Membangun Psikologi Pembelajaran Matematika Berdasarkan Gejala Jiwa Siswa Belajar Matematika

By Siti Nurrochmah Dani

10313244004

Pendidikan Matematika International

Abstrak

Dalam pembelajaran matematika, gejala kejiwaan siswa ketika belajar merupakan hal yang sangat berpengaruh baik di dalam proses belajar itu sendiri maupun hasil yang diperoleh dari pembelajaran matematika. Gejala kejiwaan siswa belajar matematika dapat dilihat dari seluruh aktivitas pembelajaran matematika. Di dalam siswa belajar matematika pasti terdapat hal- hal baik dari dalam diri siswa atau pun dari luar diri yang akan mempengaruhi proses pembelajaran matematika. Hal-hal dari dalam dapat berupa pengindraan, persepsi, motivasi, emosi, berfikir dan intelegensi. Sedangkan hal-hal dari luar dapat berupa interaksi dengan guru, teman, dan lingkungan sekitar. Sesuai dengan hakekat siswa belajar matematika maka ketika siswa belajar matematika, siswa seharusnya dapat belajar secara individu, berkolaborasi dengan teman yang lain, memahami matematika secara kontekstual, serta memiliki persiapan dan motivasi yang baik ketika belajar matematika.  

Pendahuluan

Psikologi berasal dari kata psyche yang berarti jiwa dan logos yang berarti ilmu. Dakir(Sugihartono.2007:2) menyatakan bahwa psikologi membahas tingkah laku manusia dalam hubunganya dengan lingkungan. Sedangkan Muhibbin  Syah(Sugihartono.2007:2) menyatakan psikologi adalah ilmu pengetahuan yang mempelajari tingkah laku terbuka dan tertutup dalam hubunganya dengan lingkungan. Secara garis besar psikologi adalah ilmu yang mempelajari gejala kejiwaan manusia. Dalam pembelajaran matematika, psikologi yang dimaksud melingkupi gejala kejiwaan siswa belajar matematika dan guru di dalam pembelajaran.

Gejala kejiwaan siswa belajar meliputi seluruh gejala jiwa ketika siswa belajar matematika, yaitu dari aspek kognitif(pengenalan), afektif(perasaan), konasi(kehendak) dan psikomotorik(campurana). Di dalam belajar matematika, pasti terdapat perbedaan gejala jiwa antara orang yang satu dengan lainnya. Ada beberapa bentuk gejala jiwa manusia yang mendasar yang banyak muncul dalam bidang pendidikan diantaranya pengindraan dan persepsi, memori, berpikir, intelegensi, emosi serta motivasi.

Sedangkan matematika merupakan ilmu yang obyeknya berada di dalam dan di luar pikiran manusia, sehingga dalam siswa belajar matematika perlu disesuaikan dengan hal tersebut. Gejala-gejala selama siswa mempelajari matematika akan mempengaruhibaik proses maupun hasil dari belajar matematika itu sendiri.  Pengindraan, persepsi, memori, berfikir dan intelegensi akan berperan dalam siswa memecahkan matematika secara langsung. Sedangkan motivasi dan emosi akan cenderung mempengaruhi kejiwaan siswa dalam belajar matematika.

Belajar matematika menurut pandangan Jean peaget.

Belajar matematika membutuhkan pengamatan sebagai dasar pemikiran mempelajari matematika, sehingga belajar matematika  haruslah mengalami sendiri dan terlibat langsung secara realistik dengan obyek yang dipelajarinya. Sehingga belajar harus bersifat aktif dan sosial. Menurut Jean Peaget perkembangan kognitif siswa mempengaruhi proses pembelajaran. Berdasarkan perkembangan kognitif siswa dibagi menjadi empat tahap (Sugihartono.2007:109) yaitu (1) sensorimotorik (0-2 tahun), (2) praoprasional (2-7 tahun), (3) oprasional konkrit (7-11 tahun), (4) oprasional formal (11-14 tahun).

Berdasarkan tahap-tahap perkembangan kognitif siswa, maka siswa sekolah dasar seharusnya mempelajari matematika secara konkret berdasarkan objek konkret yang ada di sekitarnya, sehingga  matematika menjadi mudah dipahami dan diresapi oleh siswa. Pelajaran matematika akan lebih bermakna karena obyeknya dengan siswa dan konkret untuk dipikirkan. Lain halnya dengan siswa menengah, belajar matematika memasuki level yang lebih tinggi dalam perkembangan kognitif siswa, di mana objek- objek abstrak sudah dapat di mengerti oleh siswa. Tetapi pendekatan secara realistik tetap perlu diterapkan di dalam pembelajaran matematika.

