INNOVATION IN TEACHING LEARNING PROCESES of MATHEMATICS

Introduction
Although the Mathematics subject is so important and occupies a central position since ancient times is still a lot of interest students. The gap was found between aspiration and achievement. Mathematics is very abstract. This deals with ideas rather than objects, the manipulation of symbols rather than manipulation object. This is a tightly-knit structure in which ideas are interrelated. Mathematical concepts is hierarchical and interconnected, like a house of cards. Except under the concept of a controlled rate, a higher level concept can not be understood. The innovation process generally described as consisting of three important steps, beginning with conception an idea, which is then proposed and finally adopted. Although many ideas have been prepared to bring about change in teaching mathematics, It remains to be proposed and adopted.
Objectives of Teaching Mathematics
Education provided to achieve certain goals and objectives. Range of subjects of the school curriculum is a different means to achieve that goal. So with each subject several inherent objectives to be achieved through teach the subject. According to Sidhu (1995) the purpose of teaching mathematics are as follows:
•    To develop mathematical skills such as speed, accuracy neatness, in short, estimates, etc. To develop logical thinking, reasoning power, analytical thinking, critical thinking.
•    To develop a decision-making power.
•    To develop problem-solving techniques.
•    To identify the adequacy or inadequacy of the data provided in connection with problem.
•    Develop a scientific attitude is to predict, locate and verify the results.
•    To develop the ability to analyze, to draw conclusions and generalizations from the collected data and evidence.
•    To develop attitudes and heuristics to find solutions and evidence with own independent efforts.
•    To develop a mathematical perspective and outlook to observe the natural world and society.
Innovations in Teaching Mathematics
Innovations in teaching of mathematics can be diversified in terms of Methods, Pedagogic Resources and Mastery Learning Strategy used in teaching-learning process.
1.    Mastery Learning Strategy
Teaching strategy is a general plan for the lesson and include specific structure to follow. BS Bloom's Mastery Learning Strategy has been developed. This is a new instructional strategies used to develop a mastery learning and curriculum objectives can be realized. It consists of different steps: division of content into the unit, the formulation of objectives associated with each unit, teaching and the instructions are organized to realize the objectives of each unit, manage the unit tests to evaluate the level of mastery and diagnose learning difficulties, repair instructions are given to eliminate the difficulties and reached the level of mastery by each student. This strategy plays an important role to learn from the basics and fundamentals such as operating in various number of systems - Natural numbers, Integers, Rational numbers, Real number
2.    Method
Method is a style of presentation of content in the classroom. The following is an innovative method that can be used to make the teaching-learning Mathematical process effectively.
-    Inducto-Deductive Method
-    Analytico-Synthetic Methods
-    Play-Way Method
-    Laboratory methods
3.    Pedagogic Resources
Is the source of pedagogical resources that teachers can integrate the Transaction methods with specific content and take advantage to advance students learn.
-    Teaching Aids
-    Activity

In order to promote learning and skills using the library and resource center should be encouraged. Receive regular feedback for teaching and learning should be an inbuilt component of the learning process. Once teachers find innovative ways to generate interest and enthusiasm in the classroom, he will be able to use idea again next year, because they will be new and exciting for a different classes. But teachers should keep in mind that over time, the the world changes, the environment around the student changes and their needs change, so we must continue to modify and find new ways of teaching that proves he's a better teacher

Refrences :
http://www.waymadedu.org/StudentSupport/Rachnamadam.pdf
http://en.wikipedia.org/wiki/Mathematics_education

Way of mathematic teaching traditional and inovative

Traditional teaching related to the teacher as controlling the learning environment. transfer of knowledge can only be said by the teacher or controlled by the teachers, and students just listen to what the teacher taught them. They regard the students as having 'knowledge holes' that need to be filled with information. In contrast to innovative teaching, because the adaptation of innovative learning model of learning fun. Learning is fun is the key to which is applied in innovative learning. If the student has invested this in mind there will be no more students are passive in class, feeling pressured by the task deadline, the possibility of failure, lack of choice, and of course boredom. To be able to implement innovative learning teachers must be able to:
•    Understand the properties owned subsidiary,
•    Getting to know children as individuals,
•    Use the child's behavior in the organization of learning,
•    Develop critical thinking skills, creativity, and problem solving skills,
•    Develop a classroom as an engaging learning environment,
•    Make use of the environment as a learning resource,
•    Providing good feedback to enhance learning,
•    Differentiating between physically active and mentally active.
but the traditional methods are different by innovative methods that make students construct their own knowledge the teacher and the task of the teacher is to facilitate students. For the traditional mathematical methods only make mathematics itself as an object outside, but in innovative methods of mathematics or mathematical object is its own students. Innovative points in math teaching method is to make students active in student learning or the center of the learning and teaching and the teacher just facilitating them. To explore students' knowledge should be facilitated by good teachers to make students active in teaching and learning. This can also be performed in all general education not just for mathematics education

