PEMBELAJARAN MATERI PENENTUAN AKAR SUATU BILANGAN DENGAN CARA PEMFAKTORAN DI SMP (Sebuah Catatan PPL)

a.      Latar Belakang dan Alasan Pemilihan Masalah

Matematika seringkali diidentikkan dengan bilangan. Ketika kita berbicara matematika maka interpretasi masyakarakat umum adalah kita akan berbicara mengenai bilangan meskipun sebenarnya di dalamnya masih ada banyak pembahasan lainnya. Matematika dan bilangan menjadi sesuatu yang melekat erat.

Hal ini juga sesuai dengan tujuan pembelajaran matematika di sekolah. Dalam materi bilangan di sekolah terbagi menjadi beberapa sub bab. Mulai dari  operasi bilangan bulat, bentuk pangkat, menentukan akar bilangan bulat, hingga mengenai barisan dan deret. Dalam makalah ini tidak dibahas secara keseluruhan mengenai bilangan akan tetapi hanyalah pada sub-bab menentukan akar bilangan.

Materi ini merupakan sub topic operasi hitung bilangan bulat yang merupakan KD pertama untuk kelas VII semester 1. Kompetesi dasar tersebut adalah melakukan operasi hitung bilangan bulat dan pecahan. KD ini terbagi kedalam dua topik yakni operai hitung bilangan bulat dan operasi hitung bilangan pecahan. Di dalam operasi bilangan bulat ini termuat materi akar bilangan bulat yang akan dibahas dalam makalah ini.

MENJADI MANUSIA SUPER PENEMBUS RUANG DAN WAKTU

Refleksi 4 Kuliah Filsafat Pendidikan Matematika Prof. Marsigit

Oleh : Rosalia Hera NS (09301244003)

Menjadi penjelajah ruang dan waktu mungkin adalah sesuatu yang awalnya kita pikir hal yang mustahil. Cerita tentang penjelajahan ruang dan waktu ini nampaknya hanya kita saksikan dalam dongeng saja. Ia menjadi sebuah cerita fiktif dan menjadi angan-angan manusia saja. Ia menjadi sebuah potensi yang mungkin ada dalm kehidupan kita. Dalam angan kita, kita akan berangapan bahwasanya menembus uang dan waktu ini hanya dapat dilakukan oleh manusia super dengan teknologi super cangih pula yang samapai saat ini belum diketemukan oleh umat manusia. Padahal sebenar-benarnya kita telah menjadi penembus ruang dan waktu. Bahkan dari orang awam yang tidak tahu apa-apa, hingga batupun juga telah menembus ruang dan waktu.

Bagaimana hal ini bisa terjadi?

MITOS, dan BERFIKIR

Refleksi Perkuliahan Fisafat Pendidikan

Oleh : Rosalia Hera NS

P.Mat Bil’09/ 09301244003

Berfikir merupakan hal yang senantiasa berlangsung sepanjang hidup kita. Otak kita sebagai pusat dari sistem syaraf kita senantiasa berfikir untuk mengolah berbagai fenomena yang ada. Proses berfikir ini terjadi tidak hanya pada orang dewasa akan tetapi juga pada anak-anak bahkan yang baru saja lahir. Hal yang membedakan proses berfikir ini adalah kualitas dari proses yang dilakukan. Perbedaan inilah yang membedakan cara dan hasil pemikiran seseorang. Dengan seiring perkembangan psikologis seseorang diharapkan mampu untuk meningkatkan kualitas dari pemikiran seseorang.

Selain dari kualitas ini sebenarnya berfikir dapat dibedakan dengan seberapa jauh yang kita pikirkan, apa yang kita pikirkan dan bagaimana kita memikirkannnya. Tentuya setiap orang memiliki cara yang berbeda-beda. Saat kita berfikir kadang kita memikirkan sesuatu yang tidak kita ketahui dengan pasti. Yang demikian inilah yang disebut dengan mitos.

Mitos ini tentunya bukan sesuatu yang asing dalam kehidupan kita. Banyak mitos berkembang disekitar kita. Misalnya saja mitos yang ada di Yunani mengenai pelangi atau yang dekat dengan kita yakni mitos mengenai Nyi Rara Kidul. Mungkin pemikiran ini hal yang tidak dapat diterima akal pikiran kita jika hanya mengunakan panca indera kita tanpa mencoba mencari tau. Modern ini mitos-mitos tersebut diangap sebagai sesuatu yang salah padahal sebenarnya tidak semuanya dapat dipersalahkan. Mengapa demikian?