Pada dasarnya matematika sebagai mata pelajaran akan lebih mudah dipahami siswa ketika matematika dekat dengan kehidupan siswa. Tetapi seperti yang kita ketahui, matematika di sekolah justru cenderung berorientasi pada simbol-simbol angka yang susah dipahami oleh siswa. Jika ditinjau lebih jauh maka simbol-simbol formal dari matematika adalah seperti puncak dari ice berg dimana masih banyak bagian yang belum terlihat di bawah puncak tersebut. Maka di kenallah fenomena gunung es atau ice berg di dalam pembelajaran matematika.

Fenomena Ice Berg ketika Siswa Mempelajari Matematika

Fenomena ice berg di dalam pembelajaran matematika terdiri dari (1) konkret, (2) skema, (3) model, dan (4) formal. Ada tiga dari empat bagian fenomena ice berg di dalam matematika yang jarang sekali di sentuh dan di gali lebih dalam. Padahal hal tersebut sangat dekat dan sangat riil di dalam kehidupan.

Pada dasarnya matematika dapat digali dengan membuka wawasan siswa terhadap lingkungan sekitar yaitu seperti dalam fenomena ice berg yang pertama “konkret”. Dengan melihat segala sesuatu yang konkret siswa akan lebih mudah untuk memahami. Setelah menemukan masalah konkret maka dibentuklah skema permasalahan dengan berimajinasi menghubungkan informasi-informasi yang ada dengan matematika. Selanjutnya adalah membentuk model sesuai informasi yang diterima. Model ini sebagai representasi masalah yang akan di pecahkan. Dan terakhir adalah notasi formal matematika , dimana siswa seharusnya dapat mengubah informasi yang diterima melalui hal-hal konkret ke dalam notasi formal matematika. Maka siswa akan memahami matematika dengan mudah.

Peran guru di dalam pembelajaran ini juga dibutuhkan dalam membangun dan memotivasi siswa untuk memecahkan masalah konkret ke dalam simbol matematika formal. Guru juga dapat membantu siswa dalam menghubungkan dari setiap tahap ke tahap yang lain seperti dari masalah konkret ke skema atau skema ke model dan seterusnya dengan memberikan pancingan pertanyaan. Dan sebagai tantangan besar bagi guru adalah menagarahkan siswa dalam melihat permasalahan konkrit yang ada di dalam kehidupan.

Belajar matematika dengan konsep ice berg ini akan membuka pemikiran siswa untuk memahami matematika secara utuh tidak hanya simbol tetapi juga permasalahan nyata di dalam kehidupan. Hal ini akan mendorong siswa untuk berfikir kritis dalam memecahkan suatu permasalahan dan memahami secara konseptual. Selain itu siswa dapat belajar bahwa matematika itu dekat dengan kehidupan dan pada hakekatnya objek matematika itu berada di dalam pikiran manusia dan yang ada di luar pikiran manusia.

Hakekat siswa mempelajari matematika dan gejala kejiwaannya

Ebbutt dan Straker menyatakan empat hakekat siswa belajar matematika akan mempengaruhi gejala siswa belajar matematika. Hakekat siswa belajar matematika yaitu:

1.      Siswa mampu belajar matematika dengan persiapan dan motivasi yang baik.

Dengan adanya motivasi yang baik, siswa dapat belajar dengan penuh semangat dan dengan persiapan yang matang maka proses belajar pun akan terlaksana sesuai dengan tujuan dari belajar matematika itu sendiri.

2.      Siswa mampu belajar matematika secara individual.

Belajar matematika merupakan belajar terhadap apa yang ada di dalam pikiran dan belajar apa yang ada di luar pikiran manusia, sehingga siswa seharusnya mampu belajar matematika secara individu berdasarkan kemampuannya melalui investigasi. Dengan belajar secara individu, siswa dapat memaknai dan memahami apa yang dipelajarinya.

3.      Siswa mampu belajar matematika dengan berkolaborasi dengan yang lain.

Selain secara individu, dalam mempelajari matematika, siswa seharusnya dapat belajar dengan berdiskusi dalam memecahkan masalah. Diskusi juga akan memupuk kepercayaan diri siswa dalam mengemukakan pendapat serta melatih kreativitas dalam pemecahan masalah bersama.