Mathematics Learning Delivery Methods

Mathematics is a field of study for this is still considered the scourge of most students, whether it's from the primary schools, junior high schools, senior high schools, and even universities. no doubt that mathematics has become one of the lessons are more difficult than other subjects. There are several reasons that push students' thinking that mathematics is a difficult subject, one of which is the notion that mathematics is a collection of formulas that are difficult memorized, mathematics is not just rely on logic alone, but the precision in the work. fact that such things can be minimized by teachers, so students are not particularly think that mathematics is a difficult subject, one solution is the method of delivery. delivery of a material having an important role in the learning. submission of a rigid, will affect students' interest in learning to follow, otherwise delivery will be flexible and attractive to students interested to follow it. Interest is what makes the students become more interested in following lessons.
There is some mathematical way of delivering learning materials, such as:
a.    interaction between teachers and students
interaction that goes on here is between teacher and student. in this case there are several methods that can be used, such as the lecture method, the teacher conveys the material in front of their students, then there is a method of discussion, in which the teacher role here is as tutors and students to participate actively in the learning so that students can add their experience in receiving a subject matter. other than that students could also be given the material by using appropriate instructional media, so that students will be more challenged and interested in learning the material being taught.
b.    student interaction and material
interaction here means that students interact directly with the material being taught. students in this regard is expected to discover a new concept through the material provided by teachers, with a concrete example is given in accordance with the material. the material here could be the formula associated with the daily life of students, so students can understand the concept of a formula or formulas are easily
with both of these methods, students are expected to kana more interested in mathematics and the learning environment will foster motivation to learn mathematics in the patterns of thought, so there is no longer thought that mathematics is a difficult lesson, but learning is fun.

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DEVELOPING MATHEMATICS EDUCATION IN INDONESIA

By: marsigit

Saat ini studi tentang matematika dan ilmu pendidikan di Indonesia telah indikasi bahwa prestasi anak-anak dalam mata pelajaran matematika dan Ilmu pengetahuan masih rendah, seperti ditunjukkan oleh hasil tahun Meninggalkan Nasional (EBTANAS) Pemeriksaan oleh tahun baik di Sekolah Dasar dan Menengah. Penguasaan anak-anak di Matematika dan konsep Ilmu Pengetahuan dan keterampilan proses Sains cukup memprihatinkan. Penelitian juga menunjukkan ketidakcocokan bahwa di antara tujuan pendidikan, kurikulum, dan sistem evaluasi . sistem pelatihan guru untuk Matematika dan guru Ilmu kurang terorganisir, terintegrasi dan sistemati baik dari segi konten dan manajemen. Di bidang kurikulum, ditemukan bahwa: banyak guru yang masih mengalami kesulitan dalam menganalisis isi dari pedoman untuk program pengajaran (GBPP), sejumlah Matematika dan topik Science dianggap sulit bagi guru untuk mengajar; Kebanyakan anak menganggap Matematika dan Sains sulit untuk mengerti, guru menganggap bahwa mereka membutuhkan pedoman untuk melakukan proses mengajar oleh menggunakan ilmu pendekatan keterampilan proses. Untuk meningkatkan mutu pendidikan (IMSTEP) telah bekerja sejak 1 Oktober 1998. Untuk pertama-empat tahun di sana memiliki banyak kegiatan telah dilakukan di tiga universitas (Universitas Pendidikan Indonesia UPI, Universitas  Negeri Yogyakarta-UNY dan Universitas Negeri Malang-UM). Tujuan dari uji coba adalah untuk memberikan kontribusi terhadap peningkatan pendidikan matematika dan ilmu pengetahuan di sekolah dengan mencoba beberapa hal yang dikembangkan dalam proyek ini yang langsung berhubungan dengan sekolah. Pemerintah Indonesia juga berusaha untuk menerapkan kurikulum baru "kurikulum berbasis kompeten" untuk pendidikan dasar dan menengah yang secara efektif dimulai pada tahun akademik 2004/2005. Kebijakan ini secara logis akan menyiratkan ke beberapa aspek berikut: program otonomi pendidikan, mengembangkan silabus, meningkatkan kompetensi guru, fasilitas belajar, anggaran pendidikan, memberdayakan masyarakat, sistem evaluasi dan jaminan kualitas.

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THE ROLE OF KANT’S THEORY OF KNOWLEDGE IN SETTING UP THE EPISTEMOLOGICAL FOUNDATION OF MATHEMATICS

                                                    

By: Marsigit

Filosofi matematika bertujuan untuk menjelaskan dan menjawab pertanyaan-pertanyaan tentang status dan dasar dari objek dan metode matematika, yaitu mengklarifikasi secara ontologis apakah ada objek matematika, dan mengklarifikasi secara epistomologis apakah semua pernyataan matematika yang berarti memiliki tujuan dan menentukan kebenaran. Sebuah pandangan sederhana dari filosofi matematika menunjukkan bahwa ada empat pandangan utama yaitu Platonisme, logicism, Formalisme, dan Intuitionism.

