Prosedur Penelitain

Prosedur yang digunakan dalam penelitain ini, mengembangkan sebagaimana yang lazim digunakan dalam penelitian dengan menggunakan siklus (cycle). Dalam penelitian tindakan kelas ini terdiri dari tiga siklus, setiap siklus dilaksanakan sesuai dengan perubahan ke arah peningkatan dan perbaikan proses dalam mengajar. Sebelum tahap- tahap dilaksanakan dalam peneltian yang menggunakan siklus- siklus terlebih dahulu dilakukan studi kelayakan sebagai penelitain pendahuluan dengan tujuan untuk meningkatkan perbaikan dalam mengajar. Mengidentifikasi permasalahan dan gagasan yang tetap sesuai dengan masalah dalam pengembangan pembelajaran yang ada di kelas. Dalam kegiatan ini peneliti dan guru secara langsung sudah melibatkan diri untuk aktif dan kreatif dalam rangkaian kegiatan yang ada di sekolah.

Model siklus yang digunakan berbentuk spiral sebagimana dikembangkan oleh kemmis dan Taggart (Kasbolah, 1998/1999: 14) yaitu merupakan momen- momen dalam bentuk spiral yang meliputi : perencanaan (plan), tindakan (act), pengamatan (observe) dan refleksi (reflect). Kemudian pada siklus kedua dan seterusnya jenis kegiatan yang dilakukan peneliti pada dasarnya sama, tetapi ada modifikasi pada tahap perencanaan.

Siklus kegiatan dapat digambarkan sebagai berikut.

Secara operasional tahapan- tahapan kegiatan penelitain dalam setiap siklus dapat dijelaskan sebagi berikut :

1.Tahap Perencanaan

Kegiatan perencanaan diawali dengan merencanakan ide penelitian kemudian ditindak lanjuti dengan observasi pelaksanaan pembelajaran di kelas. Data awal diperoleh dari hasil evaluasi mata pelajran matematika yang sudah terdekomentasikan dalam daftar nilai siswa dan dari hasil pengamatan lansung dalam setiap pembelajaran matematika. Hal ini membantu peneliti dalam menentukan kelmahan dan hambatan siswa dalam belajar matematika yang selanjutnya difokuskan pada strategi penemuan pada geometri yang dijadikan bahan bagi peneliti.

2. Pelaksanaan Tindakan

Pada tahap ini, peneliti melaksankan tindakan sesuai dengan perncanan yagn telah dirumuskan. Dengan alat pengumpul data yang telah disusun, tim observasi mencermati jalannya pembelajaran berlangsung secara wajar. Bertujuan untuk meningkatkan kualitas pembelajaran yang dilaksanakan guru dan peningkataan hasil belajar siswa.

3. Tahap Observasi

Tahap observasi dilakukan peneliti dengan menggunakan pedoman observasi yang telah disiapkan sebelumnya. Observasi merupakan teknik pengumpulan data dalam penelitain tindakan kelas yaitu mengamati segala sesuatu yang berlansung saat proses pembelajaran untuk melakukan refleksi dan revisi terhadap rencana tindakan yang telah dilakukan untuk menyusun rencana berikutnya.

4. Tahap Refleksi

Hasil penemuan pada pelaksanaan kegiatan pembelajaran ditindaklanjuti dengan kegiatan refleksi. Refleksi merupakan kegiatan analitis sintetis, interpretasi dan ekspanasi (penjelasan) terhadap semua informasi yang diperoleh dari pelaksanaan tindakan. Refleksi merupakan bagian yang sangat penting untuk memahami dan mencari makna terhadap proses dan pelaksanaan tindakan sebagai dampak adanya intervensi tindakan yang dilaksanakan.

C. Lokasi dan Subjek Penelitian

Pelaksanan tindakan kelas (PTK) di SDN I Ciseureh Kecamatan Purwakarta Kabupaten Purwakarta, penelitian tindakan ini dilaksanakan untuk memudahkan koordinasi dengan peneliti, guru dan kepala sekolah karena sebagai tempat tugas. Sampel yang diteliti yaitu siswa- siswi kelas V SD Negeri I Ciseureh Purwakarta, pada semester II tahun ajaran 2006- 2007 yang berjumlah 27 siswa, yang terdiri dari 18 orang siswa laki- laki dan 9 orang siswa perempuan.

Dengan dipilihnya sekolah ini untuk penelitain karena dengan beberapa pertimbangn yang diambil yaitu, sebagai berikut :

1. sebagai tempat mengajar, sehingga peneliti dengan guru dan siswa sudah saling mengenal tetapi peneliti tidak lalai dalam melaksanakan tugas dan tidak semata- mata hanya sebagai tempat penelitian.

2. adanya anggapan bahwa pelajran matematika adalah pelajaran yang membosankan, serta dengan rendahnya nilai matematika pada akhir semester satu.

3. Letak sekolah dekat dengan tempat tinggal peneliti yang jarkanya kurang lebih 500 meter, dan merasa tanggung jawab secara moril untuk meningkatkan kualitas pembelajran matematika.