Siapa Namamu?

Refleksi ke-3 mata kuliah Filsafat Pendidikan Matematika

Oleh : Rosalia Hera NS

09301244003

Pendidikan Matematika Bilingual 2009

Siapa namamu? Tentunya dengan yakin dan mantap kita akan menjawab dengan nama yang sesuai dengan identitas kita yakni nama yang telah diberikan oleh orang tua kita. Namun hal yang mengejutkan terjadi ketika kita berada di kelas filsafat. Jawaban kita bukanlah jawaban yang tepat. Mengapa demikian? Hal ini disebabkan dalam pandangan filsafat kita senantiasa berubah. Kita satu detik yang lalu berbeda dengan kita saat ini. Oleh karena itu, nama yang kita miliki saat ini tidak mampu membedakan kita dari kita yang sebelumnya dengan kita saat ini padahal kita berbeda.

BERAWAL DARI TANYA

Refleksi Perkuliahan II Filsafat Pendidikan Matematika

Oleh : Rosalia Hera NS

09301244003

P.Mat Bilingual 2009

Berawal dari tanya perkuliahan kali ini dimulai. Diawali dengan mencoba mengali berjuta tanya yang ada dalam benak. Hal ini sejalan dengan refleksi sebelumnya yang berjudul mengali dalam tanya, untuk memulai belajar berfilsafat hendaknya kita memulai dengan sebuah pertanyaan yang kemudian kita renungkan jawabannya. Namun disini sedikit berbeda, dalam perenungan menemukan jawaban kami dibantu oleh bapak Marsigit, MA dengan cara memberikan penjelasan jawaban atas pertanyaan-pertanyaan yang muncul dari benak kami yang kemudian menstimulus kami untuk berfikir lebih dalam lagi.

Berawal dari pertanyaan-pertanyaan yang muncul dari masing-masing mahasiswa menjadikan proses diskusi menjadi berkembang. Berbagai jenis pertanyaan bermunculan dari yang cukup mengelitik hingga yang cukup membuat berfikir dengan keras. Dari pertanyaan-pertanyaan ini membuat kami kembali berfikir, kembali merefleksikan. Membuat kami belajar tentang filsafat yakni dengan berfikir reflektif, berusaha menerjemahkan dan diterjemahkan.

Mengali Dalam Tanda Tanya (Sebuah Pengantar)

Refleksi 1 Mata Kuliah Filsafat Pendidikan Matematika

Oleh : Rosalia Hera NS

NIM. 09301244003

P.Matematika Bilingual 2009

Ketika kita mendengar kata filsafat pastinya semua orang memiliki pengertian yang berbeda-beda. Banyak orang yang berfikir bahwa ia tau apa itu filsafat namun sulit untuk mengungkapkannya kedalam kalimat-kalimat yang sistematis. Banyak pula yang memiliki asumsi yang salah mengenai hal ini. Secara umum banyak orang yang berangapan filsafat merupakan hal yang rumit dan cukup membuat kita ‘kebingungan’. Selain itu, banyak yang berangapan bahwa filsafat merupakan makanan bagi orang tua. Hal itu bukanlah asumsi yang salah namun kurang tepat karena filsafat juga dapat dilakukan oleh semua orang akan tetapi levelnya berbeda.

TO BE A PROFESIONAL TEACHER

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TO BE A PROFESIONAL TEACHER

By : Rosalia Hera Novita Sari

NIM : 09301244003

Class : Mathematics Education 2009

A. INTRODUCTION

Now days everything develop and move forward including education. The development makes all aspect of education need to increase their quality. Not expect for teacher. Teacher should develop their professionalism also. And in order to do that, there are some items that needed to do. One of them is make a scientific publication.

We, as the next generation of mathematics teacher also need to study that one as one of the steps to preparing our professionalism. Its also same as the government want that the student that wants to graduate from the university should publish their journal. Because of that there is no reason for us to didn’t studying about the scientific publication.

The scientific publication here refers to the publication of our scientific paper. That the paper have some properties that should be done. The paper should based on the theories/reference or base on the fact or data in the reality. Another that there are also the other properties that will be discuss here.

