PURSUING GOOD PRACTICE OF SECONDARY MATHEMATICS EDUCATION THROUGH LESSON STUDIES IN INDONESIA

By Dr.Marsigit,M.A

Reviewed by Fitria Yelni (http://fitrialikemath.blogspot.com)

Hasil studi yang berlangsung tahun 2005 tentang Lesson Study menyebutkan bahwa telah terjadi perbaikan dalam hal pengajaran matematika. Praktik pengajaran matematika akan menjadi bermakna jika menerapkan dan mengembangkannya berdasarkan lingkungan yang dialami siswa dan berbasis pada kehidupan sehari-hari, tidak hanya bersifat teori saja. Kenyataannya kegiatan pembelajaran matematika di Indonesia masih didominasi oleh guru sehingga perlu diterapkan metode pengajaran baru yang lebih fleksibel agar siswa dapat mengeksplorasi bakatnya serta membangun pengetahuannya sendiri. Paradigma tentang guru yang sebelumnya disebutkan mengajar sekarang harus diubah menjadi belajar, maksudnya adalah siswa dan guru sama-sama belajar. Sumber belajar tidak hanya dari guru saja. Dengan kata lain guru tidak lagi sebagai pentransfer ilmu, tetapi sebagai pembangun pengetahuan siswa.

Sayangnya hal di atas tidak diimbangi dengan kurikulum yang ada. Kurikulum masih teralu padat dan terdapat ketidakcocokan antara kurikulum, tujuan, dan sistem penilaian pendidikan. Dari masalah-masalah di atas, maka dilaksanakan Lesson Study, di mana para guru bekerjasama dengan dosen dan ahli dari Jepang. Tujuannya adalah untuk mengubah paradigma tentang belajar sebagai suatu kegiatan sepanjang hayat dan untuk meningkatkan perbaikan dalam bidang pengajaran, terutama matematika. Dari kegiatan Lesson Study dapat disimpulkan bahwa guru merasa pembelajaran kelasnya semakin hidup, lesson study mampu meningkatkan keterampilan guru dan guru terdorong untuk lebih memahami inovasi-inovasi baru dalam pendidikan. Bagi siswa, siswa merasa antusias dan terlibat aktif dalam pembelajaran, adanya kegiatan di laboratorim menjadikan siswa lebih memahami materi dan meningkatkan keterampilannya. Namun dalam penerapannya masih terdapat beberapa kendala, yaitu perlunya adaptasi bagi guru sebelum mengajar, terdapat perbedaan persepsi antara guru dan dosen tentang paradigma baru, dan banyaknya siswa dalam satu kelas membuat guru tidak mampu memenuhi semua kebutuhan siswanya.

Berdasarkan uraian di atas, maka saran bagi kepala sekolah adalah mempromosikan berbagai metode pembelajaran, memberi kesempatan kepada guru untuk mengembangkan kelasnya, dan melakukan kerjasama dengan lembaga pendidikan lainnya. Sedangkan pemerintah perlu menciptakan kurikulum yang lebih sederhana, mendefinisikan kembali peran guru, kepala sekolah, sekolah, dan pengawas, serta menciptakan sistem penilaian yang baik.

“LOOKING FOR ALTERNATIVE MODELS IN REFERENCE TO JAPANESE EDUCATIONAL EXPERIENCES” MATH PROGRAMS FOR INTERNATIONAL COOPERATION IN INDONESIA

By Dr.Marsigit,M.A

Reviewed by Fitria Yelni (http://fitrialikemath.blogspot.com)

Secara umum, sistem pengajaran di Indonesia masih terpusat pada guru, sehingga siswa cenderung pasif. Untuk mengatasinya, diperlukan peran guru untuk meningkatkan keterampilan siswa, terutama dalam matematika. Hasil studi menyebutkan bahwa prestasi siswa dalam matematika masih cenderung rendah. Banyak hal yang menjadi penyebabnya, seperti dari pendidik masih banyak input pendidik yang memiliki potensi rendah, guru kurang memahami kurikulum, guru masih menggunakan metode konvensional, dan menggunakan satu buku acuan yang dianggapnya paling baik karena diterbitkan oleh penerbit tertentu. Dalam hal penilaian, guru cenderung menilai siswa dari aspek kognitif saja, dan sangat jarang bahkan ada yang melupakan aspek-aspek lain seperti afektif dan psikomotorik siswa.

