The Dread of Theoretical Notions about Mathematics Education

By: Indah Septia D.N

There are many mathematicians that develop or discover theoretical of mathematics education. Many of the mathematicians that developed new method to teach mathematics and the way teacher explain the concept of mathematics. One theorem is connecting to other theorem. One notion is connected to other notions then makes a theorem.

Problem solving activity is one of the theoretical notions of mathematics education. Problem solving activity in mathematics became recognized since constructivism proposed and became popular in education field. Humans have been solving problems from the beginning of their existence, usually by trial and error. However, effective and reliable problem origination, prevention, solution, and challenge of solution did not begin until our scientists recognized and developed the experimental method, the method of science, most commonly called the scientific method or scientific method.

One of the mathematicians that promote problem solving in mathematics is George Pόlya. He spent considerable effort on trying to characterize the methods that people use to solve problems, and to describe how problem-solving should be taught and learned. He wrote four books on the subject: How to Solve It, Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving; Mathematics and Plausible Reasoning Volume I: Induction and Analogy in Mathematics, and Mathematics and Plausible Reasoning Volume II: Patterns of Plausible Reasoning.

In addition to his works directly addressing problem solving, Pólya wrote another short book called Mathematical Methods in Science, based on a 1963 work supported by the National Science Foundation, edited by Leon Bowden, and published by the Mathematical Association of America (MAA) in 1977. It shows that problem solving activity has been beginning for many years ago.

From several years ago, problem solving had begin applied in school. The method of teaching that has transformed from teacher center to students center create many innovation on teaching. Besides problem solving activity, there are other method of teaching, like discussion, investigate, etc.

The ultimate goal of any problem-solving program is to improve students' performance at solving problems correctly. The specific goals of problem-solving in Mathematics are to:
1. Improve pupils' willingness to try problems and improve their perseverance when solving problems.
2. Improve pupils' self-concepts with respect to the abilities to solve problems.
3. Make pupils aware of the problem-solving strategies.
4. Make pupils aware of the value of approaching problems in a systematic manner.
5. Make pupils aware that many problems can be solved in more than one way.
6. Improve pupils' abilities to select appropriate solution strategies.
7. Improve pupils' abilities to implement solution strategies accurately.
8. Improve pupils' abilities to get more correct answers to problems.

Problem solving activity is one of the methods of teaching that make student more active than before. Students will find the answer of the problem by themselves. There are some phases to solve the problem, which are: understand the problem, make planning with the previous experience to solve it, try the plan and if it didn’t work then look back what’s wrong with it and try again. If students do all the phases, students will more active and understand the concept by themselves.

In Indonesia, teachers now begin applied this method to teach students. Not only using problem solving method, but also using other method then combined it so that can be suitable with condition of class. Sometimes, one method that always be applied will make students bored and not enjoy with the lesson. Teachers have to more creative to make the atmosphere of study become pleased.

Most teacher in Indonesia using traditional method to teach students before applied problem solving activity. In traditional method, teachers just transfer their knowledge to students. Consequently, students become passive and wait for explanation from their teachers. Students will assume that their teachers are sources of knowledge.

Constructivism paradigm had changed the perspective of teachers about the way they teach their students. The orientation has change. Not teacher oriented but students oriented. Problem solving activity just one of the method that can be used to applied this paradigm.

In problem solving activity, teacher should give support or encouragement to students, give students questions and let them to answer it, make a simple example and involve students to make it, and soon. Students should support this activity too, so that this activity can run well.

Sources:
http://library.thinkquest.org/25459/learning/problem/ access on March, 3th 2012, 04:44 p.m
http://www.problemsolving.net/history.html access on March, 3th 2012 08:47 a.m
http://en.wikipedia.org/wiki/Polya access on March, 3th 2012, 06:50 p.m
http://pbmmatmarsigit.blogspot.com/2008/12/problem-solving-matematika-hakekat-dan.html access on March, 3th 2012, 09:17 p.m

Gejala-Gejala Kejiwaan Siswa Belajar Matematika

Indah Septia Dewi Nugraheni

10313244029

Pendidikan Matematika Inter.