4.      Siswa mampu belajar matematika secara kontekstual.

Matematika secara kontekstual di sini merupakan hal yang penting tapi terkadang terlewatkan di dalam belajar matematika. siswa belajar mulai dari hal-hal konkret, kemudian mulai sedikit demi sedikit memaknai ke dalam bentuk formal yaitu dalam bentuk simbol matematika. Belajar secara kontekstual akan membangun siswa yang lebih memahami matematika, apalagi susana pembelajaran yang mendukung akan menambah semangat di dalam belajar matematika. 

Penutup

Gejala kejiwaan siswa dalam belajar matematika akan mempengaruhi proses dan hasil dari pembelajaran matematika, sehingga dalam mempelajari matematika, siswa perlu adanya motivasi, belajar secara mandiri maupun bekerjasama dengan yang lain, serta mampu belajar matematika secara kontekstual. Pada tahap awal dalam mempelajari matematika, siswa memulai dengan mempelajari matematika secara konkret, selanjutnya secara bertahap siswa mempelajari matematika secara formal yaitu melalui simbol-simbol matematika.

Daftar pustaka

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.  http://staff.uny.ac.id/sites/default/files/penelitian/Marsigit,%20Dr.,%20M.A./Paper%20APEC%20Tsukuba%20Sapporo%20Marsigit%20at%20al%20Indonesia.pdf

Marsigit. 2010. The Iceberg Approach of Learning Fractions in Junior High School: Teachers’ Simulations of Prior to Lesson Study Activities.

Marsigit. 2008. Kegiatan Penelitian sebagai Usaha untuk Meningkatkan Profesionalisme Guru Matematika.

Sugihartono. 2007. Psikologi Pendidikan. Yogyakarta. UNYPress

Psychological Aspect of Mathematics Learning

By

Siti Nurrochmah Dani

10313244004

Abstract

Psychological aspect in mathematics learning is importance to known.  Psychological aspect in math learning influence in student achievement indirectly. There are two paradigm of mathematics learning that influence student psychology. The first paradigm is old paradigm. It is also called traditional paradigm. It can create student to be unconfidence and weakness person. In the other hand the second paradigm that is new paradigm or constructivist method of teaching. It build character student to be good person and good personality. Teacher as person that knows development of soul of student must organize psychology of student.  Teacher should make planning and develop student activity in class. Teacher also has good personality, ability and pedagogy. 

A.   Introduction

Definition psychology

Psychology descends from words psyche and logos, where pshyche means soul and logos means study. So, psychology can be defined as study about soul. Psyche or soul is difficult to define, because soul is object that has abstract characteristic, difficult to see, although we can aware the existence.  In this era soul term is changed by psychic. Some experts learn the psychic of human from psychic phenomena or indication.

Psychic phenomena of human can be distinguished by four phenomena. Those are cognitive, affective, conation, and psychomotor.  Cognitive or introducing phenomena is a process or effort human for introducing many stimulation or information from senses then saving, connecting, analyzing, and solving problem base on stimulation. Perceptions, association, memory, thinking, intelligence are include in cognition. Affective or feeling phenomena is capability to feel a getting stimulation, where sad, happy, boring, angry, hate, and love are inside. Conation or desire is intention that is had by human.  Whereas psychometric is mixing or merging from cognitive and affective. For example reading, studying, walking and eating.

Dakir (1993) said that psychology discussing human behavior and relation with environment. Muhibbin Syah (2001) conclude that psychology is study learning opened human behavior and closed human behavior as individual or group in relation between environment and them.

From definition above, we can conclude that psychology is study that learn about behave of human as individual and relation with environment. Human behavior can be seeing, but sometime can’t be see. It also can be conscious and unconscious. The meaning of behavior of human is very large; all of act or do is behavior. So the object of psychology is very large.

Psychology in general is more complex about soul of human, but here we want to talk about psychology in mathematics learning. Psychology of mathematics learning is study surround souls of student and teacher in a process learning mathematics. Here it is more prominent in student soul.