DEVELOPING THE DESIGN OF INNOVATIVE TEACHING LEARNING PROCESS

DEVELOPING THE DESIGN OF INNOVATIVE TEACHING LEARNING PROCESS

By : Rosalia Hera NS

09301244003

Mathematics Education 2009

Education was so important for our life. By the education we can develop the people resources. And when we have good resources we can apply it to develop our life or the other aspect in our life. As what written in the aim of our country, one of them is to make the people’s life smart. And in order to realize that there are many activity or programs that developed continuously by the government or the education exert. But whenever we talk about education we can’t forget about the teaching learning process. It was the main activities that cover or contain all part of education. Or we can say that teaching learning process was the tools or ways to realize the aim of education.

Our governments also understand about the urgency of teaching learning process. As one action to show that the governments try to arrange the curriculum. The curriculum was developed for time to the time and now days we use the KTSP curriculum. Based on the GOI the direction of education was change from the center into the province and more specifically in the school level. The governments just give the sign of the standard of competency that should be past by the student. The standard competency expanded into some basic competency also. Then the teacher in each school can improve and developed in order to raise the competency that expanded into some indicators. The developing and also the improving should be according to the student condition and the environment of student. And hopelly the teachers can present or show the innovative teaching learning that needed to realize the goals of education now days.

And in order to create the innovative teaching learning process there are needed some steps start from the preparation until the reflection. To prepared it teachers should seen some aspect such as the theory, paradigm, ideology, approach, design, method, and also the material. There was some example approach or design that can be implement by the teacher in their teaching learning process. They are constructivist, realistic mathematic, problem based learning and cooperative learning.

The constructivism approach means that the teaching learning process should be in order to construct the student knowledge not just a transfer of knowledge. When ever teacher applied that in their teaching learning the student can construct their own knowledge and the student will be understand it well and the not just remembering that. So the knowledge can be saved for a long time.

Then the realistic mathematics was an approach that based on opinion that mathematics is our daily life. This method was developed in many country such as USA and Japan. The realistic mathematics wants make the student easily to understand the material. According to Freudenthal(in Siti Ummu, 2009) mathematics should start from human activity because Mathematics is a human activity. So in this approach the teacher should bring the material nearest to the student daily life. Its also help the student to imagine the abstract mathematics into the real one.

In problem based learning the student start the learning from a problem. From here they develop their own creativity to solve the problem and also develop and build their own knowledge. And in cooperative learning they can collaborate or sharing each other to develop their knowledge.

Then to implement the approach we can use some method such as discussion method, inquiry method, investigation, practical work, individual work and problem solving. All of the method wants to created the student self. Where the student can develop and build their own knowledge. Its same like what Mehl-Mills-Douglass said (in Oemar Hamalik. 2001 : 172) : “one learns only by some activities in the neural system: seeing, hearing, smelling, feeling, thinking, physical or motor activity. The leaner must actively engage in the “learning”, whether it be of information a skill, an understanding, a habit, an ideal, an attitude, an interest or the natural of a task. ”

The other aspect in preparation that needed to be pay attention was the material. The material consist of the lesson plan, student worksheet, hand out, text book and media or teaching aid. All of them needed to be prepared before the teacher teach in the class. All of the material should support the method that use to give an opportunity to the student to develop their own knowledge.

After the preparation we need to implement that. And to do implement it there was a lot of thing that’s needs to pay attention by the teacher. They are developing and implementing lesson plan; apperception; Various method of teaching, media or teaching aids, interaction; schema for achieving student competency, small group discussion, student reflection, student worksheet and assessment.

In the teaching learning process can be also call as the time to observation. When the teaching learning happened, it’s also can be observed how was the teaching learning. Is it like what we panning before? Is there any less? Is there the effective teaching learning etc. ant the data from here can used to reflected the teaching learning process. The reflection needed to planning the next activity of teaching learning. The evaluation can construct the next teaching learning process. The reflection can be give from the teacher, the observer. The reflection also can be a summary of the teaching learning process. Hopelly by using that steps the teacher can be batter and batter to develop the design of innovative teaching learning process.

Reference :

Hamalik, Oemar. 2001. Proses Belajar Mengajar. Bandung : Bumi Aksara.