I.     Pendahuluan

Bagi sebagian siswa, mempelajari matematika merupakan hal yang sulit dan tidak menyenangkan. Bagi sebagian lainnya, mempelajari matematika sangatlah menarik dan menyenangkan. Kesukaan atau ketidaksukaan siswa dalam belajar matematika dipengaruhi oleh banyak faktor. Gejala-gejala kejiwaan mereka seperti senang mempelajari matematika, suka bekerja sama dengan kelompok dalam menyelesaikan soal, pandangan mereka terhadap cara mengajar guru dan lain-lain merupakan salah satu faktor yang dapat mempengaruhi suka tidaknya siswa dalam belajar matematika.

Bila siswa sudah menganggap matematika itu sulit, maka matematika itu akan menjadi sulit diterima oleh siswa. Peran guru sangat penting disini untuk memberikan pemahaman pada siswa. Siswa sudah menganggap matematika itu sulit, maka guru harus menjadi fasilitator yang menyenangkan dan bisa membuat siswa merasa nyaman dalam belajar matematika.

Setiap individu memiliki keunikan dan kemampuannya masing-masing. Guru harus peka dan jeli terhadap keadaan seperti ini. Memahami psikologi siswa merupakan cara terbaik untuk menilai cara apa yang tepat untuk membuat siswa dapat memahami matematika. Menciptakan suasana kelas yang kondusif dan menyenangkan akan membuat siswa merasa lebih nyaman dalam belajar matematika. Bila siswa sudah merasa nyaman dalam belajar, semua aspek pendukung seperti aspek kognitif, afektif dan psikomotorik siswa akan berkembang dengan baik.

II.  Pembahasan

Di sekolah, siswa mempelajari hal-hal yang bersifat sederhana menuju pada hal-hal yang bersifat kompleks, dari hal-hal yang bersifat real menuju hal-hal yang bersifat abstrak. Semua dipelajari selama bertahap disesuaikan dengan psikologi dan perkembangan siswa tersebut. Sesuai dengan teori belajar Robert Gagne, siswa belajar dengan cara bertahap, mulai dari yang sederhana sampai hal-hal yang bersifat kompleks.

Anak kelas satu sekolah dasar tentu belajar sesuai dengan usianya. Operasi matematika yang dilakukan masih sangat sederhana dengan bilangan yang kecil. Semakin beranjak besar, anak akan mempelajari system operasi bilangan yang lebih kompleks. Mereka akan mengetahui 1+1 tidak mutlak bernilai 2, karena 1 pensil+ 1 buku berbeda dengan 1 pensil+ 1 pensil. Mereka akan mulai memahami tentang konsep variabel. Begitu pula dalam penghitungan bangun ruang. Siswa akan melihat bangunan real atau nyata sebelum berpikir abstrak. Pertama siswa akan melakukan pengindraan dan membuat persepsi mengenai apa yang ia lihat, kemudian ia akan memikirkan dan mengidentifikasi bangun apa itu. Setelah mengenali suatu bangun, siswa tidak perlu lagi melihat bangun tersebut untuk dapat membayangkan bentuknya. Ia akan membuat konsep dan skema dalam pikirannya dan membangun imajinasi.

Selain itu, siswa akan mudah dalam belajar matematika jika matematika itu memiliki nilai kebermaknaan bagi siswa. Untuk mendapatkan nilai kebermaknaan dari matematika, guru harus menjelaskan mengenai arti penting matematika dalam kehidupan sehari-hari. Hal ini bisa dilakukan dengan praktik secara langsung. Misalnya saja anak-anak kelas 1 SD diberi sejumlah uang dan diminta untuk membelanjakan uang tersebut. Secara matematika, tanpa sadar, anak-anak tersebut telah menggunakan prinsip matematika. Anak-anak tersebut akan mulai mengerti dan memahami pentingnya matematika dalam kehidupan sehari-hari setelah melakukan praktik langsung.

