Nama  : Siti Nuruniyah
NIM    : 09301241023
Prodi   : Pendidika Matematika Subsidi


  1. INTRODUCTION
The education is very important to construct our country. It as the effort to make human life be prosperous. So the education was looked as a based of the country because the country’s destiny in the future hanged on the education of citizen. Then, the government pay attention how important the education for a country. The legitimate of education in Indonesia related with the teaching and learning activities in the school. The fact in Indonesia the quality of education still in low. Commonly, the number of teacher just employ one method to teach. That is the traditional method. The teacher just explain the teaching content, giving the task, and in the final thy give an exam to evaluate. If this method still employ, then the quality of education in Indonesia doesn’t increase.
Many effort have  done by the government to improve the quality of education. Suppose have done many research to develop the education. The research have done related with the curriculum development and development of teaching and learning method. From the result of this research hoped that it can use to improve the education quality. The development of curriculum in Indonesia results KTSP (Kurikulum Tingkat Satuan Pendidikan) that is practiced in the school. The student should have the standard competence and based competence.
Every school teach the school mathematics. The aims of it is to prepare the student in order to use mathematics and mathematics thinking pattern in their daily life. But now, the number of teachers still employ one method to teach mathematics. They just use traditional method which only explain the material then giving the task to the student, and in the final they give the final exam to evaluate. Surely, it is not effective. So very important to the teacher to improve their teaching and learning method in order to help the students reach the standard competence and based competence. But, the most important is to help the student have the mathematics thinking pattern. Besides that, the professionalism of the teacher is need too. The teacher should have skill in teaching, managing the class, and evaluating the learning. Then, the teacher need to spread their knowledge about mathematics education and the teaching mathematics method.
  1. DEVELOPING TEACHING AND LEARNING PROCESS OF MATHEMATICS
The number of teachers in Indonesia still employ the traditional method in teaching and learning process. But, this method doesn’t make the student to be active. To change the teacher method need to change all that related in teaching and learning, there are several aspects such as:
1.      Lesson plan
2.      Student work sheet
3.      Small group discussion
4.      Various interaction
5.      Various teaching method
6.      Student’s reflection
7.      Cognitive scheme
8.      Student’s conclusion
9.      Apperception
10.  Assessment
11.  Various media
12.  Various teaching aids
This is the little essay about how to develop teaching and learning process:
1.      Lesson plan
Lesson plan is a teacher’s description of the course of instruction for one class. It developed by teacher to guide class instruction. Lesson plan is well if reflects interest and need of students. Lesson plan can be flexible as they adapt to student need and learning method. It should correlate with the textbooks are used in the class.
      Most lesson plan contain some or all of this element: the title, the time required to complete the lesson, the list of required materials, the list of objectives, an instructional component, the independent practice, the summary, an evaluation component, and a continuity component. If the lesson plan can accord with the student’s need than it can assist the teacher to give the learning.
2.      Student worksheet
It’s better that contain of problem to solve by student may be will there are many different solving from the student. In the process of solving the problem, teacher just as a leader. The teacher gives them the investigation steps to find the formula. From this, student can learn and find the concept by themselves. Direction between student and teacher can be formed. So, hope that students have new knowledge by themselves and doing selves. But there are some difficulties, such as there are a teachers that less understand to make student worksheet and every student have different ability to doing it so there are student that success to find the formula but there aren’t. so to giving the student worksheet maybe better if it doig in small group/ so the students can discuss with the others and change their arguments while the teacher as the leader and identify their difficulties.

