PENGEMBANGAN KOMPETENSI GURU MATEMATIKA SMP RSBI MELALUI LESSON STUDY

By : Dr. Marsigit, M.A., Dr. Hartono, Sahid, M.Sc , Aryadi Wijaya,  M.Sc.

Reviewed by Yustia Rahmawati (p.matswa 09 / 09301244005)

The main objective of this research is to improve the competence of teachers junior high school mathematics RSBI through Lesson Study. More specifically, this study aims to describe the work done in improving the competence pedagogical, professional and social development in middle school mathematics teachers RSBI through Lesson Study. As for Junior High School math teacher I Wates, who successfully developed competencies emphasis on the application method of discussion on the realistic approach to mathematics education (RME) to enhance students' mathematical thinking competencies methods class VIII.

Education has a very important role in the improvement process quality of human resources. Therefore, education is expected to be be one vehicle to prepare the nation's generation, so the birth human resources that are reliable and have the ability to deal dynamic development of science and technology today are fast, precise and effective. Mathematics learning objectives, namely: 
1. Train the way of thinking and reasoning in drawing conclusions, for example through investigation activities, exploration, experimentation, showing similarities, differences, consistent and inconsistencies. 
2. Develop a creative activity involving imagination, intuition, and discovery by developing divergent thinking, original, curiosity, make predictions and allegations, and to experiment. 
3. Develop problem-solving capabilities. 
4. Develop the ability convey information or communicate ideas, among others, through verbal conversations, notes, charts, maps, and diagrams 
(Balitbang Depdiknas, 2003: 6).

So, Lesson Study activities are held at large running smoothly, but due to the eruption of Mount Merapi, then there are adjustments and The scheduled repair activities. Lesson Study activities developed capable of overarching activities student research by developing an instrument of reference was selected. Teacher Competencies developed include: 1. Competence to developed realistic approach to mathematics, 2. Developing Mathematical Competence Thingking and 3. Competence developed a method of discussion, between teachers with pupils and between pupils and students, problem-solving methods (Problem solving) and the method of discovery (investigation). Teacher competence in the field of mathematical thinking developed attitude, include: trying to ask, trying to understand a mathematical problem, try find a mathematical problem, trying to solve mathematical problems, sought to link mathematics with each other, trying to using data to solve the problem, try to record & communicate the problem-solving activities, trying to arrange & Arrange the objects of mathematics. 

Competence of teachers in the development of problem solving activities that successfully developed include: making math relevant to / be able to explore mathematics of everyday life - the day, able to use mathematics to solve everyday problems, capable of using various learning resources, the idea / problem-solving ideas are pure or derived from own experience, able to solve mathematical problems or issues, and translate the mathematical problem.  Competence in the development of successful methods of discussion developed include: understanding and infer other people's opinions, ideas, the idea is original, free and contain initiatives, the ability to discuss which is supported by the confidence, language skills and relationships. A good personal, able to solve mathematical problems, and discussions to all directions (between students and students with a teacher). Student activities related to teacher competence is examined and the analysis with separately by the student for the purposes of writing Thesis.
  

Pembudayaan Matematika di Sekolah untuk Mencapai Keunggulan Bangsa

By : Dr. Marsigit, M.A.

Reviewed by Yustia Rahmawati (p.matswa 09 / 09301244005)

          Materially, mathematics can be either concrete objects, pictures or models of cubes, colorful emblem or large numbers of small, square-shaped pond, pyramid-shaped roofs, the pyramids in Egypt, easel-shaped roof of a right triangle, wheel-shaped circle, and so on. Formally, the mathematics may take the form of pure mathematics, mathematical axiomatic, formal mathematics or mathematics deductively defined.