Interaksi antara guru dan siswa menjadi sangat penting dalam proses pembelajaran. Semua proses belajar mengajar harus berpusat pada siswa (students center). Guru harus mulai mengurangi penggunaan metode ceramah yang selama ini banyak digunakan. Menjadi fasilitator siswa dalam pengembangan potensi dirinya merupakan salah satu peran penting guru. Komunikasi efektif dari guru dan siswa juga akan membantu guru mengetahui kesulitan yang dihadapi oleh siswa dan dapat mengupayakan bantuan bagi siswanya.

Pada hakikatnya, menurut Ebbut dan Straker hakikat matematika sekolah meliputi empat hal, yaitu:

a.       Matematika merupakan kegiatan penelusuran pola dan hubungan.

b.      Matematika adalah kreativitas yang memerlukan intuisi, imajinasi dan penemuan.

c.       Matematika adalah kegiatan problem solving

d.      Matematika merupakan alat komunikasi.

Matematika sekolah membiarkan siswanya berkembang sendiri sesuai dengan potensinya masing-masing. Guru hanya menjadi fasilitator yang membantu siswa dalam membangun konsep matematika dalam pikirannya. Dengan demikian siswa akan lebih aktif dan kreatif dalam mencari informasi terkait dengan konsep dan materi yang mereka butuhkan. Mereka seperti biji yang akan tumbuh dengan sendirinya menjadi pohon yang besar dengan fasilitas dari guru.

Dalam mempelajari matematika, gejala jiwa siswa yang cukup tampak adalah berpikir secara kreatif. Kreativitas merupakan salah satu kemampuan berpikir divergen untuk menjajaki berbagai macam jawaban dari suatu persoalan. Dengan berpikir secara kreatif, siswa akan melihat soal dari sudut pandang baru. Karena solusi dari masalah matematika itu tidak tunggal, maka siswa dapat mengerjakan soal matematika dengan berbagai macam kemungkinan cara. Selain itu, siswa dituntut untuk menyelesaikan masalah matematika dengan caranya masing-masing.

Siswa akan belajar dengan baik bila mereka memiliki motivasi untuk menjadi lebih baik. Pada hakikatnya, belajar adalah suatu proses yang dilakukan manusia agar menjadi lebih baik. Ada dorongan dari dalam diri siswa yang mendasarinya melakukan sesuatu. Siswa memiliki motivasi yang berbeda-beda dalam belajar. Motivasi sering dikaitkan dengan emosi. Emosi diartikan sebagai tergugahnya perasaan yang disertai dengan perubahan-perubahan dalam tubuh, misalnya otot menegang dan jantung berdebar. Emosi meliputi perasaan senang, sedih, kecewa bahagia, dan lain sebagainya. Bila siswa merasakan emosi bahagia dan senang dalam belajar matematika, maka ia akan memiliki motivasi untuk terus belajar matematika. Namun apabila siswa merasa kecewa atau takut menghadapi matematika, maka motivasinya untuk belajar matematika akan berkurang.

Setiap siswa adalah pribadi yang unik. Mereka memiliki kemampuan yang beragam dalam berbagai bidang. Ada siswa yang lebih senang belajar sendiri dan ada pula siswa yang lebih senang belajar secara kelompok. 

Masing-masing siswa juga harus memiliki kesiapan sebelum menghadapi proses belajar mengajar. Baik kesiapan secara mental maupun secara materi yang telah dipelajari. Bila siswa sudah siap terhadap materi yang akan diberikan, maka proses belajar mengajar pun akan berjalan dengan lancar. Kesiapan siswa memegang peran yang cukup penting. Bila siswa tidak siap, maka belajarpun akan menjadi seperti bencana bagi siswa.

Membangun suasana kelas yang kondusif dan menyenangkan merupakan salah satu peran guru. Namun demikian, siswa juga berperan penting dalam penciptaan suasana belajar yang menyenangkan. Guru dan siswa harus bersinergi dalam mewujudkan kondisi kelas yang dapat membangun kekondusifan dan keefektifan proses belajar mengajar.