B.   Basic Principles of Mathematics Learning

There are many kind of psychology. One of them is psychology of mathematics learning. But, before we learn more deeply about psychology of mathematics learning, we must know about basic principle of mathematics learning.  There are four basic principles in psychology of mathematics learning. They are:

1.      Education

Education is defined as a person process to become educate. Education also can be defined as a process to change attitude and behavior of person or group to make them adult. Poerbakawatja and Harahap (in Sugihartono. 2007:3) said that education is a willful effort of adult to upgrade the maturity.

2.      Student

Student is person in society that effort to develops potency on her/him self through education. Usually student gets education in school, where he/she can study about many things and science.

3.      Learning

Learning is acquiring new or modifying existing knowledge, behaviors, skills, values, or preferences and may involve synthesizing different types of information(wikipedia.org).  Moreover, (1) Learning as a quantitative increase in knowledge. (2) Learning as memorizing. (3) Learning as acquiring facts, skills, and methods that can be retained and used as necessary. (4) Learning as making sense or abstracting meaning. (5) Learning as interpreting and understanding reality in a different way (infed.org).

From explanation above, learning has meaning that a human process to increasing knowledge, skills, information from the experience of sense.

4.      Mathematics

Mathematics is a branch of study that deals with numbers. Counting, measuring, adding, subtracting, dividing, and multiplying are the kind where we live. But some people think it is a complicated subject to learn. But they can not avoid living with it. So mathematics is needed to learn.

There are two kind of Mathematics learning, they are pure mathematics and elementary mathematics. Elementary mathematics is learned by primary students at elementary school and junior high school. The reason why elementary mathematics given to primary student is they can not accept abstract materials. It must be explained by concrete object so the material is easier to accept. Examples of concrete objects are drum, tube, wheel and others object that similar with mathematical object. They are learned by observation.

The abstract material on math will be given to adult people like students in university and students in senior high school. As geometry, algebra, matrices, calculus are beyond mind of people, so it must be given slowly and with right method.

The different between abstract and concrete object lays on the characteristic of object. Object in pure mathematics is perfect object that is main object. But in concrete object that just on measurement and shape. It is not mathematical object. To get mathematical object we use abstraction. It means take certain characteristic that we want to learn. And we use idealism. It means put down as the perfect characteristic.

Mathematics is not release from problem solving, proving and building theorem systematically. It is also developed in formal system form. Math in this case is also called pure mathematics. The formal system form is called mathematics axiomatic. But just particular people absolutely learn mathematics in high grade.

On the other hand, mathematics in primary school always have problem to communicate mathematics. For younger people, math is difficult to understand. So, in school, we need easier way to talk math. Moreover, mathematics can be good and easy to learn for younger people.  So, mathematics can be adaptable in teaching learning.

For explanation before we have seen about education, student, learning and mathematics. In psychology of mathematics learning they can not separate one with each other because they are uniting the world of mathematics learning.

C.   Paradigms of Mathematics Learning that Influence the Psychology of Student in Mathematics Learning

Developing psychology of student in mathematics learning depend on how a teacher subjected the student in class. What the student become a subject or object learning. How method’s teacher is used in learning mathematics, lesson study or explanatory. How a teacher develop skill and ability of student. How the experience teacher teach mathematics. They are matters which influence the psychology of student in mathematics learning. They can uncover in paradigm of mathematics learning.

There are two paradigms in mathematics learning that influence the psychological of student. The first paradigm is old paradigm. It is also called traditional paradigm, where teacher is very active and dominant in class and student is more passive. Teacher transforms her/his knowledge to student. He/she explains mathematics with explanatory method and usually blackboard is media to teach. Student just listens and does worksheet if teacher give problem.

This method has applied on mathematics learning since yore until now. How about development of psychology of student if the method always use in mathematics leaning?

From a little research, some students claim that explanatory method is boring. Topic in mathematics is to be abstract and more theoretical. So they accept lesson difficulty. But they also claim that they need the explanatory method in some topic in mathematics learning, whereas the topics is more complicated and needed to understanding more.

Not only boring is effected by traditional method, but also it makes student to be afraid to say her/his opinion in front of class and afraid to the teacher. It can be happened if teacher teach math gruffly and seriously. Indirectly make character of student to be weak and unconfident person. In addition, student does not understand the real purpose of learning mathematics.

There are some reasons, traditional method is still used. They are (1) it make controllable condition in class, (2) it is more efficient communication between teacher and student, (3) it can make student more discipline, (4) it is easy to use.