Kultsum, Siti Ummu. Penerapan Pendekatan Matematika Realistik Untuk Meningkatkan Pemahaman Siswa Terhadap Konsep Bilangan Bulat (Penelitian Tindakan Kelas terhadap Siswa Kelas VII-E SMP 2 Banjaran Kab. Bandung). (On Line). In : http://matematika.upi.edu/v2/index.php?option=com_content&view=article&id=32:penerapan-pendekatan-matematika-realistik-untuk-meningkatkan-pemahaman-siswa-terhadap-konsep-bilangan-bulat-penelitian-tindakan-kelas-terhadap-siswa-kelas-vii-e-smp-2-banjaran-kab-bandung&catid=14:pendidikan-matematika.

TWO POLE IN TEACHING LEARNING PARADIGM

Rosalia Hera Novita Sari

09301244003

Mathematics Education 2009

A. Introduction

Time has been change. Not just that anything in our live also moving forward. There was a lot of thing that change not only in technology but also in how people life and the paradigm including in education. Education was perform a dynamically changes. The change based on the experience from the educational expert. Not just that it’s also based on an analyzing the fact in the environment of education.

The education developed in many aspects. Including teaching learning process as the main activities in education. Teaching learning process also developed from the traditional one to the innovative one. Although there was moving forward many teacher still use the traditional method or paradigm in their teaching learning. The paradigm developed from the transfer of knowledge into the teacher as the facilitator. There were many differences between two paradigms. And to identify them, we can see from the characteristic.

B. Discussion

As what we discuss before there was two pole of teaching learning paradigm that appears now. They were the traditional one and also innovative one. Each other have a different characteristic. Its can be look from the example that perform in the teaching learning process, the activity, the programs, the models, the scheme, etc.

In the traditional teaching learning, education was an investment for the future. But in the innovative one, education was something that we needed. Based on that we can said that in the traditional one education was prepared we to survive in the future. We feel that learn was a demand that we should do. Its effect we didn’t enjoyed it. Different with that in the innovative one, education was a needed. So we have more motivation to learn it. We can more enjoy the process, and do as well as we can do because we need it. Not just for fulfill the duty but to fulfill our needed. Its will be sound more interesting than just as a duty.

Another that, in traditional it’s was a behaviorism paradigm and in the innovative one there was a constructivism. In the traditional one, the aim of teaching learning is to make or construct the behavior of students. And the learning was a behavior. Different with that in the constructivism the aim of teaching learning is to construct the student knowledge. So that, they can develop their own knowledge not just bounded with general knowledge. It’s more facilitated the diversity of student than in the traditional one.

The difference was not only two aspects before but also in the paradigm and theory. In the traditional one teaching learning was in order to transfer the knowledge and as we discuss before the innovative one wants to construct the student knowledge.

Another that in the traditional one the teacher was the supervisor but in the innovative one the teacher became a facilitator. So here we can say that the traditional the teacher become the center of learning and in the innovative method student was the center of learning. There was also the difference in the religion and philosophy aspect. In the design, scheme and models also different.

C. Conclusion

There was two pole of teaching learning process. They are traditional and innovative teaching learning. They have many differences from many character such as the paradigm, theories, design, scheme, models, programs, activities and example.

COMPLEXITY OF TEACHING LEARNING MATHEMATICS

By : Rosalia Hera NS

NIM : 09301244003

Class : Swadana Class of Mathematic Education 2009

A. Introduction

Education was so important for our life. By the education we can develop the people resources. And when we have a good resources we can applied it to develop our life or the other aspect in our life. As what written in the aim of our country, one of them is to make the people’s life smart. And in order to realize that there are many activity or programs that developed continuously by the government or the education exert. But whenever we talk about education we can’t forget about the teaching learning process. It was the main activities that cover or contain all part of education. Or we can say that teaching learning process was the tools or ways to realize the aim of education.

Maybe when we hear about the teaching learning process we will tough it’s easy. But when we look deeper it’s was so complex. There was many factor or aspect in teaching learning process that needed to understand by us. All aspect such as interaction and teaching method had a contribution to determine the teaching learning was success or not. All of that’s component was related each other and make a complex relation. No one aspect could be ignored by us. Not except in mathematics. Although it’s have the different characteristic with the other subject but generally it’s also contents many important aspect.

B. The Complexity of Teaching Learning Mathematics

Such as was explained before there are many aspects in teaching learning process. They are student, teacher, interaction, education facilities, media, teaching method, psychology aspect etc. all of that aspect need to look deeper to realize the innovative teaching learning in order to catch the aim of that.