Student worksheet has many purposes:
a.       Alternative for teacher to direct studying
b.      The studying activity can more faster
c.       Optimalization the teaching aids
d.      Improve the student motivation to study
3.      Small group discussion
It formed after the teacher explain a part of teaching contents. It consists of three or four students. This group is formed in order the student can discuss their problem, change their arguments and solve the problem together. It will make the student more active. In this small group we can solve the problem together. Teacher will approach them and try to identify their difficulties and offer solution. In the small group there are many different solving because avery student solve their problem based on yheir knowledge. So, they are will discuss to find the same concept. The result of discussion between one group and another may be different.
4.      Various interaction
Interaction is important in teaching and learning process. There are many interaction that can make by the teacher in their teaching. The various interaction will make the student feel comfort and enjoy. The various interactions such as: whole class, small group, and individual interaction. The whole class is happen when the teacher explained the material in the class. In here, there are interaction between the teacher and all of the student. The small group is when the teacher give the problem to solve their problem by discussion. So in the small group there are interaction between the student and other student also between the student and the teacher when the teacher identify their difficulties. The individual interaction is when the student presented their discussion’s result to another student.
5.      Various teaching method
The teaching method could divide by two parts. There are traditional method and modern method. In traditional method, the teacher just explain the material to student. After that, the student will giving the problem or the task to the student. To increase their ability, the traditional method the teacher giving them the drill. To evaluating the teacher just use the final exam. But in the modern method just as the facilitators that lead the student to uncover their knowledge. Because in the modern method, teacher doesn’t as a central, the central is the student. There are characteristics of the modern method:
a.       Explanation the material
b.      Giving the task
c.       Discuss the task in small group
d.      Identify the student difficulties in each group
e.       Offer solution
f.       Each group presents their worksheet
6.      Student’s reflection
This is a process of interpreting experience to obtain the new knowledge. After discussion in a small group, each group will perform their presentation. Between one group and another group will have different results so need to present the result in front of class. A student from one group present and explain their discussion result to another while another group give their opinion. So it will make the concept more complete. When the student explain in front of class, the teacher can observe their shortage. From this activity, student not only get a new knowledge but they can learn to communicate to their friends and to explain with another, and can learn to give their arguments. After all of group presented, the teacher together with student make a review about what the student understanding and then the student will make their own resume.
7.      Cognitive scheme
      Cognitive scheme is related with the order of the  material provide by the teacher. The order of the material will influence the student. If the teacher give wrong order, the student will difficult to understand. Because the next material is related to the material that teach now. So, before the student learn the next material they should have enough knowledge about the material before it. For example, before the student learn about integral, they should have enough knowledge about differential. Beside that the material should accord with the cognitive ability of the student. Because it will make the student easy to understand the material and don’t make them confuse.
8.      Student’s conclusion
      Student’s conclusion is he concept that form by student based on their knowledge that they get after they do investigation in their worksheet and discuss it. After student giving their presentation, teacher giving review to the student but in here, the position of the teacher as facilitator and lead them. In here, the teacher let alone to make conclusion about the learning. They will made conclusion based on their thinking so it more meaning for them and they can more easy to remember it. It will give the learn experience to the student.
9.      Apperception
      It means the readiness to study or to learn, the teacher develop it in order the student can get the material well. It’s not enough if the teacher just speaking in class. Apperception is to link the old knowledge with the new knowledge. The teacher try to dig the student’s potency by their teaching method.
10.  Assessment
                        It is to uncover the student understanding so to evaluate not enough from the final exam but do in beginning up to final, then, it will get the record that really accord with student condition. There are characteristic of authentic assessment:
a.       implemented during and after the learning process
b.      can be used for formative and summative
c.       which measured the skills and performance
d.      continuous
e.       can be used as feedback
f.       objective

11.  Various media
To support the teaching and learning in the class, the teacher use many kind of medias. It is make the process of learning fluent. The kinds of media such as: computer, LCD, whiteboard, etc. However, the media basically grouped into two parts, namely the media as carriers of information and media as a means of instilling the concept, such as the teaching aids. Altough the media don’t guarantee the succesfull the learning but it make fluent.
12.  Various teaching aids
To make the student easy to learn commonly a teacher use the teaching aids. It will make the material more real. The various teaching aids such as cube, cone, the number line, etc. Therefore in learning mathematics are often used the teaching aids. By using the teaching aids:
a.       The learning process motivated
b.      Abstract mathematical concepts in the form of concrete are delivered
c.       The relationship between abstract concepts with different objects in nature around more can be understand

  1. CONCLUSION
To help the student have based competence and standard competence so the teacher should improve their teaching and learning process. Teachers don’t employ one method but more. To develop the teaching and learning process related to develop such as :
  1. Lesson plan
  2. Student work sheet
  3. Small group discussion
  4. Various interaction
  5. Various teaching method
  6. Student’s reflection
  7. Cognitive scheme
  8. Student’s conclusion
  9. Apperception
  10. Assessment
  11. Various media
  12. Various teaching aids

