster.

A foundation will give aid shaped reconstruction unit house for 50 families or more who losses their house caused by tsunami in NAD. The contractor provide two types unit house, there are type A and type B. For each unit house type A is needed 20 pouch cement and 1000 m³ sand. While for each unit house type B is needed 25 pouch cement and 800 m³ sand. The foundation has 1500 pouch cement and 56000 m³ sand. So how many unit house type A and type B are built supposed produced units house at the most?

We can make mathematic model from the case above.

x +y ≥ 50

20x + 25y ≤ 1500

1000x + 800y ≤ 56000

The solution set from model above are (42,8), (60,0), and (0,56). In order to produced units house at the most, the foundation prefer choose unit house type A, because with all the materials was provided will produced 60 units house.

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Beautiful song: Your Love

Ever heard the songs sung Gita Gutawa featuring Delon?
The song is very beautiful to hear, especially if we interpret every word and sentence in the lyrics. To get the song, you can download at 4shared.com or other websites very easily, and free, hehe.
Honestly, my listening skills are not good, so I'm looking for lyrics of the song in topikliriklagu.blogspot.com. Here goes the lyrics:
Every time I close my eyes
And say my prayer at night
I thank God each day for your love
That Gives me wings to fly up high
To reach my dream aim from the sky
You always said
Your head up high
Smile on your face and wish
That you Will always be loved
The stars Will lead you every step you take
Do not you ever be afraid
Believe in you
And I'll be there to guide you Wherever you may go
Thank you for your love, forever

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Pendekatan Matematika Realistik pada Pembelajaran Pecahan Di SMP

By: Dr. Marsigit, M.A.
Reviewed by: Ambar Sito Jati(10305144042)
Concluding Remark

Realistic mathematics more emphasis at construction of the context of real things as initial point for the students to purpose obtain mathematics concept. The real things and objects of around area can be used as context mathematics learning to develop dependability of mathematics by social interaction. So the teachers must to give a chance for the students to construct they are knowledge alone. Realistic approach to mathematics learning fractions in Junior High School have purpose such as contextual problem solving and finding the concept of fraction number from the contextual problem which be found; to understand the concept of fraction number, to explain the connections between concept and to implication the concept of fraction number as flexible, accurate, efficient and exact for problem solving; to use reasoning on the pattern and attitude, to execute of manipulation and to make generalization of fraction number; to communication the concept and the use of fraction number; and also have an attitude to appreciate the use of fraction number in the daily life.

Students should be given opportunities to explore and reflect on alternative concepts of fraction ideas. In addition students are also given the opportunity to acquire new knowledge about fractions by forming number.

It can be concluded, that on the realistic approach to mathematics learning fractions in Junior High School will be successful if the students can discover the characteristics of problem solving fractions. Teachers should act as a facilitator of learning.

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SUPPORTING EVIDENCES AND MONITORING TO DEVELOP SCHOOL-BASED CURRICULUM FOR JUNIOR HIGH SCHOOL MATHEMATICS IN INDONESIA

By : Dr. Marsigit, M. A.
Reviewed by: Ambar Sito Jati (10305144042)
Kesimpulan Membaca
 
Meningkatkan kecerdasan bangsa dan memajukan kesejahteraan umum seperti yang diamanatkan dalam Pembukaan UUD 1945 selalu menjadi perhatian utama Pemerintah Indonesia. Namun sayangnya, menurut hasil penelitian (Herawati Susilo, 2003), prestasi anak-anak Indonesia dalam pelajaran matematika dan ilmu pengetahuan alam masih rendah. Selain itu, kemampuan anak dalam memahami konsep dan proses matematika juga masih rendah. Hal ini ditunjukkan dengan hasil Ujian Nasional yang kurang maksimal. Sebagai tindak lanjut untuk mengatasi permasalahan ini, pemerintah berusaha menekan adanya isu-isu pendidikan dan segera mengimplemantasikan kurikulum baru yaitu Kurikulum Tingkat Satuan Pendidikan (KTSP) yang mulai diterapkan pada tahun 2006/2007. Kebijaksanaan ini tentu berkibat pada aspek kemandirian program pendidikan, pengembangan silabus, peningkatan kompetensi guru, fasilitas pembelajaran, anggaran pendidikan, keterlibatan masyarakat, sistem evaluasi dan jaminan mutu. Dalam pengembangan silabus, standar kompetensi harus terperinci sesuai dengan kompetensi dasar.

Pengembangan kurikulum, khususnya Kurikulum Tingkat Satuan Pendidikan (KTSP) untuk matematika SMP, membutuhkan penelitian yang mendalam dan komprehensif dalam semua aspek yang meliputi: (1) kesempatan belajar matematika bagi semua, (2) kurikulum bukan kumpulan bahan pelajaran akan tetapi seharusnya merupakan refleksi yang koheren dengan kegiatan matematika, (3) pengajaran guru yang sesuai dan komprehensif, (4) pengembangan konsep matematika yang mendalam, (5) penilaian pembelajaran yang dilakukan guru, dan (6) menerapkan berbagai metode pembejalaran yang sesuai. Kurikulum Tingkat Satuan Pendidikan (KTSP) dapat menjadi titik awal bagi guru matematika di Indonesia untuk merefleksikan dan mengubah paradigma mereka tentang mengajar. Mukminan dkk (2002) menguraikan bahwa Kurikulum Tingkat Satuan Pendidikan (KTSP) untuk SMP menekankan pada kompetensi siswa yaitu pada kompetensi kognitif, afektif dan psikomotorik. Dengan hal ini, pemerintah harus mendukung sepenuhnya peran guru untuk mengembangkan keahlian dan kemampuan siswa dengan mengoptimalkan lingkungan sekitar untuk mendukung kegiatan belajar siswa.

Untuk pengawasan akan implementasi Kurikulum Tingkat Satuan Pendidikan (KTSP) dapat dilihat dari segi siswa, guru, dan masyarakat. Hasil dari pengawasan tersebut dijadikan refleksi untuk selalu meningkatkan kemampuan semua aspek yaitu pengembangan kurikulum itu sendiri, guru, kepala sekolah dan pengawas, fasilitas pembelajaran, anggaran pendidikan dan juga sistem pendidikan. Hasil evaluasi pelaksanaan kurikulum baru ini mengajarkan kepada kita bahwa ketika kita menerapkan suatu kurikulum, kita akan kita selalu harus memperbaikinya.

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