1. Student and Teacher

Student and teacher, when we discuss about them we should understand that the main rule of teacher here are as the facilitator. The teacher should facilitate the student to develop their own creativity. And in order to do that teacher needed to implement and develop the other aspect of teaching learning too.

2. Interaction

Interaction is a kind of action that occurs as two or more objects have an effect upon one another. Interaction is also needs in teaching learning activity. In the tradition method of teaching learning, the learning was dominated by the teacher and the student has been the passive learner. The communication just in one direction, but in the innovative teaching learning, there are needs an interaction between the student and the teacher. When the student active they will be more interesting to follow the lesson.

There are some types of interaction that can be use in teaching learning activity. First whole class interaction. The second type is group interaction. By using the second interaction teacher can more satisfy what the student need. The last is individual interaction. It’s mean that there the interaction just between teacher and one student or student and student. Another that the interaction also can made from the student with the school component and environment.

3. Educational facilities

Education facilities influence the confidence of the student whenever they ware studying. Although it’s not the main aspect that must be fulfill but it’s influence the teaching learning process. Because we realize or not the confidence is influence our psychology and it’s influence us to understand the material. The examples of educational facilities are whiteboard, table, and chair.

4. Teaching Aids and Media

All of we knows that mathematics was an abstract subject and not all student have a good abstraction. Because of that we need to help them to understand the abstract object with something that real. Another that by using the media and teaching aids there was a lot of advanced. Such as makes the student more interesting to pay attention and easily to understand the material.

5. Teaching method

Whenever the teacher want to held the teaching learning process they needed to create a strategy to teach or we can call it the teaching method. Teaching method is ways to teach that can be applied in the learning process in all subjects. Teaching method used to make the learning process more effective and efficient. There are no right methods that can be implemented in all condition. The specific method just can be right for several conditions. Because of that, teacher needs to developing and implementing various methods in their teaching according the conditions of the student.

6. Psychological aspect

Our body consists of two aspect physic and psychology. They also influence our concentration. When ever one of them was not good our concentration will be also not good. Because of that, them needed to be getting attention. Another that the psychological aspects also determine how does the studying type from a student and also the level of the understanding.

7. Context of teaching learning

The context of teaching learning was an important one because it determined the culture of them. The culture will be determine the methods, the attitude etc in teaching learning that should be use in order to help student developing their own knowledge.

8. Lesson Plan and syllabi

They were one of the main components in teaching learning process. Lesson plan giving the teacher direction how to held the teaching learning process in a specific times. But syllabi giving more generally direction for the teaching learning process in each semesters. Or we can say that from syllabi we expand it into lesson plan.

9. Student Worksheet

Student worksheet was an innovative tool that can be implement in the teaching learning process. Student worksheet is a collection of problem that given by the teacher to the student that related to the topic. But its not just an arbitrary collection. The student worksheet must be consists of the problem that by doing this the student can construct their own knowledge. Another that there are some steps that’s given in order to direct the student solve problem or gets new material. It’s one of the media of teaching learning and also one way to facilitate the student.

There was several benefit of using worksheet in teaching learning process. They are student can work independently and for teacher worksheet can use to develop a wide range of activity that can use to learn. By this way hope student can find the material or concept by their self. So they can more understand because it’s based on their own experience.

10. Assessment

The assessment should held in the process of learning not just in the end of teaching learning process. Educational assessment is the process of documenting, usually in measurable terms, knowledge, skills, attitudes and beliefs. The term assessment is generally used to refer to all activities teachers use to help students learn and to gauge student progress. Though the notion of assessment is generally more complicated than the following categories suggest, assessment is often divided for the sake of convenience using the following distinctions: formative and summative, objective and subjective, referencing (criterion-referenced, norm-referenced, and ipsative), informal and formal.

11. Technology

As we know that in this era technology was moving so fast. Because of that we needed to follow the development. Another that its also can help the teaching learning process.

Another that there are the other aspects that also effect the teaching learning process. And to implementing them we need to correlate them in to one framework of teaching in order to catch the aim of education.

C. Conclusion

There was a lot of aspect in teaching learning mathematics that need to pay attention by the teacher and education care. They was an important aspect but they can walk alone. They need to collaborate and related each other to realize the trued teaching learning process. It’s also made the mathematics is complex not only in the material but also in the teaching learning process.