LESSON STUDY ON MATHEMATICAL THINKING: Developing Mathematical Methods in Learning the Total Area of a Right Circular Cone of the 8th Grade Students of Indonesian Junior High School

By Marsigit, Mathilda Susanti, Elly Arliani

Reviewed by Rosa Ardiyati (http://rosardiyati.blogspot.com/)

Regular Mathematics Education 2009 ( NIM. 09301241032 )

Menurut surat keputusan Sisdiknas no. 20 tahun 2003 bahwa system pendidikan di Indonesia harus  mengembangkan intelegensi dan kemampuan individual  dan kepedulian social. Menyikapi surat ini, pemerintah Indonesia mengaplikasikan kurikulum baru yaitu KTSP yang menitikberatkan pada sekolah berbasis kurikulum. Katagiri, S menyatakan bahwa inti yang paling penting bukanlah kemampuan untuk mengkoreksi dan mengerjakan tugas dengan cepat tapi lebih kepada kemampuan untuk memilih apa yang harus mereka lakukan atau berapa ongkos yang dibutuhkan dengan melakukannya.

Dalam pengajaran matematika, ada beberapa metode yang biasa digunakan. Pertama adalah metode matematika. Matematika memiliki berjuta cara untuk menyelesaikan suatu masalah. Oleh karena itu pengolahan pemikiran yang harusnya menjadi tujuan dari pengajaran matematika. Selain itu pengajaran matematika bisa menggunakan metode pertanyaan yang bisa memancing terjadinya pemikiran matematika. Ada lagi yaitu metode penyelidikan. Pengajaran yang ditujukan untuk mengetahui luas daerah dari tabung dan bola dan juga volume dari kerucut. Desain pengajaran yang dilakukan dibagi beberapa langkah, antara lain persiapan, pelaksanaan, dan pengamatan.

Dari pengajaran ini, para siswa selaku peneliti mendapat petunjuk dari gambar yang mana para guru telah berjuang untuk menunjukkan metode matematika sesungguhnya dalam luas daerah tabung dan bola dan juga volume kerucut. Pengajaran ini bias dinyatakan sebagai metode matematika untuk siswa melalui aktifitas pengajaran sebagai berikut.

Pertama, pembentukan masalah dan pengertian yang dimunculkan ketika siswa mengamati, mengidentifikasi, mendefinisi model tabung, bola, dan kerucut. Kedua, membuat sebuah pandangan yang dimunculkan ketika siswa mencari luas daerah tabung, bola, dan volume kerucut, mempelajari tinggi tabung sama dengan lebar segi empat; dan keliling lingkaran sama dengan panjang segi empat, mengikuti instruksi guru untuk mengetahui prosedur bagaimana menemukan volume kerucut, dan ketika memecah model dari tabung. Ketiga, melaksanakan hasil yang dimunculkan ketika siswa mencoba mencari luas alas dari tabung, luas daerah tabung, luas daerah bola, dan saat mengumpulkan data tentang pengukuran volume kerucut dengan perbandingan dengan volume tabung.

PENINGKATAN PROFESIONALISME GURU ADMINISTRASI PERKANTORAN KOTA YOGYAKARTA melalui LESSON STUDY

Presented : Workshop MGMP Administrasi Perkantoran Kota Yogyakarta

Pada Hari Kamis, 10 Januari 2011

By : Dr. Marsigit, MA

Reviewed by : Rosa Ardiyati (http://rosardiyati.blogspot.com/)

Regular Mathematics Education 2009 (NIM. 09301241032)

Most of us know how to learn mathematics in school is going. There are students and a teacher who explain all of the material. Looks like a simple thing, but actually the teachers need some competence to make the learning activity better. One of the four competent that matter to teacher is professionalism. What is professionalism as a teacher? It means that a teacher has to understand all of the material of the learning activity, especially in this case mathematics subject. Moreover, the teacher has to have knowledge in characteristic of the students due to the better learning; also the teacher has to understand which teaching methods that fit with each material. To develop this competence there are some ways that can be used. Lesson study is one of them.

Lesson study is some kind of cooperation scheme among teachers (mutual subject) to improve their own learning skills altogether by having some research and reflection systematically. The purpose of lesson study is to develop teacher’s service to students. So, it can be said that he basic concept of lesson study is cooperation of some teacher or lecturer to observe, investigate, and reflect the learning activities.

How can lesson study improve teacher’s skills? It’s because teachers need innovation. Innovation can make the learning more effective and efficient. There are few things that can be the point of this lesson study. Those are student centre, constructivist approach, realistic approach, contextual teaching learning. Moreover, there are also few things can might be our concern because they can support the success of lesson study. The teachers must be open minded, let other people opinion come to them. Lesson study is about observing and reflecting all the things about the learning activity. So, at the end each teacher can share their ideas about how the learning activity should be going.

Then, how to run a lesson study? Just 3 basic step actually. That is plan, do, and see. ‘Plan’ : in this step teachers planning their schedule, lesson plan, work sheet, and all the things that matter in learning activity. And the second step, ‘do’: the teachers model’s doing the learning activity while the other teacher obverse it. Then the third step is ‘see’: in this step the result of the observation will be reflected, usually lead by MGMP chairman. In this third step all the teacher, including the model teacher can reflect their learning activity, share about how’s the learning’s going, is there any constraint or problem while leading the class and many other things. And the other teacher can share their critics and suggestion.