Upaya untuk menanggulangi masalah di atas adalah dengan membentuk kerjasama, seperti JICA sebagai contoh bentuk kerjasama Indonesia-Jepang. Bentuk kerjasama tersebut berupa mengadakan uji coba (piloting) yang mengacu pada pengembangan instrumen, metode pengajaran, model bahan ajar, dan sistem evaluasinya. Dari haisl uji coba tersebut, siswa mengalami peningkatan prestasi, guru juga mendapatkan pengalaman sehingga dapat menerapkan metode pengajaran yang lebih bervariasi, seperti memberikan kesempatan kepada siswa untuk membangun pengetahuannya sendiri. Sayangnya, semua itu perlu proses sehingga tidak mungkin guru berpindah metode pengajaran secara instan.

Sedangkan pembelajaran matematika di Jepang lebih mengau pada keterampilan dan kemampuan siswa. Guru lebih menekankan pengajaran dan pemahaman dibanding perhitungan dengan mengutamakan siswa yang harus aktif. Di Jepang terdapat komite yang mengawasi penggunaan buku teks/ bahan ajar. Di Jepang, penilaian dilakukan dengan cara pemeriksaan dan pengamatan terhadap kegiatan siswa dan memperhatikan kesalahan siswa. Gaya mengajar di Jepang didasarkan pada pemecahan masalah. Jepang juga menggunakan penelitian tindakan kelas sebagai alternatif peningkatan mutu pembelajaran, yang bekerjasama dengan professor dari universitas.

Hal positif dari Jepang yang dapat dicontoh antara lain:

1.     Rata-rata kemampuan guru dan kualitas kelas relatif tinggi

2.     Desain pengajaran yang tepat

3.     Lingkungan dan kondisi pendidikan cenderung homogen

4.     Guru yang rajin

5.     Prinsip kesetaraan

6.     Tanggung jawab guru yang tinggi

7.     Adanya perpindahan guru ke sekolah lain dalam jangka waktu tertentu.

KEGIATAN PENELITIAN SEBAGAI USAHA UNTUK MENINGKATKAN PROFESIONALISME GURU MATEMATIKA

By Dr.Marsigit,M.A.

Reviewed by Fitria Yelni (http://fitrialikemath.blogspot.com)

Mathematics learning research is consists of qualitative research and quantitative research. Quantitative research view that study mathematics can be measured. Whereas qualitative research, it’s observe about of mathematics learning process and the environment of mathematics learning. Mathematics learning can be drawn in hermeneutic cycle. Hermeneutic cycle show that mathematics learning and it’s components are interrelated.

There are two factors of practice mathematics learning, that are the learning and the value. If teacher want to construct education systematically, he/ she can use historical research. There are many research, such as descriptive research, it is to describe the situation and the events of mathematics learning. Development research is to investigate the growth of students. All of them need regularly plan so the research can be success.

Perception about mathematics character is influence of mathematics learning. Students don’t like mathematics because of the mathematics learning method. So, teacher’s role is very important. How to manage class is a part of teacher’s role. In Elementary School, Junior High School, and Senior High School the materials of mathematics are facts, concepts, logic, algorithm, problem solving and investigation. Shigeo Katagiri (2004) say that mathematics in school consists of attitude, method, and content. To apply that, teacher must to provide or make an interesting class, use various methods, and understand students’ characteristic.

To make a change of mathematics education, mathematics research is important. So before the class is begins, teacher should to:

1.     make a mathematics environment plan

2.     develop students’ social environment

3.     make mathematics activities plan.

Mathematics Teaching Across Multicultural Context

A. Introduction

Mathematics teaching is something familiar to all who engaged in the world of education, especially mathematics education, not least also in other parts of the world. Talking about mathematics teaching, with regard to how the teaching activities of teachers in building students' knowledge in order to set up such knowledge can be absorbed, embedded and applied in solving daily problems related to mathematics. Each country with each culture has its own paradigm of all things, including about mathematics teaching. The paradigm is what makes mathematics teaching in each state has the different context.

B.           Australian Context

In the Australian context, mathematics teaching is not only aims to teach students about how to solve the problem, but also able to bring it to critical thinking and independent thinking to understand the math problems they face. In teaching mathematics, teachers need to better understand the mathematical thinking to create better learning plan and organized. This relates to the determination of learning activities, learning materials, the expected student responses and student responses that may arise in mathematics learning that held.