PERAN INTUISI DALAM MATEMATIKA MENURUT IMMANUEL KANT

Posted on 06.22

By :Marsigit, M.A
Reviewed by :SitiNuruniyah/09301241023
According to Kant, the construction and understanding of mathematic is obtained by first finding "pure intuition" in the mind. Mathematics that are "synthetic a priori" can be constructed through the three stages of intuition, that" intuition sensing "," intuitive sense ", and" intuition mind ". Mathematics is a reasoning that is constructed concepts synthetic a priori in concepts of space and time. Pure intuition is the foundation of all reasoning and decision mathematics. Pure mathematics, especially geometry can be objective reality when it comes to sensing objects. Intuition sensing itself is a representation which depends on the existence of the object. So it seems impossible to find such a priori intuition, because a priori intuition not rely on the existence of the object.
Kant also argues that the propositions of arithmetic should be synthetic in order to obtain new concepts. If only rely on the analytical method, then it will not be obtained for new concepts. For example, if seen from the structure of the sentence, the statement "2 + 3 = 5" has "2 +3" as the subject and "5" as a predicate. Concepts contained in the predicate of the concept of five, not contained in the concept of "2 +3", namely that the subject does not contain predicate. This is according to Kant as synthetic principle in arithmetic. According to Kant, the concept of numbers in arithmetic obtained by the intuition of time. On the sum 2 + 3, 2 must precede the representation of representation 3, and 2 +3 precedes representation 5. To prove that 2 + 3 = 5, according to Kant, we must pay attention to what happened. Currently, given 2, as then administered 3 and the next moment again proved the result 5. Thus the concept of arithmetic found in the construction sequence of steps in the intuition of time. Kant's intuition connecting arithmetic with time as a form of "inner intuition", in order to obtain that intuition of time causes the concept of numbers became concrete in accordance with the empirical experience.
Intuition in Geometry, according to Kant, on the steps to prove that 2 is konkruen geometry, then the intuition that there must be a priori, and the steps are synthetic. If not, then acquired the concept and not merely empirical certainty apodiktik be obtained, namely that the procedure of proof is not clear. geometry is the science which determines the spatial properties of a synthetic but a priori.
Intuition in Decision Mathematics. According to Kant, the mind and intuition, the ratio held argument (mathematics) and combine the decisions (mathematics), namely awareness of the nature of complex cognition that have characteristics associated with the objects of mathematics, either through intuition or through the concept, encompassing both the concept of mathematical concepts on the subject and predicate, is a pure reason in accordance with pure logical principle, involving the laws of mathematics are constructed by intuition, and declare the truth value of a mathematical proposition. According to Kant, all decisions are a function of representation. "All Fs are Gs" is a decision that is universal. "F is G" is a singular decision. "Fs are Gs" is an affirmative decision. "There are no Fs are Gs", is a negative verdict. "Fs are non-Gs" was the verdict of infinite. According to Kant, all synthetic and the decision shall be based on intuition. So the truth of mathematics is not a truth of logic or truth or truth-based analytic concepts of truth but that is synthetic or truth based on intuition.

