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

International Perspective on Developing Method to Uncover Psychological Phenomena of Learning Mathematics

By: Indah Septia D.N

Every country has different way to teach Mathematics to students. The way Indonesian’s teacher teach Mathematics in Indonesia different with the way Australian’s teachers teach Mathematics in Australia. There are many way to teaching one subject in Mathematics, too. For example, there are many way to calculating. 10+9+8=9+9+9. Even the number in right side and left side are different, but the result is same. Plus, minus, times, divided and soon, is the nature of mathematics properties.

Teachers have a role to promote paradigm to students. Students should know the paradigm so that they can understand what the purposes they studied. In the Realistic Approach, the first thing that should be teachers do is introduce the material. Students introduced with the term, symbol, formula, etc, about the material first. After that, students be expected make model or create model based on the concept that they understand. Then, from the model that made, they can give a reason and explain about the models, like proved some formula in mathematics. The next step is students can applied the theory or concept that they have understood in daily live. From introduce, creation/modeling, reason and explanation, and application students can make reflection about what that they have been got, because participation students can we look through the reflection.

 

Different country has different way to teach students. In Australia, there are five kind of subtraction. First is part whole, second is quotient, third is ratio, fourth is operator and the last is measure. There are two kind of fraction that is partition and quotient.

Teachers should develop teaching material. To make students understand about material easier, teachers should be creative to make teaching learning process can be fun and enjoyable. Teaching has scheme to make teaching learning process can be success.

1.      Lesson plan

Teachers should develop the lesson plan. Before teach students, teacher should make lesson plan such that teacher have guidance to teach the students. Lesson plan have to fill the students need about the material. With lesson plan, teachers can focus to the material that they will give to the students.

2.      Apperception

Teaching learning process will go smoothly if students already have readiness to study. Students should prepare the material that they will be studied before join the class, so that they can ready to accept the material that given by teachers.

3.      Small group discussion

Small group discussion only has a few members. If there are many members in the group, there are students that will dependent to others. Then, discussion process cannot be effective. If there are two or three members in the group discussion, all members will collaborate to discuss the problem and discussion time will be effective.

4.      Various method

To make students more interesting to study mathematics, teachers should develop the method of teaching. Teachers can combine many kinds of teaching method that suitable with condition in the class.

5.      Various interaction

Interaction between teachers and students is one of the important things that can make teaching learning process run well. Interaction between students and interaction among students and teachers can develop their ability in social live. Interaction

6.      Various media

In the era of globalization, technology is growing rapidly. A lot of software that helps teachers to teach the material to students. Teachers is required be able to develop instructional media.

7.      Students reflection

Reflection from students is very important. As teachers, we can know how understand students and how the subject become meaningful for students through reflection.

8.      Scheme achieving competence

Students should reach the competencies that determined by teachers based on curriculum.

9.      Students conclusion

Students are able to make conclusion about the material.

10.  Student’s worksheet.

Student’s worksheet is one of the things that important as indicator whether students can solve the problem or not. Teachers can develop student’s worksheet by themselves and adjusted to condition of the class. Student’s worksheet can help teachers to know how deep the ability of students.

According to Shigeo Katagiri, there are three mathematical thinking, which are:

1.      Mathematics attitude

2.      Mathematics thinking related to method

3.      Mathematics content.

Mathematical thinking allows for understanding of necessity of using knowledge and skills and how to learn by one self and the attainment of the abilities required independently learning.

There are many ways to study mathematics. Each country has different way to teach mathematics to students. Sometimes, this is affected by culture too. But, almost of the students in the world will study well if they study:

1.      Self, students study by themselves

2.      Collaboration, students study collaborate with friends and teachers

3.      Motivation, students can study well when they have motivation

4.      Contextual

How students study mathematics? The first is students learn mathematics from see the shapes then make perception. They can distinguish the object on the separate cases. Then they will think hierarchies and able to imagined the object and formally defined the object. 

The scheme of how students study mathematics is shown below:

 

References:

Marsigit, dkk. LESSON STUDY: Promoting Student Thinking on the Concept of Least Common Multiple (LCM) Through Realistic Approach in the 4^th Grade of Primary Mathematics Teaching, Indonesia

http://www.pdfcari.com/Shigeo-Katagiri.html, accessed on Dec 11^th 2011, 08.39 a.m