          Civilize mathematics in aspects of the school have an understanding of the nature of mathematics, the nature of mathematics school, the nature of mathematics education, the nature of the mathematics, nature study mathematics, the nature of mathematics teaching and learning process, the nature of mathematics civilizing the school. In general, whatever we are talking about, is always associated with 2 (two) things, the question is: what object and what method? Mathematics, mathematics education,learning math, etc, have the meaning contained in the object. Explicitly civilizing mathematics based on: (1) knowledge of mathematics in various dimensions, which include the nature, justification and occurrence, (2) mathematical objects at various dimensions which include the nature and origin, (3) the use of formal mathematics include its effectiveness in science, technology and other sciences, and (4) practices mathematics in a variety of dimensions more generally, including the activities of the mathematicians or mathematics activities from elementary school students.

          Various Views About Math and How Learn

          Acknowledged that the content and formal mathematical methods, because in principle, make mathematics as abstract, general, formal, objective, rational, and theoretical. This is the essence science and mathematics. With this approach the absolutist building, Formal mathematics is regarded as neutral and value free (Shirley, 1986). The things bound with the social implications and the values ​​attached to them, explicitly, the removal. The unwavering absolutist stance in looking at it objectively neutrality of formal mathematics. New mathematical knowledge on the scope social, are objective and thus new knowledge on the scope of individual will is subjective. Thus, social interactions in learning mathematics became very important to bring knowledge of mathematics to the subjective knowledge objectives. It will thus be easily understood and implemented if teachers concerned also understand the assumptions referred to earlier.

          Cultivating Learning Mathematics Through Communication Mathematics

          Hartman (1942) outlined that anything about the object of thought, including mathematics, always have value includes 4 (four) things: value due to its meaning, value due to purpose or benefit, because the value of the function and value due to its uniqueness. In order to an attempt is made to civilize mathematics at school, then we should use material dimensions of mathematics or mathematics on the dimensions of the transition to formal mathematics.

          So To be able to cultivate an understanding of the meaning of mathematics is required mathematics in various dimensions. Dimensional mathematical meaning can be seen from the side dimensional mathematical objects to concrete objects and mathematical dimensions to object mind. Mathematical communication includes communication materials, formal communication, normative communication and spiritual communication. In relation to learning math then we are more suitable to define mathematics as the mathematics school, but for college-level mathematics we define as formal or axiomatic mathematics. Acculturation of mathematics can contribute to nation of excellence through innovation pembelajran conducted on a continuous mathematical and again. In relation to gain superiority nation then we can think mathematics, mathematics learning and mathematics education at various hierarchy level or the level of intrinsic, extrinsic or systemic. 

LESSON STUDY ON MATHEMATICAL THINKING: Developing Mathematical Methods in Learning the Total Area of a Right Circular Cylinder and Sphere as well as the Volume of a Right Circular Cone of the Indonesian 8th Grade Students

By : Marsigit, Mathilda Susanti, Elly Arliani.

Reviewed by Yustia Rahmawati (p.matswa 09 / 09301244005)

          Keputusan Menteri No 22, 23, 24 tahun 2006, Pemerintah Indonesia telah menerapkan kurikulum baru untuk pendidikan dasar dan menengah, yang disebut KTSP " Kurikulum Berbasis Sekolah ". Kurikulum berbasis sekolah ini menggabungkan dua paradigma yaitu kompetensi siswa dan proses belajar siswa.

          KERANGKA TEORITIS

Katagiri, S. (2004) menegaskan bahwa kemampuan yang paling penting yang perlu didapatkan siswa saat ini dan di masa depan, sebagai masyarakat, ilmu pengetahuan, dan memajukan teknologi secara dramatis, bukan kemampuan untuk benar dan cepat melaksanakan tugas-tugas yang telah ditentukan dan perintah, melainkan kemampuan untuk menentukan sendiri apa yang harus mereka lakukan atau apa yang mereka harus lakukan. Tentu saja, kemampuan untuk benar dan cepat mengeksekusi masalah matematika yang diperlukan juga diperlukan, tetapi dari sekarang, bukan dari cekatan untuk meniru metode yang terampil atau pengetahuan orang lain, kemampuan yang akan datang dengan ide-ide siswa sendiri, tidak peduli seberapa kecil, dan untuk mengeksekusi siswa sendiri kemerdekaan, tindakan lebih baik akan sangat penting. Kegiatan matematika tidak dapat hanya ditarik keluar dari topik, mereka harus dipilih dengan cermat sehingga anak-anak bentuk konsep, mengembangkan keterampilan, mempelajari fakta-fakta dan memperoleh strategi untuk menyelidiki dan memecahkan masalah.

