Pembelajaran Matematika Berbantuan Kalkulator: Studi Kasus Penggunaan Kalkulator Texas Instrument TI 89 pada PBM Matematika di SMK MUHAMMADIYAH IV YOGYAKARTA

By: Dr. Marsigit, M.A.
Reviewed by : Ramadian Radite (09301244020)

Students still have problem to understand relation between aritmatic and algebra. According to Lee and wheeler, this problem came from student’s readiness to use algebra to solve algebra problem. In mathematics learning process, teacher must have scheme of learning. With the scheme, teacher expect to have systematics in teaching mathematics. So that teaching learning mathematics will be structured an systematic.
The type of calculator have been developt. From the utilization, calculator consist of two types. They are ordinary calculator and scientific calculator. Ordinary calculator commonly used in daily life. One of the scientific calculator is graphic calculator. Graphic calculator have some advantage, they are ability to solve mathematics problem quickly and display them graphical form. Another advantage is graphic calculator could make program that could solve mathematics problem.

Using calculator as teaching aid has some stage, they are:
1. Fisrt stage, understand the importance of graphic calculator. The essens of the understanding is explained in detail and basically about graphic calculator.
2. Second stage, understanding theorem and using graphic calculator to solve equality and inequality problem.
3. Third stage, entering data’s input of the problem to the graphic calculator. It is change mathematics laguange to graphic calculator language.
4. Fourth stage, interpretate of the screen on graphic calculator and make a conclution.
From this research, we know that there is some aspect of using graphic calculator in mathematics learning:
1. Graphic calculator can be used to determine and match graphic picture
2. Graphic calculator can be used to determine and match the answer of solution set
3. Graphic calculator could give real experience about graphic picture
4. Solving problem about equality anf inequality can use the command, manipulation of the symbol and graphic
5. Graphic calclutaor bermanfaat to give answer that calculate without calculator and mepercepat solving mathematics problem
6. Graphic calculator make learning mathematics be more interesting and it is easier to solve the problem
7. If using graphic calculator without ability to understand procedure of the operation and mathematical thinking, it can be cause addicted, losing self effidence, and lazy.
The constraint of the using graphic calculator is change mathematics languace to calcluator language and expressing calculator’s screen to the mathematics language

Asumsi Dasar Karakteristik Matematika, Subyek Didik dan Belajar Matematika Sebagai Dasar Pengembangan Kurikulum Matematika Berbasis Kompetensi Di SMP

By : Drs. Marsigit, MA
Reviewed by: Ramadian Radite (09301244020)

The main base of problem is how to planning, developing, and implementation of curriculum which appropriate with the teaching learning activity what be hoped. In the mathematics education is based of competence emphasize on the competence which it is should has by graduate, so the curriculum should be developed appropriate explaination of competence standart be came to the base competence that it include afective skill, cognitive, also psichomotoric. Therefore, in order to be reached mathematics education then it is need rowed syllabi of mathematics lesson so include lesson substance which it refer on the characteristic of mathematics appropriate with what is reached.
Ebbutt dan Straker (1995: 10-63) define school mathematics and then called as mathematics ,that:
1. Mathematics is activity to research pattern and relation.
2. Mathematics is creativity which it need imagination, intuition, and innovation.
3. Mathematics is activity of problem solving
4. Mathematics is communication tool.
In the developing of cognitive aspect, Ebbutt dan Straker (1995: 60-75) also give define about characteristic of student and implication of mathematics learning so potention of student can be developed optimally, that they are:
1. Student will study if they get motivation.
2. Student study with their method.
3. Student study stand alone and cooperation.
4. Student need the context and situation which different in their study.
In the hierarchy of afective aspect according to Krathwhol, Paul, dan Krech that about attitude can be get the conclusion that the meaning of attitude that it is disposing of sense to psychology object, it is evaluation of object.
In the developing of psychomotoric aspect that student activity is toke to demonstrate about skill and competence to do physic activity like that draw triangle, square, cyrcle, etc.
Implemetation in curriculum then the Basis Competence Curriculum be planed so in the learning mathematics process, student can do searching of pattern and relation activity; develop creativity and imagination; intution and discovery; and communicate about their mathematics thought to other.
Experience and study activity should be did by student so they can reach the base competence and substance lesson. Study experience can be got in class or out of class and it is be supported by axistance of object source. Developing of experience and study activity is essence of Basis Curriculum Competence system which it include mathematics charracteristic, child subject, and mathematics learning.

PENDEKATAN MATEMATIKA REALISTIK PADA PEMBELAJARAN PECAHAN DI SMP Di sampaikan pada Pelatihan Nasional PMRI Untuk Guru SMP Di Yogyakarta 3, 4, 5 Juni 2010

By: Dr. Marsigit M.A.