From the advantages and disadvantages of using traditional method, we must push on how about psychological aspect of student if this method is still used. If teacher aware about it so teacher should use the second paradigm. It is new paradigm.

New paradigm is also called constructivist method or innovative teaching. It shows that teacher as facilitator and student is center of mathematics learning process. Innovative teaching builds relationship between teacher and students, where each of them will contribute in teaching learning. Teacher is to be their friend. So they can share their problems to the teacher without being afraid. Teacher also know well how to teach student where each student has a unique ability. Mathematics is empowering of students, so mathematics as education can not transform from teacher to student.

This paradigm is marked by group discussion and lesson study. There is creativity of student to think and solve mathematics problem. There is communication one student to each other to say the opinion about the problem. So intelligent of student more develop. Student is created to be good person in character because he/she strives for creative, active and confidence. In addition student knows what the purpose of leaning mathematics.

D.   Psychological aspects in mathematics learning

In learning mathematics, teacher must know about met cognition and social-psychologist perception of student. Met cognition is person knowledge as a process and result study that happen in student mind and other things related. So teacher must understand and help student. Socio-psychology perception means how far the student understands math through perception process and the situation of related it. Result attitude cover cognitive, affective, and psychomotoric aspect. Teacher is expected can anticipation changing attitude aspect. It starts with good planning and developing class activity.

With effective learning mathematics, teaching learning process is expected to create student: (1) be autonomous person, (2) be effective learner, (3) be Productivity worker, (4) be part of good society. To create high human quality like that, there are four learning quality must be developed to student. They are: (1) learning to do, (2) learning to learn, (3) learning to be, (4) learning to live together.

Incarnated nice teach, character of mathematics teacher should be:

1.      Has big proclivity on mathematics learning.

2.      Has ability to predict personality of student.

3.      Has forbearance and sensitivity to built spirit of mathematics learning.

4.      Has imaginative thinking (conceptual) and practice when explain mathematics to student.

5.      Has qualifying in mathematics and good method to teach.

6.      Have flexibility and experimental method and technique.

7.      Be diligent.

8.      Has strong responsibility of sense.

9.      Has average high ability and quality.

Not only explanations above to create good student in mathematics learning. Teacher must pay attention on motivation, caring, and remembering. What is mean? Teacher should motivate student to study or learn more deeply about mathematics, so that student is not to be frustration. Teacher also cares about problem of student to understand the mathematics topic. In influence, student achievement is increase. Teacher has to remembering student about mathematics topic.

What should teacher do to establish good character of student?

Teacher must know the nature of mathematics and the nature of student learning mathematics. The natures of mathematics are:

1.      Mathematics research for pattern and relationship.

2.      Mathematics is problem solving activity.

3.      Mathematics is investigation activity.

4.      Mathematics is a mean of communication.

There are four items on the nature of student learn math, so student learn math effectively.

1.      Student has good motivation and good preparation.

2.      Student can learn math in collaboration with others.

3.      Student can learn math individually.

4.      Student learn math contextually.

If teacher know the nature of student learn mathematics, he/she also know what the necessary of student learning mathematics and how to teach mathematics so that create good character of student, because psychology of student was organized by teacher.

E.   Conclusion

Psychological aspect in mathematics learning is psychological aspects about anything in teaching learning process about mathematics include how teacher teach mathematics, how teacher create student to be a good person and how attitude of student when he/she learn mathematics as a lesson, how student accept topic on mathematics. All is must knew by a mathematics teacher.

Bibliography

Marsigit. 2004. Developing Mathematics Education in Indonesia. Paper.

Siswoyo. 2008. Ilmu Pendidikan. Yogyakarta. UNYPress

Sugihartono. 2007. Psikologi Pendidikan. Yogyakarta. UNYPress

http://mathematics-nurrochmahdani.blogspot.com/2011/05/paradigm-of-mathematics-in-teaching.html, access on Oct, 13^th 2011 at 10.40 a.m.

http://www.infed.org/biblio/b-learn.htm , access on Oct, 13^th 2011 at 09.58 a.m.

http://en.wikipedia.org/wiki/Education, access on Oct, 14^th 2011 at 11.35 a.m.

http://en.wikipedia.org/wiki/Learning, access on Oct, 14^th 2011 at 11.28 a.m.

http://akhmadsudrajat.wordpress.com/2010/01/02/psikologi-pembelajaran-dan-pengajaran/, access on Oct, 12^th 2011 at 15.26 a.m.