          Dalam Lesson Study, para peneliti telah berusaha untuk mengungkap gambaran yang telah guru diupayakan untuk mempromosikan metode matematika dalam mempelajari total luas silinder dan bola serta volume kerucut lingkaran tegak. Hasil penelitian dapat dinyatakan bahwa metode matematika siswa dapat ditelusuri melalui skema kegiatan belajar mengajar sebagai berikut:

1. Masalah Pembentukan dan Pemahaman para siswa:

a. model tertentu diamati dari silinder lingkaran tegak, bidang lengkung, dan model tertentu dari kerucut lingkaran tegak.

b. mengidentifikasi komponen-komponen dari silinder lingkaran tegak, bola, dan kerucut.

c. mendefinisikan konsep silinder lingkaran tegak, bola, dan kerucut     .

d. mendapat pertanyaan dan pemberitahuan dari guru untuk mencari konsep-konsep

2. Membangun Perspektif para siswa:

a. Model yang digunakan beton untuk mencari luas total silinder, area bola dan volume kerucut lingkaran tegak.

b. belajar bahwa tinggi silinder yang tepat adalah sama dengan lebar nya persegi panjang, dan keliling lingkaran adalah sama dengan panjang persegi panjang.

c. panduan belajar guru untuk memahami prosedur bagaimana untuk mencari

volume kerucut lingkaran tegak.

d. dapat menguraikan komponen-komponen model silinder lingkaran tegak.

3. Solusi Pelaksana yang muncul ketika para siswa:

a. mencoba untuk mencari tahu area lateral silinder lingkaran tegak

b. mencoba untuk mengetahui total luas silinder lingkaran tegak

c. mengumpulkan data dari pengukuran volume kerucut dibandingkan dengan volume silinder.

PERAN INTUISI DALAM MATEMATIKA MENURUT IMMANUEL KANT

By : Dr. Marsigit, M.A.

Reviewed by Yustia Rahmawati (p.matswa 09 / 09301244005)

          According to Kant, mathematics as a science is possible if the concept constructed based on mathematical and spatial intuition of time. According to Kant, mathematics was not developed only with the concept of a posteriori because if so math will be empirical. However, empirical data  gained from experience  isrequired for sensing explore the mathematical concepts that are a priori. This is where the uniquethe role of Kant's theory, which attempts to give solution (middle) of extreme conflict between the rationalist and the empiricist in build the foundation of mathematics. According to Kant, intuition becomes the core and key the understanding and construction of mathematics.

          Preliminary. Kant's view of mathematics can contribute significantly in terms from the philosophy of mathematics, especially regarding the role of intuition and construction concepts of mathematics. Michael Friedman (Shabel, L., 1998) mention that what was achieved Kant has given the depth and accuracy of the mathematical foundation, and by because it's achievements can not be ignored.

          Intuition as the Basis for Mathematics. According to Kant (Kant, I., 1781),, and the construction of mathematical understanding is obtained by first finding pure intuition in the sense or mind. The mathematics are synthetic a priori can be constructed through three stages of intuition ie intuition sensing, intuition is reasonable, and intuitive mind.

          Intuition in Arithmetic. Kant (Kant, I., 1787) argues that the propositions of arithmetic should are synthetic in order to obtain new concepts. If you just rely on method analytic, 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 acquire new concepts other than those referred to it, and this of course 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 is 5; and so of course it is synthetic.