It is helpful for teachers to consider that solving problems with mathematics requires a wide range of skills and abilities, including:

(1) deep mathematical knowledge, (2) general reasoning abilities, (3) knowledge of heuristic strategies, (4) helpful beliefs and attitudes, (5) personal attributes such as confidence, persistence and organization, and (6) skills for communicating a solution. There are four fundamental processes, in two pairs, and showed how thinking mathematically in mathematics teaching very often proceeds by alternating between them:

• specialising - trying special cases, looking at examples

• generalising - looking for patterns and relationships

• conjecturing - predicting relationships and results

• convincing - finding and communicating reasons why something is true.

The considerable mathematical thinking on behalf of the teacher is necessary to provide a lesson that is rich in mathematical thinking for students. She uncovered that in mathematical thinking it needs for students to understand mathematical concepts and develop connections among concepts and the links between concepts and procedures. She also draws on important general mathematical principles such as : (1) working systematically, (2) specialising – generalising: learning from examples by looking for the general in the particular, (3) convincing: the need for justification, explanation and connections, and (4) the role of definitions in mathematics. In the case of teaching mathematics, the solver has to bring together expertise in both mathematics and in general pedagogy, and combine these two domains of knowledge together to solve the problem, whether it be to analyse subject matter, to create a plan for a good lesson, or on a minute-by-minute basis to respond to students in a mathematically productive way. If teachers are to encourage mathematical thinking in students, then they need to engage in mathematical thinking

throughout the lesson themselves.

C.           British Context

Mathematics teaching should stimulate the growth of mathematical thinking in students. Mathematical thinking is not only used for students to solve current problems, but should be able to build long-term thinking that can solve the problem for the foreseeable future with more sophisticated concepts. The teacher must provide meaningful experiences and useful to students so that students can be honed thinking skills early on and helped to develop smart and innovative thinking to the new situation and the future.

There are two ways of building mathematical concept:

1) the first is from the exploration of a particular object whose properties he focus on and use first as a description – ‘a triangle has three sides’ – and then as a definition – ‘a triangle is a figure consisting of three straight line segments joined end to end’.

2) the second arises from a focus on a sequence of actions and on organizing the sequence of actions as a mathematical procedure such as counting, addition, subtraction, multiplication, evaluation of an algebraic expression, computation of a function, differentiation, integration, and so on, with the compression into corresponding thinkable concepts such as number, sum, difference, product, expression, function, derivative, integral.

Cognitive development process through three stages, namely (1) conceptual embodied and (2) proceptual which is the symbolic realm of thought where the definitions based on known concept, and then enter into stage (3) where there is a formal axiomatic definitions based on the transition from concept known to the formal concept based on definitions.

D.  Japan Context

Abilities that needed by students is not how they answered quickly and correctly and complete the tasks given, but how they determine his own problems or what they will do  and how they account for what they've done. The ability to correctly and quickly in answering questions certainly needed, but it would be needed again is the ability to replicate the methods and knowledge of others to be applied to other things, the ability to bring students' ideas, as well as the ability to train and run the independence of students. Questions related to mathematical thinking and method must be posed based on a perspective of what kinds of questions to ask. Question must be created so that problem solving process elicits mathematical thinking and method. The lists of question analysis designed to cultivate mathematical thinking as follows:

a. Problem Formation and Comprehension

1)      What is the same? What is shared? (Abstraction)

2)      Clarify the meaning of the words and use them by oneself. (Abstraction)

3)      What (conditions) are important? (Abstraction)

4)      What types of situations are being considered? What types of situations are being proposed? (Idealization)

5)      Use figures (numbers) for expression. (Diagramming, quantification)

6)      Replace numbers with simpler numbers. (Simplification)

7)      Simplify the conditions. (Simplification)

8)      Give an example. (Concretization)

b. Establishing a Perspective

1)      Is it possible to do this in the same way as something already known? (Analogy)

2)      Will this turn out the same thing as something already known? (Analogy)

3)      Consider special cases. (Specialization)

c. Executing Solutions

1)      What kinds of rules seem to be involved? Try collecting data. (Induction)

2)      Think based on what is known (what will be known). (Deduction)

3)      What must be known before this can be said? (Deduction)

4)      Consider a simple situation (using simple numbers or figures). (Simplification)

5)      Hold the conditions constant. Consider the case with special conditions.