Reviewed by: Ramadian Radite (09301244020)

Realistic mathematics emphasizes the construction of the context of concrete objects as a starting point for students to acquire mathematical concepts. Concrete objects and environment objects can be used as a context for learning mathematics in building mathematical connections through social interaction. Concrete objects manipulated by the student within the framework of efforts to support students in the process matematisasi concrete to the abstract. Students should be given opportunities to construct and produce mathematics in a manner and language of their own.

We can examine the number rupture in junior high school mathematics learning through the formal position of the two sides of the split numbers in the context of curriculum and syllabus, and a review of substantive number rupture itself. In the curriculum development guidelines stated that in learning mathematics can be started with an introduction to issues appropriate to the situation (contextual problems). By asking a contextual problem, learners are gradually guided to master math concepts. The purpose of learning fractions in school may be mentioned as follows:

1. Solve problems and find the concept of numbers contextual broke from contextual problems solved

2. Understand the concept of numbers broke out, explain the link between concept and apply the concept of numbers broke, flexibly, accurately, efficiently, and accurately in solving problems

3. Using the reasoning on the pattern and nature, to manipulate and make generalizations about the numbers broken

4. Communicating the concepts and use numbers broken

5. Having respect for the usefulness numbers break in daily life.

Type of having realistic characteristics buttom-up approach in which students develop their own models and then the model is used as the basis for developing formal mathematics. There are two kinds of models that occur in the process that is a model of the situation and to model mathematically. In the realistic model emerged from students' informal strategies in response to real problems for later formulated in formal mathematics, this kind of process in accordance with the historical development of mathematics itself (Sugiman, 2007).

PROMOTING PRIMARY AND SECONDARY MATHEMATICAL THINKING THROUGH THE SERIES OF SCHOOL-BASED LESSON STUDY ACTIVITIES To be presented at 1st International Conference on Lesson Study FMIPA UPI 31 July to August 2, 2008

Oleh: Dr. Marsigit M.A.

Reviewed by: Ramadian Radite (09301244020)

Dalam Kurikulum Berbasis Sekolah, dinyatakan bahwa matematika di sekolah dasar dan sekolah menengah harus mendorong siswa untuk berpikir logis, analitis, sistematis, kritis, kreatif dan mampu berkolaborasi dengan orang lain. Dalam memecahkan masalah, siswa perlu kreatif dalam mengembangkan banyak cara dan alternatif, mengembangkan model matematika, dan memperkirakan hasil. Untuk membuat belajar matematika primer lebih efektif, guru juga perlu mengembangkan sumber daya seperti teknologi informasi, alat bantu mengajar dan media lainnya.

Kurikulum menguraikan tujuan dari belajar mengajar matematika adalah sebagai berikut, untuk memahami konsep matematika, menjelaskan hubungan antar konsep dan untuk menerapkan konsep untuk memecahkan masalah secara akurat dan efisien, untuk mengembangkan keterampilan berpikir untuk belajar pola dan karakteristik matematika. Serangkaian kegiatan Lesson Study dapat merupakan seperangkat budaya kegiatan yang diselenggarakan dilakukan oleh guru atau kelompok guru untuk mempromosikan anak-anak matematika berpikir. Namun, diskusi kelompok kecil yang menarik di mana untuk mengeksplorasi partisipasi anak berinteraksi antara yang lain di alami terjadi berpikir berakhir terbuka.

Mengajar matematika dapat dirasakan sebagai proses konstruksi siswa matematika makna, dimana siswa dapat mempunyai pengalaman berpikir matematika yang serupa proses dibandingkan dengan proses yang diciptakan matematika. Arti dari penemuan adalah langkah-langkah dalam pembelajaran hasil sementara arti konstruksi adalah proses belajar. Selain itu, prinsip reinvention juga dapat terinspirasi oleh prosedur solusi informal.

Katagiri (2004) menjelaskan bahwa berpikir matematis melibatkan 3 (tiga) penting aspek yaitu metode berpikir, sikap dan konten. Secara khusus, ia menunjukkan bahwa aspek berpikir matematika meliputi:

a. matematika thingking terkait dengan sikap, yaitu antara lain mencoba untuk memahami masalah sendiri atau tujuan atau substansi oleh diri sendiri, mencoba untuk menemukan masalah matematika dalam fenomena, mencoba untuk mengambil tindakan yang sesuai dengan tujuan, mencoba untuk berpikir berdasarkan data yang dapat digunakan, dipelajari sebelumnya item, dan asumsi,mencoba untuk merekam dan mengkomunikasikan masalah dan hasil jelas dan ringkas, mencoba untuk mengevaluasi berpikir baik secara obyektif maupun subyektif, dan untuk memperbaiki pemikiran.

b. berpikir matematika terkait dengan metode matematika, yaitu antara lain, berpikir induktif, berpikir analogis, berpikir deduktif, berpikir integratif , berpikir pembangunan, berpikir abstrak , berpikir general, berpikir yang mengkhususkan, berpikir melambangkan, berpikir yang mengekspresikan dengan nomor, mengkuantifikasi, dan tokoh.

c. berpikir matematika terkait dengan isi matematika yaitu antara lain, memperjelas objek untuk pertimbangan dan objek dikeluarkan dan memperjelas kondisi untuk dimasukkan, mencoba untuk memformalkan metode operasi (ide dari algoritma), mencoba untuk memahami gambaran besar dari objek dan operasi, dan menggunakan hasil dari pemahaman, berfokus pada aturan dasar dan sifat, mencoba untuk mengekspresikan proposisi dan hubungan sebagai rumus, dan membaca artinya ini adalah pemikiran matematika yang berbeda dari pengetahuan sederhana atau keterampilan.