          Intuition in Geometry. While Kant (Kant, I, 1783), argues that the geometry should based on pure spatial intuition. If the geometry of the concepts we remove the empirical concepts or sensing, the concept of spatial concepts and time will still remain; namely that the concepts of geometry are a priori.

          Intuition in Decision Mathematics. According to Kant, with the intuition of mind, we hold the ratio of the argument (mathematical) and combine the decisions (mathematics). Decision mathematics is awareness of the nature of complex cognition that have the characteristics: a) relating with mathematical objects, both directly (through intuition) and are not directly (through concepts), b) include both mathematical concepts and predicate concepts entirely on the subject, c) is a pure reasoning accordance with pinsip-pinsip pure logic, d) involve the laws of mathematics constructed by intuition, and e) state the value of the truth of a proposition of mathematics.

          Knot. Kant (Randall, A., 1998) concluded that mathematics is arithmetic and geometry is a discipline that is synthetic and independent one with the others. In his work The Critique of Pure Reason and the Prolegomena to Any Future Metaphysics, Kant (ibid.) concludes that the truths of mathematics is a synthetic a priori truths. Truths of logic and truth are derived only through the definition of the truth of which is analytic.

GERAKAN REFORMASI UNTUK MENGGALI DAN MENGEMBANGKAN NILAI-NILAI MATEMATIKA UNTUK MENGGAPAI KEMBALI NILAI-NILAI LUHUR BANGSA MENUJU STANDAR INTERNASIONAL PENDIDIKAN

By : Dr. Marsigit, M.A.

Reviewed by Yustia Rahmawati (p.matswa 09 / 09301244005)

          Entering the third millennium to the Indonesian nation-colored with the era of reform in all areas of life, which is the difficult times as a result of a severe economic crisis. Phenomenon that emerged from a prolonged crisis that indicates changes in society in various aspects of political life, economics, law and education. Even
identified the emergence of a second economic crisis which consequently may be more severe than the economic crisis first.

          At the macro level, the picture of the education system still shows characteristics of centralism that rigid, with a very strong dominance of bureaucracy, so that at every level of education occurs stagnation or stagnation. Creativity or improvisation towards innovation is very hard to do national education system because they tend to follow the guidelines from above. Our current educational system also is still closed so fosters corrupt practices and collusion; such event marked by a placement officer education is not based on professionalism and educational backgrounds but based on collusion. On the other hand, various educational reports from home and abroad implicitly mentioned the failure of the Indonesian government in the administration education.

          National education reform can be done at two levels of macro and

micro. In the macro, national education reform must be able to renew the vision and

develop educational paradigm and scrape out the constraints education while maintaining and improving the quality and National education reform can be done at two levels of macro and micro. In the macro, national education reform must be able to renew the vision and develop educational paradigm and scrape out the constraints

education while maintaining and improving the quality and ability. The lowest value of mathematics is that if only his own use, a higher value if math can be used for public interest. But the highest math scores is if systemically can be used for wider interest. But the values mathematics that was developed should be coupled with critical thinking because the math does not others do not is not is the critical thinking itself. Sharpness mathematics can wander future through a teleological concept that what happens in the future can at least photographed through the present. Nevertheless there are still values that other relation to levels of quality. At first the quality of the math scores only appear on the outside, but on the quality of the second and third and so on then the value mathematics is metaphysical. With analog thinking then what happens to disclosure of the value of mathematics can be used also in the disclosure of noble values nation.

Developing ICT for Primary and Secondary Mathematics Teacher Professional Development: The Use of Video in Lesson Study

By :Dr. Marsigit, M.A.