1)      (Specialization)

6)      Can this be expressed as a figure? (Diagramming)

7)      Can this be expressed with numbers? (Quantification)

d. Logical Organization

1)      Why is this (always) correct? (Logical)

2)      Can this be said more accurately? (Accuracy)

                                                                                   

E.                 Indonesian Context

Indonesia Education System must develop intelligence and individual skills, promote good conduct, patriotism, and social responsibility, should encourage a positive attitude of self-reliance and development. Improving the quality of teaching is one of the most important task of raising the standard of education in Indonesia. In 2006, Indonesian Government has implemented the new curriculum for primary and secondary education, called KTSP  or School-Based Curriculum. This School-based curriculum combines two paradigms in which, one side stress on students competencies while on the other side concerns students learning processes. The School-Based Secondary Junior mathematics curriculum outlines that the aims of teaching learning of mathematics are as follows: (1) to understand the concepts of mathematics, to explain the relationships among them and to apply them in solving the problems accurately and efficiently, (2) to develop thinking skills in learning patterns and characteristics of mathematics, to manipulate them in order to generalize, to prove and to explain ideas and mathematics propositions, (3) to develop problem solving skills which cover understanding the problems, outlining mathmatical models, solving them and estimating the outcomes, (4) to communicate mathematics ideas using symbols, tables, diagrams and other media, and (5) to develop appreciations of the use of mathematics in daily lifes, curiosity, consideration, and to encourage willingness and self-confidence in learning mathematics.

For the Indonesian context, the goal of mathematics education is still urgent to promote mathematical thinking and to take action. In the latest Lesson Study, Marsigit et al (2007) had sought to uncover the picture in which the teacher strived to promote mathematical thinking in learning the total area of a

right circular cylinder and sphere as well as the volume of a right circular cone. Students’ mathematical thinking can be traced through the schema of teaching learning activities as follows:

1. Problem Formation and Comprehension were emerged when the students:

a.    observed given model of right circular cylinder, observed given model of Sphere, and observed given model of right circular cone

b.    identified the components of the right circular cylinder, sphere, and right circular cone

c.    defined the concept of right circular cylinder, sphere, and right circular cone

d.    got questions and notices from teacher to search the concepts

2. Establishing a Perspective were emerged when the students:

a.    employed concrete model to search the total area of right circular cylinder, the area of sphere and the volume of right circular cone

b.    learned that the height of right circular cylinder is equal to the width of its rectangle; and the circumference of the circle is equal to the length of rectangle

c.    learned the teacher’s guide to understand the procedures how to search the volume of right circular cone

d.    broke-down the model of right circular cylinder into its components

3. Executing Solutions were emerged when the students:

a.    tried to find out the lateral area of right circular cylinder

b.    tried to find out the total area of right circular cylinder

c.    tried to find out the area of sphere

d.    collected the data of the measurement of the volume of cone in comparison with the volume of cylinder

F.                  Conclusion

Each state has different paradigms of mathematics education. This leads to differences in context in each country. In the Australian context, mathematics teaching is not only aims to teach students about how to solve the problem, but also able to bring it to critical thinking and independent thinking to understand the math problems they face. In teaching mathematics, teachers need to better understand the mathematical thinking to create better learning plan and organized. This relates to the determination of learning activities, learning materials, the expected student responses and student responses that may arise in mathematics learning that held.

In British context, Mathematics teaching should stimulate the growth of mathematical thinking in students. Mathematical thinking is not only used for students to solve current problems, but should be able to build long-term thinking that can solve the problem for the foreseeable future with more sophisticated concepts. The teacher must provide meaningful experiences and useful to students so that students can be honed thinking skills early on and helped to develop smart and innovative thinking to the new situation and the future.

In Japan context, abilities that needed by students is not how they answered quickly and correctly and complete the tasks given, but how they determine his own problems or what they will do  and how they account for what they've done. The ability to correctly and quickly in answering questions certainly needed, but it would be needed again is the ability to replicate the methods and knowledge of others to be applied to other things, the ability to bring students' ideas, as well as the ability to train and run the independence of students.

Indonesia Education System must develop intelligence and individual skills, promote good conduct, patriotism, and social responsibility, should encourage a positive attitude of self-reliance and development. Improving the quality of teaching is one of the most important task of raising the standard of education in Indonesia. In 2006, Indonesian Government has implemented the new curriculum for primary and secondary education, called KTSP  or School-Based Curriculum. This School-based curriculum combines two paradigms in which, one side stress on students competencies while on the other side concerns students learning processes.