PENGEMBANGAN KEMAMPUAN GURU Developing Teacher Training Textbooks for Lesson Study in Indonesia Oleh: Dr. Marsigit, M.A. Reviewed by: Ramadian Radite (09301244020)

Guru sebagai salah satu sumber belajar dari siswanya harus menguasai materi yang akan diajarkan.Salah satunya dengan cara menguasai konsep melalui model textbook. Disini mereka harus menguasai konsep,teori,media dan fasilitas pendukung yang lainnya.

Pemerintah melalui kementerian pendidikan nasional telah menentapkan standar minimum yang harus di kuasai oleh seorang siswa yaitu afektif, cognitif ,dan psikomotorik.Diman semua itu hanya dapat tercapai ketika guru menguasai materi yang akan disampaikan ke siswanya melalui proses pengajaran dan pembelajaran yang optimal.

Dalam proses pengajaran dan pembelajaran mereka di ajarakan tentang cara penyelesaian dan studi kasus dari suatu masalah. Sehingga pemahaman mereka akan matematika akan meningkat. Proses pembelajaran yang menarik dan interaktif dalam mengajarkan matematika juga memerlukan metode dan waktu yang tepat.

Tujuan dari pembelajarn matematika dalam usaha pembangunan lesson study melalui teks book adalah memahami apa itu matematika ,konsepnya,hubungannya dengan yang lain dan aplikasi dari matematika itu sendiri dalam kehidupan.Membangun pola pemikran dan karakter dari matematika yang mampu menjernalisir setiap masalah dengan proporsi yang tepat.Dengan Aktifitas pembelajaran yang mampu membangun konsep berfikir matematika yang real dan logis.Yang di dapat melalui proses belajar dan pengalaman di kelas atau tempat yang lainnya.

Khusus untuk kebutuhan pengembangan teksbook untuk matematika di SMP kita memerlukan gambaran bagaimana rencana dan kegiatan kelasa selanjutnya yang harus dilakukan yaitu : pemecahan masalah,proses,hasil,hubungan dalam matematika,makna matematika dan kaitan matematika dengan  lain.

Terakhir guru harus mampu mengevaluasi dari setiap kegiatan pemblajaran yang dilakukan baik metodenya,media ataupun suasana kelasnya.

“USAHAGURU” DALAM MENINGKATKAN MINAT SISWA MEMPELAJARI MATEMATIKA

Oleh: Marsigit

Reviewed by: Ramadian Radite (09301244020)

Teaching mathematic is not easy because we find that students are also not easy to learn mathematics and there is no one best way to teach mathematics. Obstacles often experienced by teachers: understanding the meaning of the theory, how to apply, the existing system, environmental conditions, and lack of learning facilities. While the difficulties of teachers include: dealing with differences in their students' math skills, encouraging students to actively learn, develop math learning technology, and the final target of achieving a high NEM and the completion of the syllabus are the two main factors why the teacher seemed to have no other alternative except to rely on mathematics teaching method of exposition.

The nature of Mathematics of the 'absolutist' to 'social constructivits': abstract to concrete, formal to informal, objective to subjective, justification to invention, rationality to intuition, reasoning to emotional, general stuff to specific things, theory to practice, work with mind to working with his hands, and so on.

The nature of School Mathematics:

1. Mathematics is the search activity patterns and relationships.

2. Mathematics is the creativity that requires imagination, intuition, and discovery.

3. Mathematics is problem solving activities.

4. Mathematics is a tool of communication

The implications of all that nature of the business teachers are encouraging students to conduct discovery, trial, and investigations by drawing conclusions so that students can take the initiative, creativity, respect other people's work and have the mindset of a structured and reflexive. Here teachers act as facilitators who assist students in learning mathematics; logical, consistent, precise, systematic and develop a system of documentation / notes in mathematics; and help encourage students to be more happy and appreciate mathematics.

The nature of Student Learning Mathematics:

1. Students will learn if given the motivation.

2. Students studying in its own way.

3. Students learn independently and through cooperation.

4. Students need the context and circumstances that vary in their learning.

The implications of the nature of the business of teachers is to provide fun activities, in accordance with the purpose of learning, providing challenging activities, respecting each student achievement because students learn in different ways and speeds, students also have socio-economic backgrounds, different cultures. With so expected that students are able to learn to work together, exchanges ideas and respect for others, independent study, creative, good at using props as needed, and understand mathematics by being able to reflect on mathematic activities.