Reviewed by Yustia Rahmawati (p.matswa 09 / 09301244005)

                Sebagian besar calon guru (matematika) memiliki sedikit kesempatan untuk mengamati pengajaran efektif dalam aktual kelas karena banyak pengalaman pertama mereka belajar berbasis di ruang kelas tradisional di mana aturan-aturan diterapkan secara metodis untuk memecahkan masalah. Dengan kata lain, mereka tidak memiliki dasar pengalaman untuk bermakna mengamati interaksi kelas yang kompleks dan cepat. Penggunaan Video Tape Recorder (VTR) adalah salah satu aspek dari pengembangan ICT untuk mempromosikan pengembangan guru profesional. 

          VTR (Video Tape Recorder) untuk pendidikan guru dan gerakan reformasi di Pendidikan Matematika, khusus untuk studi pelajaran berkembang memiliki beberapa manfaat sebagai:

a)    ringkasan singkat pelajaran dengan penekanan pada masalah utama dalam pelajaran, b) komponen pelajaran dan peristiwa utama dalam kelas, dan, c) kemungkinan masalah untuk

b)   diskusi dan refleksi dengan guru mengamati pelajaran (Isoda, M., 2006). Menurut dia, Lesson Study dibagi menjadi tiga bagian: a) perencanaan pelajaran, b) bagian observasi, dan, c) bagian diskusi dan refleksi.

Guru merasa bahwa menindaklanjuti pelatihan mereka akan membahas VTR dengan rekan mereka.  Mereka akan menyebarkan hasilnya kepada guru-guru lain dan mendiskusikan VTR di klub guru. Mereka mengatakan bahwa mereka akan mencoba untuk meningkatkan pengajaran mereka meliputi: meningkatkan Pelajaran Persiapan, Lembar Kerja Siswa, mengajar konten dan mengajar metodologi.

Guru dirasakan bahwa mereka akan mengembangkan model pengajaran setelah pelatihan dalam rangka Pendidikan Matematika Realistik dan Konstruktivis pendekatan. Guru juga menyatakan bahwa mereka akan mengembangkan diskusi dan demonstrasi metode serta berbagai metode. Menurut guru, sebagian besar siswa tidak siap atau tidak mampu mereka saat ini ide; butuh waktu bagi mereka untuk membiasakan untuk melakukan itu. Sebagian besar sekolah adalah kurangnya fasilitas pendidikan dan guru harus mampu mengembangkan media pengajaran.Yang paling yang sulit untuk menerapkan model yang baik seperti praktek mengajar adalah tentang alikasi waktu. Beberapa guru dirasakan bahwa tidak mudah untuk mengambil dalam keseimbangan antara mencapai kompetensi siswa dan mempertimbangkan proses mereka belajar.

Kant’s Concepts of Mathematics

By :Dr. Marsigit, M.A.

Reviewed by Yustia Rahmawati (p.matswa 09 / 09301244005)

          Tentang kemungkinan matematika murni. Kant berpendapat bahwa matematika merupakan produk yang murni dan menyeluruh. Selanjutnya, muncul pertanyaan: Apakah ini tidak fakultas, yang menghasilkan matematika, karena keduanya tidak juga dapat didasarkan pada pengalaman, dan mengandaikan beberapa tanah kognisi apriori yang terletak secara tersembunyi.  Namun, Kant menemukan bahwa semua kognisi matematika memiliki keganjilan : pertama kali harus menunjukkan konsep dalam intuisi visual dan memang apriori, oleh karena itu dalam suatu intuisi yang tidak empiris, tetapi murni. Tanpa ini matematika tidak dapat mengambil satu langkah; maka nya penilaian selalu visual, yaitu, intuitif;. sedangkan filsafat harus puas dengan penilaian diskursif dari konsep belaka, dan meskipun mungkin menggambarkan doktrin-doktrinnya melalui sosok visual, tidak dapat memperoleh mereka dari itu.