The Iceberg Approach of Learning Fractions in Junior High School: Teachers’ Simulations of Prior to Lesson Study Activities

By Dr. Marsigit, MA

Reviewed by Rosa Ardiyati (http://rosardiyati.blogspot.com/)

Regular Mathematics Education 2009 ( NIM. 09301241032 )

                Standar nasional pengajaran matematika di Indonesia masih minim dengan bukti siswa-siswa kita mulai dari nilai afektif, kognitif, dan psikomotornya. Itu berarti bahwa pemerintah masih harus mendorong para guru untuk mengembangkan kemampuan siswa dengan memanfaatkan lingkungan aktifitas siswa sehingga siswa bias berpikir secara logika, analitik, sistematik, kreatif, dan mampu menyatukan semua elemen itu.

                Untuk melakukan itu, matematika harus sangat dekat dengan dunia siswa sehingga mereka bisa mendapatkan pengalaman untuk menemukan matematika itu sendiri. Seperti konsep Iceberg ini yang merupakan titik awal siswa untuk mendapatkan pengalaman nyata termasuk dalam aktifitas matematika mereka sendiri. Salah satunya dengan mengajarkan matematika tentang pecahan. Ada 6 kelompok guru yang menyampaikan konsep iceberg untuk mengajarkan pecahan di tingkat SMP, yaitu pengurangan bilangan pecahan, persen dan permil, membandingkan nilai pecahan, pecahan desimal, bilangan campuran, dan pembagian pecahan.

                Memang diawal, ini tidaklah mudah untuk guru menyalurkan dan memproses benda nyata ke dalam dunia matematika. Sehingga tampak ketidakyakinan guru ketika mengenalkan model konkrit ke siswa atau menunggu siswa untuk menemukan sendiri. Untuk model, guru harus mengembangkan representasi visual sehingga tampaklah hubungan antara konsep, relasi, dan operasi pada pecahan itu sendiri. Guru merasa bahwa pengertian dugaan dari pecahan , relasi dan operasinya akan muncul dengan membentuk sebuah kelompok – kelompok diskusi kecil. Siswa akan menemukan minatnya ketika mereka mendapatkan pengertian yang sebenarnya dari pecahan itu.

                Banyak guru membawa pengaruh besar untuk usaha mereka dalam mengembangkan konsep Iceberg dalam mengajarkan pecahan. Dalam pengembangan konsep ini, para guru berharap bahwa ada minat dari para siswa untuk menyatakan bahwa pecahan tidak hanya seluruhnya angka tapi juga bilangan rasional. Meskipun konsep Iceberg menguatkan siswa untuk membangun konsep mereka sendiri tentang pecahan, masih ada kesulitan bagi siswa untuk menyelesaikan masalah yang diekspresikan dengan simbol. Akan tetapi mereka bisa menyelesaikan masalah yang serupa dalam konteks dunia nyata. Sebagian besar guru mengakui bahwa representasi dari pecahan dapat sangat abstrak dan menjadi sulit untuk siswa. Sementara itu mereka juga menemukan konsep Iceberg sangat penting dan berguna sebagai pendekatan pengajaran pecahan di tingkat SMP.

               

                

“USAHA GURU” DALAM MENINGKATKAN MINAT SISWA MEMPELAJARI MATEMATIKA

Oleh : Dr. Marsigit

Reviewed by : Rosa Ardiyati (http://rosardiyati.blogspot.com/)

Regular Mathematics Education 2009 (NIM. 09301241032)

Teaching mathematics as we know is not easy, since the students of Mathematics Education their self say: study mathematics is not easy either. Jarswoski said that “There is no such the best way to teach mathematics”. ‘No best way’ doesn’t mean teaching mathematics is impossible. We just need to change our point of view in teaching mathematics as we know these days.

Most of mathematics teacher have problems in teaching mathematics itself. Why? There are some constraints in teaching math such as understanding the meaning of the theory, how to apply the topics in daily life, the current system, environment and facilities. Moreover, teachers also often have difficulties such as how to handle a class with various student, develop technology in teaching, making the student active in class, targets in final exam (UAN), and all of those problems and difficulties lead to a decision that most of the teachers made: thought that there is no other ways to teaching mathematics except with exposition method. And that’s definitely makes most of the student getting bored and not really math subject in their class. So what do we do as a mathematics teacher?

Let’s talk about the substance of mathematics in absolute view. That is abstract, universal, formal, objective, rational, theoretical, neutral, and many more. And what about substance of mathematics in ‘social constructivist’ view? They are concrete, informal, subjective, intuition, emotional, practical, and many other things. From those 2 points of view, which is the right view to mathematics in school? In school mathematics, there are few things that might be important. First, mathematics is activities that browse the pattern and relation. Second, mathematics is creativity that needs imagination, intuition and discovery. The third, mathematics is problem solving activity, and the last is mathematics is one of the ways to communicate.

From all the information that we got, there are one more thing that must be our concern. That is  the substance of learning mathematics. First, students will study if they are motivated. Second, the students study with their own ways. Third, the students learn individually and corporately with their colleagues.  And the last is the student need different context and situation in learning mathematics. From all of that, now we can conclude what we have to do as mathematics teacher. Those are, teacher need to know the capability of his/her student. And then the teacher have to make a plan that match with the students capability. The third, the teacher have to build the knowledge and skills that they get from school and environment.

So, few things that have to evaluate in mathematics learning is definition, process, skills, fact, and result. Definition : I(teacher) want to know whether they (student) know or not. Process: I want to know what way they can use. Skills: I want to know which skills that they have can be used. Fact: I want to know what’s they remembered. And the last one is result: I want to know what they get.