Sebagai subjek peneliti dengan kinerja guru dan aktivitas belajar peserta didik, dalam pembelajran matematika dengan mengugnakan metode penemuan.

Karakteristik dari subjek peneliti adalah sebagai berikut :

1. Letak geografis sekolah sangat starategis tidak jauh dari kota sekitar km jaraknya, juga dekat dengan pemukiman penduduk.

2. Kondisi sosial ekonomi siswa rata- rata menengah ke bawah.

3. Kualifikasi pendidikan guru dari …………………guru kulifikasi pendidikannya SPG, DII, S1, sehingga penelitain ini dapat dilaksanaakn prestasi belajar dengan perolehan nilai UAS nilainya masih rendah.

D. Metode Pengumpulan Data

Untuk megetahui hasil, ketika hasil proses pelaksanaan tindakan dilakukan, maka diguankan instrumen penelitian untuk mengumpulkan data diantaranya:

a. Observasi

Yaitu alat pengumpul data yang digunakan untuk mengamati tingkah laku individu baik sisiwa atau para gurunya selama proses pembelaran berlangsung.

Data yang ingin di jaring melalui lembar observasi adalah data yang berupa perkataan dan aktifitas yaitu komunikasi interaktif antarguru. Kegiatannya menyangkut proses pembelajaran matematika serta temuan- temuan pada saat diskusi kolaboratif dengan guru mitra dan guru teman sejawat setelah pembelajaran.

b. Angket

Pembuatan angket ini bertujuan untuk mengetahui, menjaring data yang telah valid (absah) dan reliable (dapat dipercaya) mengenai tanggapan sisiwa, pendapat guru mitra penelitian, guru teman sejawatdan kepala sekolah

c. Tes Hasil Belajar

Adalah serentetan latihan soal yang digunakan untuk mengukur keterampilan, pegetahuan, sikap, intelegensi, kemampuan atau bakat yang dimiliki oleh individu atau kelompok.

Semoga bermanfaat.

Mathematical Notation

Leonhard Euler, who created and popularized much of the mathematical notation used today

Most of the mathematical notation in use today was not invented until the 16th century.^[38] Before that, mathematics was written out in words, a painstaking process that limited mathematical discovery.^[39] Euler (1707–1783) was responsible for many of the notations in use today. Modern notation makes mathematics much easier for the professional, but beginners often find it daunting. It is extremely compressed: a few symbols contain a great deal of information. Like musical notation, modern mathematical notation has a strict syntax (which to a limited extent varies from author to author and from discipline to discipline) and encodes information that would be difficult to write in any other way.
Mathematical language can be difficult to understand for beginners. Words such as or and only have more precise meanings than in everyday speech. Moreover, words such as open and field have been given specialized mathematical meanings. Technical terms such as homeomorphism and integrable have precise meanings in mathematics. Additionally, shorthand phrases such as iff for "if and only if" belong to mathematical jargon. There is a reason for special notation and technical vocabulary: mathematics requires more precision than everyday speech. Mathematicians refer to this precision of language and logic as "rigor".
Mathematical proof is fundamentally a matter of rigor. Mathematicians want their theorems to follow from axioms by means of systematic reasoning. This is to avoid mistaken "theorems", based on fallible intuitions, of which many instances have occurred in the history of the subject.^[40] The level of rigor expected in mathematics has varied over time: the Greeks expected detailed arguments, but at the time of Isaac Newton the methods employed were less rigorous. Problems inherent in the definitions used by Newton would lead to a resurgence of careful analysis and formal proof in the 19th century. Misunderstanding the rigor is a cause for some of the common misconceptions of mathematics. Today, mathematicians continue to argue among themselves about computer-assisted proofs. Since large computations are hard to verify, such proofs may not be sufficiently rigorous.^[41]
Axioms in traditional thought were "self-evident truths", but that conception is problematic. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (sufficiently powerful) axiomatic system has undecidable formulas; and so a final axiomatization of mathematics is impossible. Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.<sup>[42]

Sumber:http://en.wikipedia.org/wiki/Mathematics#Etymology</sup>

Inspiration, pure and applied mathematics, and aesthetics

Sir Isaac Newton (1643–1727), an inventor of infinitesimal calculus.

Mathematics arises from many different kinds of problems. At first these were found in commerce, land measurement, architecture and later astronomy; today, all sciences suggest problems studied by mathematicians, and many problems arise within mathematics itself. For example, the physicist Richard Feynman invented the path integral formulation of quantum mechanics using a combination of mathematical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature, continues to inspire new mathematics.^[32] Some mathematics is only relevant in the area that inspired it, and is applied to solve further problems in that area. But often mathematics inspired by one area proves useful in many areas, and joins the general stock of mathematical concepts. A distinction is often made between pure mathematics and applied mathematics. However pure mathematics topics often turn out to have applications, e.g. number theory in cryptography. This remarkable fact that even the "purest" mathematics often turns out to have practical applications is what Eugene Wigner has called "the unreasonable effectiveness of mathematics".^[33] As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: there are now hundreds of specialized areas in mathematics and the latest Mathematics Subject Classification runs to 46 pages.^[34] Several areas of applied mathematics have merged with related traditions outside of mathematics and become disciplines in their own right, including statistics, operations research, and computer science.
For those who are mathematically inclined, there is often a definite aesthetic aspect to much of mathematics. Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty. Simplicity and generality are valued. There is beauty in a simple and elegant proof, such as Euclid's proof that there are infinitely many prime numbers, and in an elegant numerical method that speeds calculation, such as the fast Fourier transform. G.H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics. He identified criteria such as significance, unexpectedness, inevitability, and economy as factors that contribute to a mathematical aesthetic.^[35] Mathematicians often strive to find proofs that are particularly elegant, proofs from "The Book" of God according to Paul Erdős.^[36][37] The popularity of recreational mathematics is another sign of the pleasure many find in solving mathematical questions.