By :Marsigit, M.A
Reviewed by :SitiNuruniyah/09301241023
Di Indonesia, umumnya proses belajar mengajar di sekolah masih menggunakan metode tradisional, yaitu guru menjelaskan dan memberikan pertanyaan kepada seluruh siswa sehingga mereka hanya mendengar dan menyelesaikan pertanyaan tersebut. Berdasarkan kelemahan praktek proses pembelajaran tradisional di sekolah, banyak usaha yang telah dibuat Indonesia untuk meningkatkan pendekatan kelas dengan membuat peserta didik lebih aktif. Selain itu, pemerintah Indonesia masih berusaha untuk meningkatkan kualitas semua tingkat pengajaran dengan peningkatan kualitas guru, penyediaan fasilitas belajar dan peralatan, perbaikan kurikulum untuk pendidikan dasar, serta pengembangan dan pemanfaatan teknologi komunikas iuntuk pendidikan. Sehingga tantangan bagi para pendidikan dahulu untuk meningkatkan belajar siswa agar lebih tinggi kecakapannya dalamMatematika.Oleh karena itu, guru harus mengatur pembelajaran yang melibatkan para siswa sehingga mereka aktif membangun pengetahuan dan pemahaman mereka sendiri. Pembelajaran ini dapat berupa diskusi kelompok, baik dalam kelompok besar maupun kecil. Dengan adanya diskusi kelompok, siswa memiliki kesempatan yang lebih banyak untuk berbicara, mengembangkan jawaban mereka dan siswa lebih terlibat sehingga mereka cenderung kurang memiliki masalah dengan konsentrasi. Selain itu, guru juga bebas memonitor serta dapat mengatasi gangguan dan perilaku tanpa menghentikan pembelajaran di kelas.
Pembelajaran tradisional dapat dihubungkan dengan eksposisi guru yang rutin di kelas dan pengawasan guru di meja kerja. Adapun alas an mengapa metode eksposisi popular adalah sebagai berikut. Pertama, secara matematis rapi dan lengkap, pelajaran masing-masing berisi presentasi dan penjelasan Matematika yang mengarah kesebuah kesimpulan.Kedua, meningkatkan harga diri guru karena ia adalah sumber pengetahuan. Ketiga, guru dapat mendapatkan kepuasan dari menyajikan urutan pelajaran dalam silabus. Dan keempat, guru sendiri sering berhasil belajar Matematika dengan cara ini dan mengharapkan murid-muridnya untuk melakukan hal yang sama.
Cara pembelajaran Matematika yang efektif adalah dengan mengerjakannya dan memecahkan masalah. Selanjutnya, masalah Matematika disarankan untuk tidak hanya focus pada Matematika itu sendiri dan pada proses saat mencari solusi, namun hasil actual atau jawaban tidak boleh digunakan untuk tujuan apapun.
Apabila siswa ingin menerapkan konsep Matematika, pengetahuan dan keterampilan, maka mereka perlu mengembangkan keterampilan mereka dalam proses kegiatan Matematika: penalaran, mengorganisir, mengklasifikasikan, mengenalipola, dan sebagainya.


By :Marsigit, M.A
Reviewed by :SitiNuruniyah/09301241023
Keberhasilan proses belajar bukanlah bagaimana keberhasilan seorang guru sebagai informatory dan fasilitator tetapi bagaimana metode pengajaran yang digunakan dapat meningkatkan interaksi guru dan siswa serta peningkatan pencapaian hasil belajar.
Sampai saat ini, masih banyak siswa yang menganggap matematika itu menakutkan, sulit dan tak banyak dibutuhkan dalam kehidupan sehari-hari. Berbagai usaha telah dilakukan oleh para guru meningkatkan motivasi belajar matematika siswa, salah satunya adalah membuat proses belajar lebih menyenangkan dan terasa dekat dengan kebutuhan sehari-hari.
Perilaku siswa dipengaruhi oleh dua faktor, faktor internal dan eksternal. Faktor internal berasal dari diri siswa dan factor eksternal berasal dari lingkungan. Guru berperan sebagai factor eksternal, sebagai motivator siswa. Terlebih lagi ketika siswa berusia 12-15 tahun yang menurut Piaget berada pada fase berpikir operasi formal. Pada fase ini terdapat perubahan pola piker dari berpikir konkrit menjadi sesuatu yang abstrak, yang hanya didefinisikan oleh angka dan symbol.Peran guru sebagai motivator tidak hanya memberikan nasihat agar siswa belajar lebih giat, tetapi juga memberikan bantuan belajar sehingga siswa bias belajar lebih giat.
Optimalisasi penggunaan alat peraga dalam proses belajar mengajar diharapkan dapat membantu siswa dalam memahami hal-hal yang dianggap abstrak.
Ternyata dengan penggunaan alat bantu peraga seperti papan paku, gelang karet, kartu, kertas transparansi dapat meningkatkan motivasi belajar siswa. Banyak siswa yang mengangkat tangan ketika diberikan sebuah persoalan, dan juga terjadi peningkatan aktivitas/peran siswa di kelas.
Oleh karena itu, para guru harus selalu menggunakan metode pengajaran yang bervariasi untuk menghindari siswa merasa bosan dan juga menggunakan penggunaan alat bantu peraga untuk menjelaskan konsep dan ide.