Filsafat pra-Kant matematika diatur sebagai perdebatan antara Rasionalis dan empiris. Kant mulai filosofi matematika dengan fokus pada pengetahuan matematika dan hubungan epistemik mereka untuk teorema dan bukti yaitu epistemologi matematika. Peran teori Kant dalam menyiapkan pengetahuan dasar epistemologis matematika muncul dari upaya Kant untuk mengatur epistemologis dasar matematika yang didasarkan pada prinsip-prinsip sintetis apriori di mana ia percaya bahwa penilaian matematika adalah contoh asli pengetahuan.

Kontribusi Kant yang paling signifikan untuk filsafat modern adalah pengakuan bahwa pengetahuan matematika adalah mungkin. Yang mengistimewakan pemikiran matematika setelah Kant tampaknya berasal dari pemikiran awal Kant yang membedakan dari model intuisi dan berpikir. Epistemologis matematika menurut Kant adalah prinsip bahwa inferensi adalah ketika seseorang menangkap sebuah arsitektur matematika di mana pembenaran kesimpulan matematika dipandang sebagai pengembangan suatu pembenaran matematika.

Kant percaya bahwa penilaian matematika dan fisika dari Newton adalah contoh untuk pengetahuan sejati. Matematika dan ilmu pengetahuan adalah obyektif dan berlaku universal, karena semua manusia tahu dengan cara yang sama. Teori Kant tentang pengetahuan mengakui konsep besar matematika dan intuisi, sehingga baik aljabar dan geometri dapat ditampung.

Dalam kecenderungan filsafat teori matematika saat ini, teori Kant ini sejalan dengan persepsi bahwa pemahaman tentang matematika dapat didukung oleh sifat fakultas persepsi. Setidaknya ada dua garis filsafat di mana mereka memiliki posisi yang berbeda dari masalah-masalah epistemologis dalam epistemologis dasar matematika. Baris pertama merasakan bahwa matematika harus dibatasi oleh sifat fakultas persepsi. Baris kedua merasakan bahwa masalah dalam matematika tidak konsisten dengan kemampuan perseptual, tetapi tidak membatasi matematika untuk apa yang mampu intuisi.

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USAHA GURU DALAM MENINGKATKAN MINAT SISWA MEMPELAJARI MATEMATIKA

By : Marsigit

Mathematics is a subject that is considered difficult by student, because mathematics uses some symbol that have not understood the student. Here, Teacher’s are required to increase the interest of student learn mathematics. It’s no easy, some teacher having problems’s :

1.      Understanding the meaning of theory

2.      Application of theory

3.      The system Used

4.      Environment condition

5.      Learning Fasilities

Teacher’s in Indonesian are still difficult to convey mathematics to student, because the character of student in defferent as well as physical and mental state of those who are different. As for some of the difficulties in conveying mathematics teacher is :

1.      To handle the different in their student mathematics skills

2.      To encourage students to active learn

3.      To develop technology learning mathematics

4.      NEM high achievement of target

5.      Teacher have no otjer alternative taching mathematics

In is this which student less like a lesson mathematics. So, teacher’s attempt to increase student interest in learning mathematics :

1.      To give student the chance to do discovery

2.      To provide for student to conduct experiment with various ways

3.      To encourage students to discover the sequence, difference, comparison, grouping,and etc.

4.      To encourage students to draw general conclusions.

5.      Help student to understand

6.      To encourage student iniriative

7.      To raise the curiosity of students

8.      To teach student to appreciate the discoveries of other

9.      To encourage student to think reflexif

10.  To develop student ability to solve problems in its own way

11.  To encourage student reading and writing mathematics

for students to love math then the learning of mathematics can be delivered demokrative, student centered, student initiative, studeny activity, orientation process and result, individual service, discussion, internal motivation, Fleksible, induktif, deduktif, assessment,and to serve.

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PENDEKATAN MATEMATIKA REALISTIK PADA PEMBELAJARAN

PECAHAN DI SMP

Dr. Marsigit

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 mathematisation concrete to the abstract. Students should be given opportunities to construct and produce mathematics in a manner and language of their own. Necessary activities so that the reflection of social activity can occur integration and strengthening of relations between subjects in understanding the structure of mathematics. According to Hans Freudental in Sugiman (2007) mathematics is a human activity and must be linked to reality. Thus, when students do activities to learn math so in her place mathematisation process.
We can examine the Numbers Break in junior high school mathematics learning through two sides of the Aircraft Numbers formal position 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 the introduction of a problem that fits the situation. By asking a contextual problem, learners are gradually guided to master math concepts. Competency Standards relating to learning fractions is to enable students to understand the properties of numbers arithmetic operations and their use in solving problems. With the Basic Materials of Aircraft Numbers Integer and then expected to be reached using two basic competencies are: Conducting the operation count fractions, and using the properties of arithmetic operation in problem solving fractions.