Sumber:http://en.wikipedia.org/

Mathematics

Euclid, Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.^[1]

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the abstract study of topics encompassing quantity,^[2] structure,^[3] space,^[2] change,^[4][5] and other properties;^[6] it has no generally accepted definition.^[7][8]
Mathematicians seek out patterns^[9][10] and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. When those mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature.
Through the use of abstraction and logical reasoning, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.^[11]
Galileo Galilei (1564–1642) said, "The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth."^[12] Carl Friedrich Gauss (1777–1855) referred to mathematics as "the Queen of the Sciences."^[13] Benjamin Peirce (1809–1880) called mathematics "the science that draws necessary conclusions."^[14] David Hilbert said of mathematics: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise."^[15] Albert Einstein (1879–1955) stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."^[16]
Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries, which has led to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.<sup>[17]


Sumber:http://en.wikipedia.org/wiki/Mathematics</sup>

History of mathematics

Greek mathematician Pythagoras (c. 570 – c. 495 BC), commonly credited with discovering the Pythagorean theorem.

The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals,^[27] was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members.
In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time – days, seasons, years.^[28] Elementary arithmetic (addition, subtraction, multiplication and division) naturally followed.
Since numeracy pre-dated writing, further steps were needed for recording numbers such as tallies or the knotted strings called quipu used by the Inca to store numerical data.^{[citation needed]} Numeral systems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus.^{[citation needed]}

Mayan numerals

The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time. More complex mathematics did not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy.^[29] The systematic study of mathematics in its own right began with the Ancient Greeks between 600 and 300 BC.^[30]
Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs."<sup>[31]

Sumber: http://en.wikipedia.org/wiki/Mathematics#Etymology</sup>

Kerjasama Pendidikan RI & Kerajaan Inggris

Pada kesempatan Kunjungan Kenegaraan Presiden SBY ke Inggris dan pertemuan beliau dengan Perdana Menteri David Cameron, beberapa dokumen kerjasama pendidikan berikut telah ditandatangani, yang melambangkan penguatan hubungan bilateral kedua negara. Beberapa poin penting yang disepakati antara lain pembentukan program beasiswa antara Dikti Indonesia dengan pemerintah Kerajaan Inggris, promosi studi di Indonesia yang merupakan kerja sama dengan Oxford University, serta memorandum saling pengertian antara beberapa perguruan tinggi terkemuka di Indonesia.
Sebagaimana diberitakan sebelumnya, Universitas Muhammadiyah Surakarta bekerja sama dengan The University of Nottingham dalam "Program Pasca Sarjana dan Doktoral Terpadu dalam Bidang Desain Bahan". Ini adalah salah satu langkah nyata UMS dalam mewujudkan program Go International.
Sementara perguruan tinggi lain yang turut bekerja sama adalah Newcastle University dan Universitas Indonesia dalam "Pembentukan Pusat Pelatihan Dokter Newcastle University-Universitas Indonesia (NUUIDTC) dalam Bidang Obat-obatan, Gigi, Ilmu Biomedis, Ilmu Kehidupan dan Nutrisi", Cranfield University dan Institut Teknologi Bandung dalam "Program Gelar Ganda (Double-Degree) pada Tingkat Pasca Sarjana dalam Bidang Teknik dan Teknologi", Northumbria University dan Universitas Bina Nusantara dalam "3 Program Baru pada Tingkat Sarjana dalam Bidang Desain Interior, Desain Industri dan Desain Media Interaktif", University of Southampton dan Institut Teknologi Sepuluh Nopember dalam "Bekerjasama dalam Bidang Pengajaran dan Penelitian, serta Pengembangan Pertukaran Akademis", serta The Open University dan Universitas Terbuka dalam "Kolaborasi dalam Bidang Penjaminan Kualitas, Pengembangan Kurikulum dan Penelitian Pedagogi".
Penandatanganan dokumen-dokumen kerjasama tersebut sebagai sebuah bentuk pengakuan atas semakin luas dan eratnya kerjasama pendidikan dan keterampilan antara Indonesia dan Kerajaan Inggris. Kerja sama kedepan dalam berbagai bidang seperti berbagi pengalaman terbaik dalam pendidikan kejuruan dan pelatihan, pelatihan guru/kepemimpinan, penjaminan kualitas dan pengembangan kurikulum.
Willetts signs UK-Indonesia agreement
UK-Indonesian partnerships agreed

Sumber :http://www.ums.ac.id/