III.   Kesimpulan

Berdasarkan uraian di atas, untuk membangun psikologi siswa dalam pembelajaran matematika memerlukan sinergi dari guru maupun siswa. Guru harus mampu memahami psikologi siswanya. Guru juga harus mampu mengenali kesulitan belajar yang dialami oleh siswa dan mengupayakan solusi tepat yang sesuai dengan kondisi siswanya. Pembelajaran matematika yang baik adalah yang menjadikan siswa sebagai pusat dari pembelajaran itu sendiri. Siswa akan lebih aktif dan kreatif dengan sendirinya. Selain itu, siswa akan belajar dengan baik bila ia memiliki motivasi, dapat bekerja sendiri maupun berkelompok dan dapat belajar secara kontekstual tidak hanya tekstual. Untuk membangun suasana pembelajaran yang menyenangkan, perlu adanya kerjasama antara guru dan siswa.

Sumber:

Sugihartono, dkk. 2007. Psikologi Pendidikan. Yogyakarta: UNY Press

http://marsigitpsiko.blogspot.com/2008/12/hakekat-matematika-sekolah-dan-siswa.html Diakses pada 13 Januari 2012.

Dr. Marsigit. 2004. Inovasi Pembelajaran untuk Meningkatkan Gairah Siswa dalam Belajar. diunduh dari http://staff.uny.ac.id. Diakses pada 14 September 2011.

Memanfaatkan Microsoft Word 2007 Sebagai Media Pembelajaran Geometri di SMP

Oleh :

Dr. Marsigit M.A.

The psychological aspect that found

reviewed by Indah Septia Dewi N (10313244029)

International Mathematics Education

In recent years, the development of technology is growing rapidly. There are many software that can help teachers to teach students. One of them is used of Microsoft Word 2007 to teach Geometry in junior high school. We can use SmartArt Graphic to create the geometry object. With SmartArt Graphic, we can create two or three dimension of geometry. It can make animation to those shapes and give ‘text’ to explain the shapes. Students can learn that from some of shapes can form a new shape. Like two triangles can form a rectangle. They can learn step by step, from line, plane then space.

The technologies of course help teachers very well. If teachers can develop this kind of method, it will be more effective to teach geometry to students. Students can explore their creativity to create the shapes too. They can recognize the shapes from very beginning then make perception and solve the problem. If students have difficulty, they will communicate or ask to their teachers. The interaction between teacher and students can make teaching learning process run well.

Source: http:/staff.uny.ac.id//

THE PSYCHOLOGICAL ASPECTS OF MATHEMATICS LEARNING

By: Indah Septia Dewi N

Abstract: Some students feel difficult to study mathematics. There are many factors that can affect students difficult to study mathematics. One of the factors is teacher. How teacher delivered the material influences the assumption students about the material. To make students interested with mathematics, teachers should make innovation on their method of teaching. Developing technology in teaching learning process is one ways to make students more interest with the subject.

I.         Introduction

Psychology is the study of psychiatric symptoms. It is dealing with human behavior. Psychiatric symptoms are covering cognitive aspect, affective aspect, conative aspect and psychometrics aspect. There are two kind of psychology; general psychology and particular psychology. General psychology study about human generally. Meanwhile, particular psychology is study about aspect and set in particular, like psychology of learning mathematics.

Basic principles of psychology consist of four important aspects that are students, learning, mathematics and education. Each aspects are influence each other. The nature of mathematics education consists of two paradigms, that are innovative and traditional. The nature students learning mathematics will be effective if students have:

1.      motivation from themselves,

2.      students able to collaboration,

3.      student able to learn mathematics individually, and

4.      students able to learn mathematics contextually.

In education cases, teachers have influences for developments students. They have important role to make students understand with the material. The method that used by teachers is one of the factor that can be support students to learn mathematics.

Generally, people think that mathematics is difficult. Mathematical problems are identical with number and counting. This is challenge for teachers to make mathematics acceptable by students well. This is challenge for teachers to change point of view students about mathematics that think that mathematics is difficult.

In the past, almost teachers use traditional method to taught students. In this method, teachers just transferring knowledge to students. Teachers give and direct. The student cannot explorer their ability because the teachers just give the lesson and not let the students to explorer the lesson by themselves. It makes students become passive.