          Kant menekankan bahwa ada representasi, tidak hanya intuisi, karena itu  jika kita menghilangkan dari empiris intuisi tubuh dan perubahan mereka (gerak) semua empiris, atau milik sensasi, ruang dan waktu masih tetap, yang oleh karena intuisi murni yang terletak apriori pada dasar empiris. Oleh karena itu, Kant menyimpulkan bahwa matematika murni, sebagai kognisi sintetis a priori, hanya mungkin dengan mengacu pada tidak lain obyek daripada indera, di mana, di dasar intuisi empiris mereka terletak sebuah murni intuisi (ruang dan waktu) yang merupakan apriori. Kant menyatakan bahwa ini adalah mungkin, karena intuisi yang terakhir ini hanyalah sekedar bentuk kepekaan, yang mendahului tampilan sebenarnya dari benda-benda, dalam hal ini, pada kenyataannya, membuat mereka mungkin, namun ini fakultas intuisi apriori mempengaruhi tidak masalah dengan fenomena yang ada.

          Matematika penghakiman. Karena akan menjadi absurd untuk dasar penilaian analitis pada pengalaman, seperti konsep ini cukup untuk tujuan tersebut tanpa memerlukan kesaksian dari pengalaman, Kant menyimpulkan bahwa penilaian empiris selalu sintetis, misalnya "Tubuh Itu diperpanjang" adalah penilaian mendirikan sebuah apriori, dan bukan penilaian empiris. Dan juga, sebelum menarik untuk berbagi pengalaman, kita sudah memiliki semua kondisi penghakiman di konsep, dari mana kita memiliki tetapi untuk memperoleh predikat menurut hukum kontradiksi, dan dengan demikian untuk menjadi sadar akan perlunya penghakiman, Kant menyimpulkan bahwa pengalaman yang bahkan tidak bisa mengajar kita.

“INOVASI PEMBELAJARAN UNTUK MENINGKATKAN GAIRAH SISWA DALAM BELAJAR”

By :Dr. Marsigit, M.A.

Reviewed by Yustia Rahmawati (p.matswa 09 / 09301244005)

          Managing the learning is not easy because we find that sometimes students have difficulty in learning (Jaworski, 1994: 83). Therefore, he stated that there is no right way to teach. On the other hand found the fact that it is not easy for educators to change the style of teaching (Dean, 1982: 32). While we prosecuted, as educators, to always adjust teaching methods us in accordance with the demands of changing times (Alexander, 1994: 20). Judging from the focus, there are at least 4 (four) views Different learning how should it be implemented (Kuhs and Ball, 1986 in Grouws, 1992): 1. The group that believes that learning should be emphasized on understanding the material (content focused - conceptual understanding); 2. Groups who argue that learning needs to be prioritize the learning outcomes (content focus - performance); 3. The group that believes that learning should learner-centric subjects, so that they can develop and build knowledge (learner focus - construction); 4. The group that believes that learning should starting from the planning of classroom management that is conducive to earning (classroom focused - effective classroom).

          Learning Through Innovation Curriculum Development. Approach to education "conforming" tend to retain the old values; pendeketan "transforming" more emphasis to the order or oriented to the market, and approach to "reforming" develop education based on human values ​​according to context (Archer, 1989). "Instrumental Curriculum" is more about academic and technical approach; "Interactive Curriculum" emphasizes approach to social and "individualistic Curriculum" more emphasis individual cognition to the development of the subject students (Becher and Maclure, 1978).

          The nature of the subject students. Ebbutt and Straker (1995: 60-75), gave his view that in order potential students can be optimally developed, assumptions about the characteristics subject students and implications for learning is given as follows: the students will learn if they have the motivation. The implications of this view for the business teachers are: (1) provides activities pleasant, (2) pay attention to the desire of students, (3) build understanding through what is known by students, (4) creating a classroom atmosphere that support learning activities, (5) provide appropriate activities with learning objectives, (6) provide activities that are challenging, (7) 4 provide activities that give hope of success, (8) respect achievement of each student.