How to Develop Teaching Learning Process of Mathematics in Junior High School/Senior High School How to Develop Teaching Learning Process of Mathematics in Junior High School/Senior High School

          

By : Rosa Ardiyati (09301241032)

Regular Mathematics Education 2009

Mathematics Education Department, Faculty of Mathematics and Natural Science

Yogyakarta State University

Learning Mathematics means doing Mathematics itself. In order to do that as a teacher has a big role in bringing the students to some kind of atmosphere so that the student can enjoy their time while they learn Mathematics. There a many things that should be concerned by a Mathematics teacher so that teaching learning process can be done perfectly.

In developing teaching learning process, at least there are many things that must be concern by the teacher. Those are lesson plan, student’s worksheet, small group discussion, various interactions, various teaching methods, various media, various teaching aids, student’s reflection/ presentation, cognitive scheme, student’s conclusion, apperception, and the last is assessment. All of those things are important to the learning process because of they include the process from the beginning of the lesson (making the plan: lesson plan) until the end of the lesson (assessment, e.g. presentation, exam, etc). Furthermore, speaking of the development of the teenager (we can say in junior or senior high school’s age), it needs many stimulus to improve their way to think. And it include the way to think in learning Mathematics. We can’t apply the same way of teaching Mathematics like when they are in elementary school. Their brain has improved. And that’s means we as the teacher have to improve our teaching learning in order to help them to improve their mind.

These are some explanations about things to develop in order to teaching learning process of Mathematics, especially in junior or senior high school.

1.      Lesson Plan

Making a lesson plan is the first step in teaching learning process. And it’s a important step actually, because it consist of the whole plan of the teaching learning process. In formal description, we can say a lesson plan is a teacher's detailed description of the course of instruction for one class. First thing about lesson plan is it’s for only one class which is usually not be concerned by most of the teacher. Most of the teacher uses the same lesson plan to different classes. Each class have different potential and skill, so the teacher should make a different lesson plan.

There are few elements in lesson, those are title of the lesson, time allocation, the list of the material, or sometimes we can also write the standard competence and the basic competence before it. Also we have the list of objective (behavioral and knowledge objective) which is we call it indicators, the instructional component, the summary of the materials, and the last is evaluation. All of those elements are important to help the teacher manage the lesson. And it can be seen as the directive when the teacher do the lesson.

There are many benefits in making lesson plan, those are the learning process become more manageable because the teacher already planned it well, and through lesson plan the teacher can share their ideas to another teacher, the lesson can be well prepared, so the lesson can run efficiently and many other benefits.

Furthermore, in order to improve the student’s skill, good lesson plans also have to focus on what student need. What they need so they can improve their skill and knowledge, especially in learning Mathematics. And don’t forget to make a note while and after the lesson (as a teacher), so that the teacher can evaluate whether the lesson plan is good or need to be fix in some element, so the next session of the lesson can be better.

2.      Student’s Worksheet

In senior high school and junior high school, the student already familiar with student’s worksheet. Even in elementary school, the student already has given this worksheet. Most of the teachers use this worksheet; prove the importance of this worksheet in developing teaching learning, especially in learning Mathematics. The student’s worksheet usually contains a lot of exercises, so that the student can improve their knowledge after the teacher explains the material.

3.      Small Group Discussion

Every student in a class is unique. So there is no 2 student that exactly have the same skill, potential and talent. That makes the teacher has to find a way to make this heterogenic class still become efficient in teaching learning process. The teacher can do that through small group discussion. In small group discussion the teacher split the class into many group that each group only consist of 3-4 people, so that every student can communicate effectively to another in their group. Then the teacher gives them some problem or topic to be discussed. It will be different if the teacher does this in whole class method. In whole class or classical method the student tend to be more individually in solving the problem, whereas the students also need another idea to help them in solving the problem. Or maybe some students who have less understanding about the problem can be helped by sharing the problem by their peer in small group.

4.      Various Interactions

There is one thing that very important in learning process, in this case is learning Mathematics. That is interaction. Every learning process involves interaction in the process. The traditional way of teaching uses one interaction. That is the teacher to the whole class, which is called classical interaction. There are many other ways to interact in learning process. Those are student to another or we called it peer to peer, this interaction makes them possible to interact with their colleagues. And there is interaction between some students (in a small group) to the teacher, this interaction usually used in small group discussion, so that the teacher can communicate with the student more efficiently. These various interactions should be used in order to make the whole lesson more interesting for the student. Because using one single interaction in whole time might make them bored and barely improved.

5.      Various Teaching Methods

Every material in Mathematics needs different approach so that the student can understand it well. That means the teacher should employ different teaching methods in the learning process. In the traditional learning method, the teacher only use one one single methods, that is expository method. The teacher explains the material, giving some example, then exercises or homework, another explanation and then exam. That makes the student become passive.

First method is lecturing. Sometimes there are materials that can be better if it’s explained by the teacher itself than using another method. Usually the teacher use this method to teach some topic that hard to understand or we can say it advance.