Now, teachers should use constructivism method to teach students. Constructivism is the term refers to the idea that learners construct knowledge for themselves as he or she learns. Through this method, students can explore their ability in mathematics. They have to be active to find information and study by themselves. Through constructivism method, the students can increase their ability to find information about mathematics.

Viewed from the psychological aspects, there are some factors that made students difficult to study mathematics. One of them is the way teachers explain about mathematics. Make students understand with the material is not a simple thing. This is challenge for teachers to make innovation on their method of teaching so that students can accept the material well.

II.      Psychological Aspects of Mathematics Learning

Based on the mini research those have been done, students already know about mathematics from kinder garden. They learn about digit and number. In elementary school, mathematics that has been taught is real mathematics. In junior high school, mathematics that is taught is real mathematics but there are abstract concepts too. In senior high school mathematics that is taught is more abstract than on junior high school but it is real too.

In senior high school, students feel difficult to study trigonometry. There are students that difficult to memorize the value of trigonometry. Some students usually memorize the value of trigonometry, but they not understand the concept. It is make them easy to forgettable.

The way teachers teach students influences to student’s assumption about mathematics. Students that like mathematics can be dislike mathematics because teacher’s factor. Otherwise, students that dislike mathematics can be like mathematics because the teachers. Because each student is different with each other to catch the material, teacher should use method of teaching that suitable with the conditions of students. Teachers should know characteristics of their students, planned the activities that suitable with the ability of students, give opportunity to students to cooperate with others and established the concept by themselves.

Generally, students need teacher that can make mathematics become interested subject. Many students have assumption that mathematics is difficult subject. They have to study hard to understand about the material. Teachers should be creative to make mathematics become easier to be studied.

One of the ways to make students interested with mathematics is change method of teaching students. Effectiveness of time to teach students should be improved. Children will reach their full potential in the schools, if teachers use in effective teaching practices. Teachers can use technology to help teaching learning process. There are many software and program that can support the subject. Studies with technology make students explorer their ability in science and technology. They not only can get the material but also can follow the developments of era. With technology, like use graph calculators, students can imagine the real graphic of the function.

Education that based on curriculum that applied now, can be alternative way to hold teaching learning process that emphasize with competences that should be students have. Teachers teach based on the curriculum, but it is not close probability for develop method to teach students.

Students will study if they have motivation. Teachers as facilitators should make study mathematics become gratify, observe what students want, established understanding based on what students know, make atmospheres in class become conducive to study, give challenge activities, give appreciate with what students do and soon.  

Sometimes students feel bored or scary to study mathematics. Teachers should make students more active in teaching learning process. To make students not bored and scary, teachers can use discussion method, use teaching aid to make students more interested and make mathematics more real in their daily life, use problem solving method and soon.

Teaching learning process will be run well if not only teachers and students that should support the process but also school. In other word, school should be support teaching learning process too. Availability of facilities that can be support students to develop their ability in all subjects, especially mathematics is the one ways to make students have spirit to study the subject.

III.   Conclusion

Teachers have big influences for their students. Teachers should support students to study mathematics. To make mathematics more interested for students, teachers can use many kind of teaching method that suitable with the condition of their students. Teachers make teaching planed that considers of students need and the ability of students self. Teacher is one of people that involve students to understand about mathematics.

References

Sugihartono, Tathiyah,Kartika Nur, dkk. 2007. Psikologi Pendidikan. Yogyakarta: UNY Press.

http://www.exploratorium.edu/IFI/resources/constructivistlearning.html, accessed on Oct, 15^th 2011

http://marsigitpsiko.blogspot.com/2008/12/hakekat-matematika-sekolah-dan-siswa.html, accessed on Oct, 15^th 2011

http://blog.unsri.ac.id/bani/pengetahuan/aspek-aspek-psikologi-yang-mempengaruhi-belajar-dan-pembelajaran/mrdetail/14772, accessed on Oct, 13^th 2011.

http://staff.uny.ac.id/, accessed on Sept, 14^th 2011