The second is presentation. The subject of the presentation is not the teacher, but the student. In this method the teacher help the student to construct their ideas about the topic so that the student can make a presentation about the topic. This method can acknowledge the speaking skill of the student and also how they share their ideas to another. Usually this method can be used in some topic that easy to understand. So that the student can learn from textbook or other sources without teacher’s help. But the teacher still has responsibilities, that is at the end of the presentation the teacher make a short conclusion about the presentation and explain some addition information about the topic and explain it if the is something wrong about the material of the presentation.

The third is demonstration and experiment. In mathematics learning doing this method may need more expenses due to the teaching aids that we need. But using this method really helps the student to understand the topic. The students need to make visualization about the topic. And doing demonstration and experiment help them to do that. The topic that usually needs to be demonstrated for example is geometry, probabilities, Cartesian diagram, and many others.

The fourth is problem solving method. First step to do this method is the teacher gives the student a problem or some problem that can be solved by their own ways. Of course the difficulties of the problem should be suitable by their knowledge. Then every student must be has different ways to solved the problem. And at the end of the lesson the teacher teach the formal way to solve the problem. Thus the student can understand the topic more meaningful.

And actually there are still many other methods that can be employed in learning Mathematics. And those methods can be hold in different meeting so that the students become more creative and not only focus on one way to learn Mathematics. Use different methods in learning also prevent student from boring.

6.      Student Reflection/ Presentation

Student reflection or presentation should be hold in order to develop mathematics learning. Reflection make the student can understand the material deeply, beside just listening what the teacher explain. And present their work can help them to improve their speaking skill and can make the whole class become more active.

7.      Cognitive Scheme

Cognitive scheme is one of the things that should be concern by the teacher. Without that scheme the knowledge that the student get won’t be contextual. We can say the application of cognitive scheme is making a mind mapping. Thus, the student can make a mapping about what they have learned. And one thing that’s necessary about cognitive scheme is the teacher should begin the learning from what the students know, then develop it to what should they know, and how could they know.

8.      Student’s Conclusion

At the end of the learning process, what students know is the most important result of the learning. Because learning is about teaching the students from don’t know the topic become knowing the topic. So student’s conclusion is really matter in the learning process. What teacher should do in order to make the student make a proper conclusion after the learning process is make a good plan in every lesson. Then in the learning process the teacher should not be too dominant, so that the student can have their time to conclude with their own ways.

9.      Apperception

What is apperception? Apperception means readiness. And who should be ready? That is the student. The teacher’s role here is to help the student to construct their mind so that they can be ready for the topic. One important thing about construct the student’s mind is the teacher should begin from what they know before the teacher introduces them to the topic.

For example the teacher gives few questions that lead to the topic. So the teacher can acknowledge the understanding or how far the students know about the topic that will be learned. If the lesson has much time allocation, the teacher can hold the apperception to be better one. For example in topic calculate the area of a arbitrary rectangle. First, the teacher gives them the problem. And the students should solve the problem by their own way. This method can construct their ideas, because every student will have different point of view in solving the problem. Maybe it will be better if the class is split into some group, so the student can share their ideas to another. And the teacher move around the class so he/she can help the student, maybe by giving them hints in solving the problem. After few minutes some of the student come forward to the class and present their work. By this, the other student can find that there are many different ways to solve the problem. Then at the end of the lesson, the teachers teach them the proper way which is more efficient to solve the problem. By doing this apperception, the students are not only get their knowledge one way from only the teacher, but also through their ideas, then it will be completed by the explanation of the teacher.

10.  Assessment

Assessment means to record or we can say evaluate. Assessment holds from the beginning of the learning process. Usually the teacher only holds the evaluation at the end of the lesson. Whereas the process of the learning also important. Doing the assessment means make a note for the whole class and each student (individually). The way to evaluate the student can be through exam, student’s presentation and demonstration, paper, homework, and etcetera. The benefits of the assessment for the student actually are for evaluate their improvement in learning, and for the teacher is to evaluate the process of learning, whether it has already well or need to be fixed in some element.

11.  Various Media and Teaching Aids

There are a lot of media and aids to developing mathematics learning. In conventional method, the teacher only uses few media that is blackboard and textbook. In this way of learning the student tend to think that the knowledge is only come from the teacher, which is wrong. In this modern era, the media of learning can be various. There are LCD, aids, internet, group discussion, seminar, and etcetera. Through LCD, the teacher can use some PowerPoint presentation, Flash Presentation, Video, or just few images to help the student improve their knowledge and understanding the topic. Not only media, but there are teaching aids which is also important. Teaching aids can be some homemade craft or some aids already have been provided in some store. These teaching aids help the student visualize the topics. Because sometimes there are some topics that hard to understand if the student are not see it as a real thing, and that the benefit of the teaching aids.

Learning Mathematics and maybe it satisfy by other subject, is about the process of the learning. We can’t concern in only few part of the process. For example only focus on the assessment and worksheet. If we just concern with only few of that process it means that the learning won’t be done well. The student can’t reflect their ideas while the learning, because the teacher doesn’t really concern about student’s reflection/ presentation. The teachers just use the conventional ways to do the learning. And that is teacher center, which is not suitable anymore to be done in this modern era. Because now we already have the new international trend which is student center, so that teacher employs various ways to teaching and the role of the teaching is not as the only source of knowledge but as the one who helps the students to understand the knowledge through many things.

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.